Notebooks/Confidence_Interval_with_inputs.ipynb

{
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  {
   "cell_type": "code",
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   "outputs": [
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     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>season_sold</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>price_100k</th>\n",
       "      <th>long_lat</th>\n",
       "      <th>district</th>\n",
       "      <th>is_seattle</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7504400290</td>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
       "      <td>3470</td>\n",
       "      <td>9.392912</td>\n",
       "      <td>12003</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.6240</td>\n",
       "      <td>-122.048</td>\n",
       "      <td>1978</td>\n",
       "      <td>Spring</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.990</td>\n",
       "      <td>(-122.04799999999999, 47.623999999999995)</td>\n",
       "      <td>Lake Washington</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6403500570</td>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>7420</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>98059</td>\n",
       "      <td>47.4944</td>\n",
       "      <td>-122.162</td>\n",
       "      <td>1996</td>\n",
       "      <td>Summer</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>(-122.162, 47.4944)</td>\n",
       "      <td>Renton</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7934000145</td>\n",
       "      <td>4</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>6400</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.5563</td>\n",
       "      <td>-122.393</td>\n",
       "      <td>1970</td>\n",
       "      <td>Winter</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>4.500</td>\n",
       "      <td>(-122.39299999999999, 47.5563)</td>\n",
       "      <td>Seattle</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>203100625</td>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>21587</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>98053</td>\n",
       "      <td>47.6384</td>\n",
       "      <td>-121.959</td>\n",
       "      <td>1992</td>\n",
       "      <td>Spring</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>(-121.959, 47.6384)</td>\n",
       "      <td>Snoqualmie Valley</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2211700160</td>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>17208</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>98006</td>\n",
       "      <td>47.5659</td>\n",
       "      <td>-122.117</td>\n",
       "      <td>1959</td>\n",
       "      <td>Spring</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>(-122.117, 47.5659)</td>\n",
       "      <td>Issaquah</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           id  bedrooms  bathrooms  sqft_living   log_lot  sqft_lot  floors  \\\n",
       "0  7504400290         5       2.50         3470  9.392912     12003     2.0   \n",
       "1  6403500570         5       2.75         2990  8.911934      7420     2.0   \n",
       "2  7934000145         4       2.75         2900  8.764053      6400     2.0   \n",
       "3   203100625         3       2.50         2620  9.979847     21587     2.0   \n",
       "4  2211700160         3       1.50         1770  9.753130     17208     1.0   \n",
       "\n",
       "   waterfront  condition  grade  zipcode      lat     long  yr_of_last_update  \\\n",
       "0         0.0          3      8    98074  47.6240 -122.048               1978   \n",
       "1         0.0          3      8    98059  47.4944 -122.162               1996   \n",
       "2         0.0          3      7    98136  47.5563 -122.393               1970   \n",
       "3         0.0          3      7    98053  47.6384 -121.959               1992   \n",
       "4         0.0          3      8    98006  47.5659 -122.117               1959   \n",
       "\n",
       "  season_sold  below_ground_ratio  price_100k  \\\n",
       "0      Spring            0.000000       5.990   \n",
       "1      Summer            0.000000       4.985   \n",
       "2      Winter            0.421569       4.500   \n",
       "3      Spring            0.000000       6.720   \n",
       "4      Spring            0.525862       4.500   \n",
       "\n",
       "                                    long_lat           district  is_seattle  \n",
       "0  (-122.04799999999999, 47.623999999999995)    Lake Washington         0.0  \n",
       "1                        (-122.162, 47.4944)             Renton         0.0  \n",
       "2             (-122.39299999999999, 47.5563)            Seattle         1.0  \n",
       "3                        (-121.959, 47.6384)  Snoqualmie Valley         0.0  \n",
       "4                        (-122.117, 47.5659)           Issaquah         0.0  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Pull in Data\n",
    "import pandas as pd\n",
    "import statsmodels.stats.api as sms\n",
    "import statsmodels.formula.api as smf\n",
    "import scipy.stats as stats\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "df = pd.read_csv('Train_Table.csv')\n",
    "df.drop('Unnamed: 0', axis=1, inplace=True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(17094, 20)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check For Multicollinearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_multicollinearity(df, independent_var_name, cutoff):\n",
    "    copy_df = df.drop(independent_var_name, axis=1)\n",
    "    # copy_df = reg_df\n",
    "\n",
    "    # save absolute value of correlation matrix as a data frame\n",
    "    # converts all values to absolute value\n",
    "    # stacks the row:column pairs into a multindex\n",
    "    # reset the index to set the multindex to seperate columns\n",
    "    # sort values. 0 is the column automatically generated by the stacking\n",
    "\n",
    "    pair_df=copy_df.corr().abs().stack().reset_index().sort_values(0, ascending=False)\n",
    "\n",
    "    # zip the variable name columns (Which were only named level_0 and level_1 by default) in a new column named \"pairs\"\n",
    "    pair_df['pairs'] = list(zip(pair_df.level_0, pair_df.level_1))\n",
    "\n",
    "    # set index to pairs\n",
    "    pair_df.set_index(['pairs'], inplace = True)\n",
    "\n",
    "    #drop level columns\n",
    "    pair_df.drop(columns=['level_1', 'level_0'], inplace = True)\n",
    "\n",
    "    # rename correlation column\n",
    "    pair_df.columns = ['correlation_coefficient']\n",
    "\n",
    "    # drop duplicates. \n",
    "    pair_df.drop_duplicates(inplace=True)\n",
    "    return pair_df[(pair_df.correlation_coefficient>cutoff) & (pair_df.correlation_coefficient <1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>correlation_coefficient</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pairs</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>(grade, sqft_living)</th>\n",
       "      <td>0.750909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(bathrooms, sqft_living)</th>\n",
       "      <td>0.742246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(grade, bathrooms)</th>\n",
       "      <td>0.650483</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "                          correlation_coefficient\n",
       "pairs                                            \n",
       "(grade, sqft_living)                     0.750909\n",
       "(bathrooms, sqft_living)                 0.742246\n",
       "(grade, bathrooms)                       0.650483"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "check_multicollinearity(reg_df, 'price_100k', 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## District -> top_5_district"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>season_sold</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>price_100k</th>\n",
       "      <th>district</th>\n",
       "      <th>is_seattle</th>\n",
       "      <th>top_5_district</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
       "      <td>3470</td>\n",
       "      <td>9.392912</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1978</td>\n",
       "      <td>Spring</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.990</td>\n",
       "      <td>Lake Washington</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>Summer</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>Renton</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1970</td>\n",
       "      <td>Winter</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>4.500</td>\n",
       "      <td>Seattle</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1992</td>\n",
       "      <td>Spring</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>Snoqualmie Valley</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1959</td>\n",
       "      <td>Spring</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>Issaquah</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  floors  waterfront  condition  \\\n",
       "0         5       2.50         3470  9.392912     2.0         0.0          3   \n",
       "1         5       2.75         2990  8.911934     2.0         0.0          3   \n",
       "2         4       2.75         2900  8.764053     2.0         0.0          3   \n",
       "3         3       2.50         2620  9.979847     2.0         0.0          3   \n",
       "4         3       1.50         1770  9.753130     1.0         0.0          3   \n",
       "\n",
       "   grade  yr_of_last_update season_sold  below_ground_ratio  price_100k  \\\n",
       "0      8               1978      Spring            0.000000       5.990   \n",
       "1      8               1996      Summer            0.000000       4.985   \n",
       "2      7               1970      Winter            0.421569       4.500   \n",
       "3      7               1992      Spring            0.000000       6.720   \n",
       "4      8               1959      Spring            0.525862       4.500   \n",
       "\n",
       "            district  is_seattle  top_5_district  \n",
       "0    Lake Washington         0.0             1.0  \n",
       "1             Renton         0.0             0.0  \n",
       "2            Seattle         1.0             0.0  \n",
       "3  Snoqualmie Valley         0.0             1.0  \n",
       "4           Issaquah         0.0             1.0  "
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://backgroundchecks.org/top-school-districts-in-washington-2018.html\n",
    "# Rankings based on student performance (math and reading test scores), dropout rates, school funding, and area poverty rates\n",
    "\n",
    "top_5_str = 'Mercer Island|Lake Washington|Snoqualmie Valley|Bellevue|Issaquah'\n",
    "reg_df.loc[reg_df['district'].str.contains(top_5_str),'top_5_district'] = 1\n",
    "reg_df['top_5_district'].fillna(0, inplace=True)\n",
    "reg_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_df.drop(['district'], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get Season Dummy Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Dummy var for season_sold, with Summer as the reference variable\n",
    "seasons = pd.get_dummies(reg_df['season_sold'], drop_first=True)\n",
    "reg_df = pd.concat([reg_df, seasons], axis=1)\n",
    "# reg_df.drop(['Summer'], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>price_100k</th>\n",
       "      <th>is_seattle</th>\n",
       "      <th>top_5_district</th>\n",
       "      <th>Spring</th>\n",
       "      <th>Summer</th>\n",
       "      <th>Winter</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
       "      <td>3470</td>\n",
       "      <td>9.392912</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1978</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.990</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>4.500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1959</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  floors  waterfront  condition  \\\n",
       "0         5       2.50         3470  9.392912     2.0         0.0          3   \n",
       "1         5       2.75         2990  8.911934     2.0         0.0          3   \n",
       "2         4       2.75         2900  8.764053     2.0         0.0          3   \n",
       "3         3       2.50         2620  9.979847     2.0         0.0          3   \n",
       "4         3       1.50         1770  9.753130     1.0         0.0          3   \n",
       "\n",
       "   grade  yr_of_last_update  below_ground_ratio  price_100k  is_seattle  \\\n",
       "0      8               1978            0.000000       5.990         0.0   \n",
       "1      8               1996            0.000000       4.985         0.0   \n",
       "2      7               1970            0.421569       4.500         1.0   \n",
       "3      7               1992            0.000000       6.720         0.0   \n",
       "4      8               1959            0.525862       4.500         0.0   \n",
       "\n",
       "   top_5_district  Spring  Summer  Winter  \n",
       "0             1.0       1       0       0  \n",
       "1             0.0       0       1       0  \n",
       "2             0.0       0       0       1  \n",
       "3             1.0       1       0       0  \n",
       "4             1.0       1       0       0  "
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_df = reg_df.drop(['season_sold'], axis=1)\n",
    "reg_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Treating bathrooms, grade, etc as continuous in this regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "\n",
    "outcome = 'price_100k'\n",
    "predictors = reg_df.drop('price_100k', axis=1)\n",
    "pred_sum = '+'.join(predictors.columns)\n",
    "formula = outcome + '~' + pred_sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>price_100k</td>    <th>  R-squared:         </th> <td>   0.714</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.714</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2841.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 09 Jul 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:31:27</td>     <th>  Log-Likelihood:    </th> <td> -31704.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 17094</td>      <th>  AIC:               </th> <td>6.344e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 17078</td>      <th>  BIC:               </th> <td>6.356e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    15</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>          <td>   25.0568</td> <td>    1.279</td> <td>   19.587</td> <td> 0.000</td> <td>   22.549</td> <td>   27.564</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>           <td>   -0.1872</td> <td>    0.017</td> <td>  -10.923</td> <td> 0.000</td> <td>   -0.221</td> <td>   -0.154</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th>          <td>    0.2461</td> <td>    0.028</td> <td>    8.645</td> <td> 0.000</td> <td>    0.190</td> <td>    0.302</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_living</th>        <td>    0.0015</td> <td> 3.01e-05</td> <td>   49.794</td> <td> 0.000</td> <td>    0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_lot</th>            <td>    0.0596</td> <td>    0.018</td> <td>    3.373</td> <td> 0.001</td> <td>    0.025</td> <td>    0.094</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors</th>             <td>   -0.1605</td> <td>    0.034</td> <td>   -4.675</td> <td> 0.000</td> <td>   -0.228</td> <td>   -0.093</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waterfront</th>         <td>    4.9186</td> <td>    0.171</td> <td>   28.745</td> <td> 0.000</td> <td>    4.583</td> <td>    5.254</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>condition</th>          <td>    0.2966</td> <td>    0.020</td> <td>   14.637</td> <td> 0.000</td> <td>    0.257</td> <td>    0.336</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade</th>              <td>    0.9434</td> <td>    0.018</td> <td>   52.811</td> <td> 0.000</td> <td>    0.908</td> <td>    0.978</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>yr_of_last_update</th>  <td>   -0.0165</td> <td>    0.001</td> <td>  -25.836</td> <td> 0.000</td> <td>   -0.018</td> <td>   -0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>below_ground_ratio</th> <td>   -0.5178</td> <td>    0.051</td> <td>  -10.064</td> <td> 0.000</td> <td>   -0.619</td> <td>   -0.417</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>is_seattle</th>         <td>    2.1254</td> <td>    0.037</td> <td>   57.961</td> <td> 0.000</td> <td>    2.054</td> <td>    2.197</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>top_5_district</th>     <td>    1.8324</td> <td>    0.031</td> <td>   59.697</td> <td> 0.000</td> <td>    1.772</td> <td>    1.893</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Spring</th>             <td>    0.2799</td> <td>    0.033</td> <td>    8.583</td> <td> 0.000</td> <td>    0.216</td> <td>    0.344</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Summer</th>             <td>    0.0181</td> <td>    0.033</td> <td>    0.552</td> <td> 0.581</td> <td>   -0.046</td> <td>    0.083</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Winter</th>             <td>    0.0766</td> <td>    0.038</td> <td>    2.036</td> <td> 0.042</td> <td>    0.003</td> <td>    0.150</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>5666.973</td> <th>  Durbin-Watson:     </th> <td>   2.004</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>33728.893</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 1.467</td>  <th>  Prob(JB):          </th> <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 9.225</td>  <th>  Cond. No.          </th> <td>3.16e+05</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.16e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             price_100k   R-squared:                       0.714\n",
       "Model:                            OLS   Adj. R-squared:                  0.714\n",
       "Method:                 Least Squares   F-statistic:                     2841.\n",
       "Date:                Thu, 09 Jul 2020   Prob (F-statistic):               0.00\n",
       "Time:                        12:31:27   Log-Likelihood:                -31704.\n",
       "No. Observations:               17094   AIC:                         6.344e+04\n",
       "Df Residuals:                   17078   BIC:                         6.356e+04\n",
       "Df Model:                          15                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================\n",
       "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "Intercept             25.0568      1.279     19.587      0.000      22.549      27.564\n",
       "bedrooms              -0.1872      0.017    -10.923      0.000      -0.221      -0.154\n",
       "bathrooms              0.2461      0.028      8.645      0.000       0.190       0.302\n",
       "sqft_living            0.0015   3.01e-05     49.794      0.000       0.001       0.002\n",
       "log_lot                0.0596      0.018      3.373      0.001       0.025       0.094\n",
       "floors                -0.1605      0.034     -4.675      0.000      -0.228      -0.093\n",
       "waterfront             4.9186      0.171     28.745      0.000       4.583       5.254\n",
       "condition              0.2966      0.020     14.637      0.000       0.257       0.336\n",
       "grade                  0.9434      0.018     52.811      0.000       0.908       0.978\n",
       "yr_of_last_update     -0.0165      0.001    -25.836      0.000      -0.018      -0.015\n",
       "below_ground_ratio    -0.5178      0.051    -10.064      0.000      -0.619      -0.417\n",
       "is_seattle             2.1254      0.037     57.961      0.000       2.054       2.197\n",
       "top_5_district         1.8324      0.031     59.697      0.000       1.772       1.893\n",
       "Spring                 0.2799      0.033      8.583      0.000       0.216       0.344\n",
       "Summer                 0.0181      0.033      0.552      0.581      -0.046       0.083\n",
       "Winter                 0.0766      0.038      2.036      0.042       0.003       0.150\n",
       "==============================================================================\n",
       "Omnibus:                     5666.973   Durbin-Watson:                   2.004\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            33728.893\n",
       "Skew:                           1.467   Prob(JB):                         0.00\n",
       "Kurtosis:                       9.225   Cond. No.                     3.16e+05\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.16e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(formula=formula, data=reg_df).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>price_100k</td>    <th>  R-squared:         </th> <td>   0.714</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.714</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   3044.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 09 Jul 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:31:27</td>     <th>  Log-Likelihood:    </th> <td> -31705.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 17094</td>      <th>  AIC:               </th> <td>6.344e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 17079</td>      <th>  BIC:               </th> <td>6.356e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    14</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>          <td>   25.0553</td> <td>    1.279</td> <td>   19.586</td> <td> 0.000</td> <td>   22.548</td> <td>   27.563</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>           <td>   -0.1872</td> <td>    0.017</td> <td>  -10.921</td> <td> 0.000</td> <td>   -0.221</td> <td>   -0.154</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th>          <td>    0.2460</td> <td>    0.028</td> <td>    8.642</td> <td> 0.000</td> <td>    0.190</td> <td>    0.302</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_living</th>        <td>    0.0015</td> <td> 3.01e-05</td> <td>   49.792</td> <td> 0.000</td> <td>    0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_lot</th>            <td>    0.0597</td> <td>    0.018</td> <td>    3.378</td> <td> 0.001</td> <td>    0.025</td> <td>    0.094</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors</th>             <td>   -0.1605</td> <td>    0.034</td> <td>   -4.675</td> <td> 0.000</td> <td>   -0.228</td> <td>   -0.093</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waterfront</th>         <td>    4.9174</td> <td>    0.171</td> <td>   28.741</td> <td> 0.000</td> <td>    4.582</td> <td>    5.253</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>condition</th>          <td>    0.2968</td> <td>    0.020</td> <td>   14.650</td> <td> 0.000</td> <td>    0.257</td> <td>    0.337</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade</th>              <td>    0.9435</td> <td>    0.018</td> <td>   52.824</td> <td> 0.000</td> <td>    0.908</td> <td>    0.979</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>yr_of_last_update</th>  <td>   -0.0165</td> <td>    0.001</td> <td>  -25.832</td> <td> 0.000</td> <td>   -0.018</td> <td>   -0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>below_ground_ratio</th> <td>   -0.5177</td> <td>    0.051</td> <td>  -10.062</td> <td> 0.000</td> <td>   -0.618</td> <td>   -0.417</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>is_seattle</th>         <td>    2.1255</td> <td>    0.037</td> <td>   57.963</td> <td> 0.000</td> <td>    2.054</td> <td>    2.197</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>top_5_district</th>     <td>    1.8326</td> <td>    0.031</td> <td>   59.709</td> <td> 0.000</td> <td>    1.772</td> <td>    1.893</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Spring</th>             <td>    0.2698</td> <td>    0.027</td> <td>    9.975</td> <td> 0.000</td> <td>    0.217</td> <td>    0.323</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Winter</th>             <td>    0.0665</td> <td>    0.033</td> <td>    2.021</td> <td> 0.043</td> <td>    0.002</td> <td>    0.131</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>5668.149</td> <th>  Durbin-Watson:     </th> <td>   2.004</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>33746.493</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 1.467</td>  <th>  Prob(JB):          </th> <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 9.227</td>  <th>  Cond. No.          </th> <td>3.16e+05</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.16e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             price_100k   R-squared:                       0.714\n",
       "Model:                            OLS   Adj. R-squared:                  0.714\n",
       "Method:                 Least Squares   F-statistic:                     3044.\n",
       "Date:                Thu, 09 Jul 2020   Prob (F-statistic):               0.00\n",
       "Time:                        12:31:27   Log-Likelihood:                -31705.\n",
       "No. Observations:               17094   AIC:                         6.344e+04\n",
       "Df Residuals:                   17079   BIC:                         6.356e+04\n",
       "Df Model:                          14                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================\n",
       "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "Intercept             25.0553      1.279     19.586      0.000      22.548      27.563\n",
       "bedrooms              -0.1872      0.017    -10.921      0.000      -0.221      -0.154\n",
       "bathrooms              0.2460      0.028      8.642      0.000       0.190       0.302\n",
       "sqft_living            0.0015   3.01e-05     49.792      0.000       0.001       0.002\n",
       "log_lot                0.0597      0.018      3.378      0.001       0.025       0.094\n",
       "floors                -0.1605      0.034     -4.675      0.000      -0.228      -0.093\n",
       "waterfront             4.9174      0.171     28.741      0.000       4.582       5.253\n",
       "condition              0.2968      0.020     14.650      0.000       0.257       0.337\n",
       "grade                  0.9435      0.018     52.824      0.000       0.908       0.979\n",
       "yr_of_last_update     -0.0165      0.001    -25.832      0.000      -0.018      -0.015\n",
       "below_ground_ratio    -0.5177      0.051    -10.062      0.000      -0.618      -0.417\n",
       "is_seattle             2.1255      0.037     57.963      0.000       2.054       2.197\n",
       "top_5_district         1.8326      0.031     59.709      0.000       1.772       1.893\n",
       "Spring                 0.2698      0.027      9.975      0.000       0.217       0.323\n",
       "Winter                 0.0665      0.033      2.021      0.043       0.002       0.131\n",
       "==============================================================================\n",
       "Omnibus:                     5668.149   Durbin-Watson:                   2.004\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            33746.493\n",
       "Skew:                           1.467   Prob(JB):                         0.00\n",
       "Kurtosis:                       9.227   Cond. No.                     3.16e+05\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.16e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Drop non-significant variables\n",
    "outcome = 'price_100k'\n",
    "predictors = reg_df.drop(['price_100k', 'Summer'], axis=1)\n",
    "pred_sum = '+'.join(predictors.columns)\n",
    "formula = outcome + '~' + pred_sum\n",
    "model = ols(formula=formula, data=reg_df).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Check Residuals!!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check Homoskedasticity\n",
    "def gq_test(data, model):\n",
    "    \n",
    "    #Graph heteroskedasticity\n",
    "    pred_val = model.fittedvalues.copy()\n",
    "#     true_val = data['price_100k'].values.copy()\n",
    "    residual = model.resid\n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    graph = ax.scatter(pred_val, residual)\n",
    "    \n",
    "    # Run Goldfeld Quandt test\n",
    "    name = ['F statistic', 'p-value']\n",
    "    test = sms.het_goldfeldquandt(model.resid, model.model.exog)\n",
    "    return list(zip(name, test))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Normality check for residuals with QQ plot\n",
    "resid1 = model.resid\n",
    "fig = sm.graphics.qqplot(resid1, dist=stats.norm, line='45', fit=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('F statistic', 1.0475445683807323), ('p-value', 0.01597415265999172)]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cNGVIOrcRFC7o7pfpJM7a2UncE6y8NI2906GRXuRFAuPIVxYLnnM9YXuhugkTRkrio+cNedyTfklNInaLsPHmXr0s37W0r8VrdG7DXkeHgn5+Ic4bZF8CWY/VmsL9z748H1c9vv84bruhFDoRJ05qSjXFkbvPV0G9N6jXDXxs71HjomHuSgRWTnDXhkFtowuSHD0vrcQ96ZfUJGK3CCsV6arwBW1jZKikLfLkF10yunlVLHp3XiSxeuSV6hwq1XoFk/JMBX/10mnjiUgTrLw0aeQmbN8zjclT5/DgyFpMnjrXNBGpAPzDiXOeE5NhKj+2DKcRMRRUVoDET88bciD+Sb8kJhG7RZh4c13Ejm5C0r0NXQTE7KXLmJgqJ7pPO1nNME4jDgDbPnINhq9d3lIn3A+FehTJ8LXL6w2jPd6Pm2pNpXLSfzEQiyEXkZMAfgagBuCyV73crNLrCQ5eTZJ1UpFOhllq5VCw8kbb8LIgzubHXqVaFzvPHKrPNXh1WfJDYeHJ0ZSBfgtvV+eajmWYhKksT/pnmTg98k1KqZ/EuL0mJqbK2PXc0fnU4GLBwtjWNYka1TTHjMd1g9FJRUA9Pdv5mu4inZmt4pFt6+e3Uey3oFT98X5s71GI1Jfxi4DQhXDSMNT3TdQa6WEiaKycYOctawA0nw+bVq9o6VCkM+5ZnfTPOpmQViamyi2P5DOVKkafCpfWHJa0xozHfYNxS0UPTBxp0lTt7Rf7Lc9WaMV+q8mIO9uoOaWAIEPkZbS14Y5IPq0+TXRCGnrX0r7588B9Hg1fuzzQuMc16d/rT8FJEJchVwCeFxEF4H8opR5zLyAi9wC4BwAGBwdDbVzX87E6F6zJ2SeFV7Zc0MmR1pjxuG8wE1PlQP21Uq3hir5WCcXKC37+9uV5A99Oz0svb04n/aS1v2aWsTNLTQ3oFX25+eMy0G9h5y3tPyGn+Sk4zcRlyDcqpc6IyHsAfEdEjimlvutcoGHcHwPqPTvDbNzPcAYlNjhPCme2nMnJkWThqXZo5wbj9nY2rV6BPd97zSgiYqZSRbFgNV28SsWTaeiOx7ZxSj/2zThsdAUxQ7AgxTivEQAtxtWdwfp2NWrfoWZ0Tsqu547SS/chljhypdSZxu+3AHwTwEfj2K5NUCMBXeEqv7ogJrW50xozHjUpySv55/EXT4cKa3Ma7berc7EYcQBYtqRPe2GODJXmj0Vaemn2Iro6KUH1dZzL2kQtLKdzRs7PVlmMy4e2DbmILBORd9t/A7gJwCvtbtfJ6OZVvt1kdAc2yEMNet8r+aXbCQ4TU2VcfKc1esHvBmNfVPfumW65IJNqixaWC40bgs4AmBiTxUyMbUKbODNTMZYS7eXa6U5l+rRbqdZwLzsWzROHtPJeAN+UelGMPgB/pZT6XzFsdx7bcDqjVtx4acRBNT78Thq3BPHItvVdf5RzS0U2On3SHemTZuyUcZ0+2u15ibQzp5KZALavEZPoF3tZ0zkcr0lNO8HM9HtQQ6/TtkeulPqRUmpd42eNUuoP4hiYm5GhEqa+eBNO7t6irZnhvtj96l4EebBprKus80r7PWQJO9InbUZc0HrS2cdCZwDue/IwruxiyntWiNuI28fFpH6M83oymcPRXWNA+O8RdwvDLJLJWiumGrFTGgEw3wE9SCLpRL/LILwkhjCTnLueO5pYSno7KAD5vKBYsFrkKt33qymFn3nISX4I4NvxngRjHxcvifFun5oqJten3zVm0hDEzWJ/YstEHLmbMNmIUdLpux12GDYV3stbTZsn7qRaU5jx6FXpJ4XVQua92/tqscWbx8VAf/2cChOOaBN0fU5MlbXH+cxMBY9sW9+yvpUXLFvSp51c73YkWbfJpEee9CRkt0vV6rwVkXr2nZuLjVolWSNsudsw2Bd8rxhxAXwn/OP+rC0fujqyvOh3fdpOio6VxYLn+uO3r8P0zpvw6Lb1qYwk6zaiuhDONTw8rCYnJzv+uaZ4TSoWrHzbN4sHJo7Mp1rnRbDhfQM4+U+VFo/n+h37PA2QANrsSmdzAwBYv+v5SKGBJk1948Y59ompcse7+2QFKyd419I+nJ+tzh+npJ44Co1WcG7c51lY7FZ23p9pdo2ZZn72YoaoiBzyqmWVSWnFD93BC3NQkyhV+8DEkaYkippSOHji3Pz/zskev0QkU9nnN9ZdrW07JgLobPVSK9fxHpblmQqu27Fv/uZGvLHj/Z3ZtQoL0Spx3oS9jDhQP1brdz2PC5Vq6OvCT1IB4GvEwxrlxZYh2lMeuc6Tvu2GkmddiE7GhL///m8bXWS2bqx7IvCr6W17Su5aKW5yqE84pnEylESj1LjJd/qIhvGivUJnbfIimFPK00h7rSsA7towqK19rvP8232i6DY6jzyTGrkOnbb8xEuvdT0KxdRTOjNT8dQIb7thoTGDXzutiamyrxEH6p3jtS45ySTlmUqsIZo5gdF8hel1FJTQVVNKq8V7rWvXW9dp9t0OWOg0PWXI/cLXwiyfBKahcPaE6shQCQd33Igf796C0c2r8MyhhcdS+3EaaJ3oHd9/3Mgri6k0BkkRFy9d9pwMj8LH37fctz2fE5PrKMy15r456Na16627mZgqI6e53no1uqWnNPKwJU9NapPEpZPf+bFrtJq1jZVrLhzlrNzoRmEhRMzZuT7uDu4kfuxa+rpjG5VqTWFAMxkelu+fvoDrV5wzmkx1Xke6ayYoy9qN03j7rVueqTSFSNrldb2ct16ObsmcRu5nXL20NCtXnwByhyFbOcH4Het8J1fajVxxj7V/SQ6vvnVRu7yVF4zfvq4pTCtMfRErJ6EKYJHu0W/lMJvAY5EguDRF3DzaKF/hd80ACBWN5I5k0qXtu280uhtPXgQPf1p/vWeFntDIvdJ6790zjaEvPT/f89GtLS/py3n2UFzSl/M9qO1md05MlTH61OGmsfoZcaDuUY3tPaotcBUEjXh2SMKIA/VEqE56nf1WrknW86uxUjTU8N2e88hQCXdtGGyZG/Iy2rorYE6pzBtxPzIlregmTNw9H50H7Lod+zy3dfFSzbfhb9BkiVdd7wPHzs7/f+7iO5EM60ylGltpWLL4uFCpYmzv0VDrRI1Ft3KCr9z6ofn//eQPABjbusboKXOp1epfPjiytqVLUZinjl7Vxm0yJa3oEmVsvEKYdIYc8JdKdOFLeRHc+bFrWsIZCcky7s5PQXj1zPULsbWXB4D7njwcGMVlImPqrlH3janTocZJ0hPSStBd1SuEye9xzk8q2bR6hfYzHn/xNI046SmcxeVMmKlUseu5o03hf37Geaay8NT88KfXBYY2ttP45S6fgl69SqakFa9EGR32iTC2dQ1GnzqslTl0EsqBY2e126YSTXqRgztuDDXJfn62itGnFxqglwLkDrtlW/+SPlSqtcBMVJPGL0D4DOxeTN3PlCG3d3ZQo2AbO7kG0D/Oub18v5A/QnoVe0Iy6HpxU60tNEA3aQpxfrY6Hx5ZU8q3kbaJrh22ummvpu5nypADCwfOeVfNae7szuQaAJ6hUZtWr5iPQ72yYOHipctGqesmE0TvffcSvPmzS8bfjZBu4fR+R4ZK2B4iVNBed2SohMlT5wIzi53YjbS9dO0kom9MuxdljUxp5E6cmY9emptXCNNtN5TmMyzzIvjw4JX4q5dOz4cIzlSqRkbcygnu2jAYuNzZn1/CsiXxlGUlJEnc3m+YKA/nsg+OrMUj29bPJ6uZ4petHCe9mrqfWUPuJKg++cRUGUNfeh7fePH0vOduVx+MEnpdnVN45tDrgcvNKXS8kiBZ3EQpWe7l/eom+91Yee9s5JnZKgb6raZOUEFDsys4npmpYHz/8URq7He710BSZCr8MApRMiQJWUw86mosbnrN5KTurNgVOwFv+dJ2qvxCgb1oN2zQa1LTa4y2rOPuWJVGdOGHPW/I/QrZE7LYyYvgxEM3G805Af5loXWTlgP9Fqa+eFOka7FYsDC98ybj5Z3BCrp4cgCBy8RVFz1ueiKOPApZ174ISZKaUi3lJPyiVR66dS2+dfgNzwlDXbGu87PV+mdEaOU3U6kaSyzOEh5AazCCc1Lz4I4bUSoWtMsEbT9s+7uk6XlDnnXti5AkKRULGNt71KichB0oEKWExO8/+/J8xIi9nWLBgknVXdP6RkE1z4Fmxy7sxGe79ZeSpOcNeZwNfQnpJexJTlPDXFMqstGarc7Ne8o1pWDlBWNb1xj1NzF9qjZZzunYhZ34THPES88bcmdECyG9ggD4wHuWtUSCeNSb0mLaOMKmYOViM1rVmsLvPfOytgGEE9On6mJAyKM7Omd086qWRhzungAm40jDU3/PG3IATZoYIb2AAvDqWxdbNN4w1XEnT52bz2o0oVKd86xMGJV3Ls8FZo+6wxv98NuUNjbdqzauBl1tlzQ0q1gUhtyGMgshC3j1sg3i7eqcpzEzrTUehoF+a77RigkXNBKRoF5Hxr2d8f3HWxIA7ZIDXgTlq3STzKXot4OzyA5DEslix7QhuBOFuiRjEp8dBQHw491bIq2rq1Eep+YdtrZLp1hUHjlAmYWQdrHrsDyybX2TpyuaCiuFEHJMO3pzWOkjzZp3WBadIbehzEJINOwY6u17pnHdjn1Yv+t5jD59WNu+rlKdQ7+BMRegLb05rPSRZs07LItKWnFiH9zff/blxPonEtLL2P63SfiifY3Zaf267bUrW4SRPqLWM08ji9aQAwsH/a6v/m8cPHGu28MhpOfxyzvqhtyZVs07LItWWnHy+G9/HI9uW0/dnJAu0a6sstihIW9gT4I+um19S5IAISRZ4pBVFjM05C5GhkoYv2NdInGxhPQqVk5CN5Nwwqfh9ljUGrkOp27GHp6E+OOs4/3AxJFQrd6A7EaKpIlYDLmIfBLAfwGQB/BnSqndcWw3DbiN+r0hehkS0su4a3dPTJXxzKFyKCOeF0lNdmSWaVtaEZE8gD8B8OsAPgjgThH5YLvbTSMjQyU+ApKOsiRK77YO4GWATcrIuplTqmtGfGKqjI27X8D1O/Zh4+4XUlFXPCpxaOQfBfBDpdSPlFKXAPw1gE/FsN1UwkQi0kkuGTQDj5t+K+c74W/lBQ9/el2TJx61E1e3sijT3CQiCnEY8hKA1xz/v954rQkRuUdEJkVk8uzZszF8bHdwl8VNp79ESDSsnOArt34I43es057by5b0NRlxZ1eeMHRTG09zk4goxGHIvY53ixuhlHpMKTWslBpescKsQ3dasUMVT+7egke2re/2cAiJjercQvU/3bOAs8pgWDklL5KKyoFpbhIRhTgmO18HcI3j/18CcCaG7WaCkaESJk+dwzdePN3toRASC2dmKr6eqVMOCWP4ghobd5KwlRLTThwe+T8C+ICIXC8iSwB8BsDeGLabGR4cWYu7NwzO9yIkJMvYmrEOpxxi3L2nYGGplcP2PdOpmFjUzXVdfOdy18cWhbYNuVLqMoDPA9gP4AcAnlRKHW13u1njwZG1OPHQzTi5ewvu3jDY7eEQkggD/VaTRx00+V+w8rh7wyDeuTyH87PV1Ews2nNd7iSmmUq162OLQiyZnUqpbyul/plS6v1KqT+IY5tZxvbQ6Z+TXmPLh65u+t9dOrZYsDDQbzXp4AeOnU3lxOLIUAn9S1rV5TSMLSzM7EyIB0fWYvja5Rjbe9S4SzkhaefAsdaIM69M6JnZhXM+zROLaR5bGFhrJUFGhkqY3nnTfGVFQf3R1KTIPiFpxM/A6WKzr9TULUrDxGKvdAmiR94BvGoer9/1PD11kjkUgOvv34e7PjaIB0fWNr2ni81eauVQsPJN76Wlvsro5lUtvUbTMrYw0DXsEmNb17BcLskkSgHfePE0Hpg40vS6zlufma2mtvt82PZwaYUeeZfwajPVvySHV9+62OWRkSzh1zrNxnYXClYu1raGT7z0WpNX7hebneZOPGkemyk05F0k6AR6//3fRk11vtYGyQ5BRhyoyyHFghW7lOc+N3tFpsgiNOQphkacxEUS8zHuBDiTZsZ2VEvWmx2nDRryFFPSPKoSkgbu/Ng1La/5PWXaUS22x25HtdjrkejQkKcYr0dVQrqNCDyjVoBWj3vT6hU4cOwsztzJ8GoAAA+oSURBVMxUkBNpecq0k2/ccej02MNBQ55i7BN413NHcX6WoYqke+RFcOKhm32X8fK4ncXkdFKhHe1Cjz06DD9MOSNDJUx9sZ5U1E5zW0LawWS+JkqHIGAh+abXaoR3EhryjOA06OxQRJJCl9lg0uIwSlq7M6qlV9LluwENecawExiKmrRnQqJSKhZw14bBFkfBNIQwTFq7V/JNr6TLdwMa8gziVcOFkHYoNSYWv3X4jSZ5Y6DfMs50NO1nO9Bv4ce7t+DgjhsDS+IyDt0MTnZmGGeoV9Tmt4QI6hOL9+6Zbnnv5+9cNt6OO468f0keFy81a95WXrDzljVG6wdFrWQpwiXpsYrqQtLJ8PCwmpyc7Pjn9jLuGX9C/Mg3QgEF+t6cNsWChWVX9IUyQl7nowC4a4N32GJYvLafplZyTuIcq4gcUkoNu1+ntNIjuIv/sFQu0ZFDPZknLxJoxIF6Vqi7NG1QBx2vCBQF73rmUchShEsnxkpppYdwZ9XZj3OUXIiTOaCtZuHuJB4vdJEm5ZkKrt+xr215IUsRLp0YKw15D+Pu3OJMLCpYOeREWjRMQkw4M1Px1X11lRABNHn2QLRkH79Ki2mjE2OlRk4w9KXnmTnaI9iad7Fg4eKly6jWkrm+B/otvF2d0+q+pnM2pWIBB3fcGPrzqZE3QyGVNPVXJNlGoW4kxrauwbaPtBa1CkuxYHmGBCoFX93XPWejI6q8kKWGEJ0YKz1ywtDFHsTOxDQ9rlZOAEGTB297jUBrSOD2PdOeE6UC4Me7t7S8rjvHonrkixWdR06NnGirLBasHASItasMCU+xYOGdy3OhQkvDerrjd6yr/9Zo3m7vUTeJrtN9ozadyFKseDehISeBiRiMUe8uY1vrCTRhIpBWhvDIS41WbID5xGNYw2xyjrnfA8BqiIZQWiFGOEMZTZJISDzY+nKQpOHEygnG71iHyVPn8PiLp32Xt5eNYhjj8pZ1k4FX9OU8OxstZjmG0gppC3coo5f39LtPThv1kCTm2LvT9kavNOi9+a6l9cv6mUPlQKP/rqV9kb3buJoW6xJmdE+AaYwV7zY05CQ0fhdwN5pgLMkLLiUUZtdJNr5/OU7+U8W3m85Sg4zdmdmqcW3wOCOWonroYQ1zGmPFuw0NOYkNt9c++tRhVDvgoidpxHNi1qm+HfIiuPNj12D42uXz4Xu6Rg4mN8mVxYKxcfQzimEMs/t4l2cqGH3qMIBgPVuXMKOLVWc1xFYYR04SYWSohPE71hk1JEgreRF8/H3Lkc+1VyhYF4v96Lb1OLl7C048dDOGr12O+589Ml/TpB1GN68y8lqlsawXtm5tWmNlbO/Rlpt2dU5hbO9Ro/F67Z+dt6zJTKx4t6FHThJDp6t7yQZppKYU/uHEubYMq52cA/iXZzWRQgpW3kguuXfPNJYtycPKie8TkYLeW/Yr9OS1jk63D9LzgeCIFhruYGjISUdwG3V3lIJXQkpYBvot/LRyOdabRLtbuqKv/tAbNDHoJ4UIwkWtAMDFSzXkc4Kiz+So39OSSaEn5825XeKaOF2sUFohHccrZXn8jnUYv31BigkrZtiP4g9/ep1xT9NOdFaaqVSxfc80rtuxDxt3v6CVJnRSSKlYmO+mAwC5EDJPbU7hZ29fxt0R2rcFtV1zSy862lSliCH0yElX0HlguhDHTatXYN/LbzRVb1xq5TEzW216FJ+YKmOplZv39v1i3uMUdwb6LczMVj1lI3cIof09nd+x2G+1SCFuYzu+/zhqIWdea0rhmUNl3HZDCQeOnTWOKAlK+DGNimE4amegISepxMvQB3WW8ZJs/OxInIlNO29Zg5GhEq7fsc93OWdhKedYz89WYeXrUsiFStXT2EaVMCrVGg4cOxsqiSZItzYdS5Ynu7MEDTnpGUy9RBuFVmNu5QXLlvThQqUaysjbk4B+dbhtzsxUPMdarSksu6IP0ztv8lzPZNt+nxkWP93aZCwMFewcbWnkIjImImURmW783BzXwAgJSxRjpYBmrf72dZjeeRN+vHsLBvqt0J9t0knezwiWXZOJG3e/gOsb+vqm1Ss8t10sWLh7wyCKBf14406i8fqeVk4w0G8xVLALxOGRP6KU+uMYtkNIW0TxWP3qduy8ZQ1Gnz5sFEmTE5lvYWbr0V51aWwv1a8MLNAqE5VnKoFa94Mja7V1S+L2jMN2vO8Ei7lSIqUV0jPoyvHq8DJwbmOw7SPXNBnOTatX4JlD5ZbPsCc4bYPr7JTjVZfGbwLWbsvnFccdpHW3a2DDGMM0hQx63fgWU6XEtqofisgYgH8N4KcAJgHcp5Q6H7Qeqx+SpHD3JtVR8jBSpi25TJKb/Dz9oEYeA/2Wdvy6xg1xkKX2aW4WS+OKyNUPReTvAPyix1tfAPCnAL6MuiPxZQAPA/icZjv3ALgHAAYHB40HTkgYbC9xYqqMsb1HW5Jh/AyTaTaj0xPVRan46fVBWr7fTShI6/bzqIO87bDZnGmiE53q00ygIVdK/ZrJhkTkqwC+5bOdxwA8BtQ9ctMBEhIFp0E3lQqiGANdWVk/g9tO9Imf1u0nLwDBTRqybAw70ak+zbSlkYvI1UqpNxr//iaAV9ofEiHxEUbHDWsMJqbKuHjpcsvrVk58Da6flu/XUKFYsHy/i59Hbf/t9Z69zSwbw6it5HqFdlP0/0hEjojIywA2Adgew5gI6Qq6Knw6YzC+/7hnREtQswZniQKgXmURWAjZG9u6xnMcdvEtHTrPuTxT0T4BONcJ+/3TRCc61aeZtjxypdS/imsghHSbsBEfOuNo0qzB5EkhbORJFMnG6W2nMaQwDGmKouk0DD8kxIGpMZiYKmtT/OOQItxG1ZZHwtZH8cPL217MxjDL0JATEoHx/ce1CT1xSBFR4qKdxt/PM3eWxaXR7g1oyAmJgE6P9mvWEIaooYC2R71Y4qpJHdYjJyQCfvXD48Bv4tKvrrlNlicuSXhoyAmJQNKG0k9nD+qfCTCKY7HRVop+VJiiT3qBJIs0eaXLu6FMsviInKJPCPEmyQgPk4nLLGRcks5AaYWQlDIyVMLBHTdqdfcsZFySzkBDTkjK4cQlCYLSCiEpJ+sZlyR5aMgJSRG6CVRmXBI/aMgJSQmLvcsNiQ41ckJSQlAZWkJ00JATkhKy3NiBdBcackJSgi6ckGGGJAgackJSAsMMSVQ42UlISmCYIYkKDTkhKYJhhuYkWesma9CQE0IyB0M1m6FGTgjJHAzVbIYeOSEkFGmQNBiq2Qw9ckKIMbakUZ6pQMGsyUUSMFSzGRpyQogxaZE0GKrZDKUVQogxaZE0GKrZDA05IcSYlcWCZ8eibkgaDNVcgNIKIcQYShrphB45IcQYShrphIacEBIKShrpg9IKIYRkHBpyQgjJODTkhBCScWjICSEk49CQE0JIxhGlVOc/VOQsgFONf68C8JOODyKYNI6LYzInjePimMxI45iAdIzrWqXUCveLXTHkTQMQmVRKDXd1EB6kcVwckzlpHBfHZEYaxwSkd1wApRVCCMk8NOSEEJJx0mDIH+v2ADSkcVwckzlpHBfHZEYaxwSkd1zd18gJIYS0Rxo8ckIIIW3QcUMuIuMickxEXhaRb4pIUbPcSRE5IiLTIjKZ0Fg+KSLHReSHIrLD4/0rRGRP4/2XROS6JMbh+sxrROSAiPxARI6KyH/wWOYTInKhsW+mReSLHRiX7/GQOv+1sa9eFpEPJzyeVY7vPy0iPxWRe13LdGQ/icjXROQtEXnF8dpyEfmOiLza+D2gWfezjWVeFZHPJjymrl57mjGNiUjZcYxu1qzre60mMK49jjGdFJFpzbqJ2ykjlFId/QFwE4C+xt9/COAPNcudBHBVguPIAzgB4H0AlgA4DOCDrmX+PYD/3vj7MwD2dGD/XA3gw42/3w3g/3qM6xMAvtXh4+Z7PADcDOBvAQiADQBe6uDY8gD+H+oxth3fTwD+JYAPA3jF8dofAdjR+HuH13kOYDmAHzV+DzT+HkhwTF299jRjGgPwHw2Or++1Gve4XO8/DOCLndxXYX867pErpZ5XSl1u/PsigF/q9BgafBTAD5VSP1JKXQLw1wA+5VrmUwC+3vj7aQC/KiKS5KCUUm8opb7f+PtnAH4AIAs1Qz8F4C9VnRcBFEXk6g599q8COKGUOhW4ZAIopb4L4JzrZee583UAIx6rbgbwHaXUOaXUeQDfAfDJpMbU7WtPs59MMLlWExlX43r/NIAn4vq8JOi2Rv451L04LxSA50XkkIjck8BnlwC85vj/dbQazPllGhfABQC/kMBYPGlIOUMAXvJ4++MiclhE/lZE1nRgOEHHw2R/JsVnoL/QOr2fbN6rlHoDqN+cAbzHY5lu7rNuXntuPt+Qe76mkaC6uZ/+BYA3lVKvat7v9L7yJJHGEiLydwB+0eOtLyil/qaxzBcAXAbwuGYzG5VSZ0TkPQC+IyLHGnfO2Ibp8Zo7hMdkmUQQkXcBeAbAvUqpn7re/j7qMsLPG5riBIAPJDykoOPRlX0lIksAbAVwv8fb3dhPYejWPuv2tefkTwF8GfXv/WXUZYzPuYfssV6nwu3uhL833sl9pSURj1wp9WtKqV/2+LGN+GcB/AaAu1RDaPLYxpnG77cAfBP1x6s4eR3ANY7/fwnAGd0yItIH4EpEezQMhYhYqBvxx5VSz7rfV0r9VCn188bf3wZgichVSY7J4HiY7M8k+HUA31dKvel+oxv7ycGbtrTU+P2WxzId32cpufacn/WmUqqmlJoD8FXNZ3Xl3Gpc87cC2KNbppP7yo9uRK18EsDvAdiqlJrVLLNMRN5t/436JM0rXsu2wT8C+ICIXN/w6j4DYK9rmb0A7EiC2wG8oDv546Khyf05gB8opf6zZplftLV6Efko6sfxnxIck8nx2Avgt6TOBgAXbGkhYbQeU6f3kwvnufNZAH/jscx+ADeJyEBDUrip8VoipOjac36ecx7lNzWfZXKtJsGvATimlHrd681O7ytfOj27CuCHqOtd040fOypkJYBvN/5+H+oz04cBHEVdkkliLDejHhVywv4MAF9C/UQHgKUAnmqM+XsA3teB/fPPUX9sfNmxj24G8DsAfqexzOcb++Uw6pNWv5LwmDyPh2tMAuBPGvvyCIDhDuyrftQN85WO1zq+n1C/kbwBoIq69/hvUZ9L+XsArzZ+L28sOwzgzxzrfq5xfv0QwL9JeExdvfY0Y/qfjfPlZdSN89XuMTX+b7lWkxxX4/W/sM8lx7Idt1MmP8zsJISQjNPtqBVCCCFtQkNOCCEZh4acEEIyDg05IYRkHBpyQgjJODTkhBCScWjICSEk49CQE0JIxvn/DtCqz8zzbPcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gq_test(reg_df, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression 2 - New Dummy Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating Dummy Variables for Floors, Grade, Condition\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>price_100k</th>\n",
       "      <th>is_seattle</th>\n",
       "      <th>top_5_district</th>\n",
       "      <th>Spring</th>\n",
       "      <th>Summer</th>\n",
       "      <th>Winter</th>\n",
       "      <th>floors_1h</th>\n",
       "      <th>floors_2</th>\n",
       "      <th>floors_2h</th>\n",
       "      <th>floors_3</th>\n",
       "      <th>floors_3h</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
       "      <td>3470</td>\n",
       "      <td>9.392912</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1978</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.990</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>4.500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1959</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  waterfront  condition  grade  \\\n",
       "0         5       2.50         3470  9.392912         0.0          3      8   \n",
       "1         5       2.75         2990  8.911934         0.0          3      8   \n",
       "2         4       2.75         2900  8.764053         0.0          3      7   \n",
       "3         3       2.50         2620  9.979847         0.0          3      7   \n",
       "4         3       1.50         1770  9.753130         0.0          3      8   \n",
       "\n",
       "   yr_of_last_update  below_ground_ratio  price_100k  is_seattle  \\\n",
       "0               1978            0.000000       5.990         0.0   \n",
       "1               1996            0.000000       4.985         0.0   \n",
       "2               1970            0.421569       4.500         1.0   \n",
       "3               1992            0.000000       6.720         0.0   \n",
       "4               1959            0.525862       4.500         0.0   \n",
       "\n",
       "   top_5_district  Spring  Summer  Winter  floors_1h  floors_2  floors_2h  \\\n",
       "0             1.0       1       0       0          0         1          0   \n",
       "1             0.0       0       1       0          0         1          0   \n",
       "2             0.0       0       0       1          0         1          0   \n",
       "3             1.0       1       0       0          0         1          0   \n",
       "4             1.0       1       0       0          0         0          0   \n",
       "\n",
       "   floors_3  floors_3h  \n",
       "0         0          0  \n",
       "1         0          0  \n",
       "2         0          0  \n",
       "3         0          0  \n",
       "4         0          0  "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Floors\n",
    "reg_df2 = reg_df\n",
    "floors = pd.get_dummies(reg_df2['floors'], prefix='floors', drop_first=True)\n",
    "reg_df2 = pd.concat([reg_df2, floors], axis=1)\n",
    "reg_df2.drop('floors', axis=1, inplace=True)\n",
    "\n",
    "#Rename floors so no decimal in column name\n",
    "reg_df2.rename(columns={'floors_1.5':'floors_1h','floors_2.0':'floors_2','floors_2.5':'floors_2h','floors_3.0':'floors_3','floors_3.5':'floors_3h'}, inplace=True)\n",
    "reg_df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>condition</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>price_100k</th>\n",
       "      <th>is_seattle</th>\n",
       "      <th>...</th>\n",
       "      <th>grade_4</th>\n",
       "      <th>grade_5</th>\n",
       "      <th>grade_6</th>\n",
       "      <th>grade_7</th>\n",
       "      <th>grade_8</th>\n",
       "      <th>grade_9</th>\n",
       "      <th>grade_10</th>\n",
       "      <th>grade_11</th>\n",
       "      <th>grade_12</th>\n",
       "      <th>grade_13</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>1978</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.990</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>4.500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
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       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1959</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  waterfront  condition  \\\n",
       "0         5       2.50         3470  9.392912         0.0          3   \n",
       "1         5       2.75         2990  8.911934         0.0          3   \n",
       "2         4       2.75         2900  8.764053         0.0          3   \n",
       "3         3       2.50         2620  9.979847         0.0          3   \n",
       "4         3       1.50         1770  9.753130         0.0          3   \n",
       "\n",
       "   yr_of_last_update  below_ground_ratio  price_100k  is_seattle  ...  \\\n",
       "0               1978            0.000000       5.990         0.0  ...   \n",
       "1               1996            0.000000       4.985         0.0  ...   \n",
       "2               1970            0.421569       4.500         1.0  ...   \n",
       "3               1992            0.000000       6.720         0.0  ...   \n",
       "4               1959            0.525862       4.500         0.0  ...   \n",
       "\n",
       "   grade_4  grade_5  grade_6  grade_7  grade_8  grade_9  grade_10  grade_11  \\\n",
       "0        0        0        0        0        1        0         0         0   \n",
       "1        0        0        0        0        1        0         0         0   \n",
       "2        0        0        0        1        0        0         0         0   \n",
       "3        0        0        0        1        0        0         0         0   \n",
       "4        0        0        0        0        1        0         0         0   \n",
       "\n",
       "   grade_12  grade_13  \n",
       "0         0         0  \n",
       "1         0         0  \n",
       "2         0         0  \n",
       "3         0         0  \n",
       "4         0         0  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Grade - Data in master table ranges from 3-13\n",
    "grade = pd.get_dummies(reg_df2['grade'], prefix='grade', drop_first=True)\n",
    "reg_df2 = pd.concat([reg_df2, grade], axis=1)\n",
    "reg_df2.drop('grade', axis=1, inplace=True)\n",
    "reg_df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.0</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>8.764053</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1970</td>\n",
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       "      <td>4.500</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1959</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 32 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  waterfront  yr_of_last_update  \\\n",
       "0         5       2.50         3470  9.392912         0.0               1978   \n",
       "1         5       2.75         2990  8.911934         0.0               1996   \n",
       "2         4       2.75         2900  8.764053         0.0               1970   \n",
       "3         3       2.50         2620  9.979847         0.0               1992   \n",
       "4         3       1.50         1770  9.753130         0.0               1959   \n",
       "\n",
       "   below_ground_ratio  price_100k  is_seattle  top_5_district  ...  grade_8  \\\n",
       "0            0.000000       5.990         0.0             1.0  ...        1   \n",
       "1            0.000000       4.985         0.0             0.0  ...        1   \n",
       "2            0.421569       4.500         1.0             0.0  ...        0   \n",
       "3            0.000000       6.720         0.0             1.0  ...        0   \n",
       "4            0.525862       4.500         0.0             1.0  ...        1   \n",
       "\n",
       "   grade_9  grade_10  grade_11  grade_12  grade_13  cond_2  cond_3  cond_4  \\\n",
       "0        0         0         0         0         0       0       1       0   \n",
       "1        0         0         0         0         0       0       1       0   \n",
       "2        0         0         0         0         0       0       1       0   \n",
       "3        0         0         0         0         0       0       1       0   \n",
       "4        0         0         0         0         0       0       1       0   \n",
       "\n",
       "   cond_5  \n",
       "0       0  \n",
       "1       0  \n",
       "2       0  \n",
       "3       0  \n",
       "4       0  \n",
       "\n",
       "[5 rows x 32 columns]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Condition \n",
    "condition = pd.get_dummies(reg_df2['condition'], prefix='cond', drop_first=True)\n",
    "reg_df2 = pd.concat([reg_df2, condition], axis=1)\n",
    "reg_df2.drop('condition', axis=1, inplace=True)\n",
    "reg_df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['bedrooms', 'bathrooms', 'sqft_living', 'log_lot', 'floors',\n",
       "       'waterfront', 'condition', 'grade', 'yr_of_last_update',\n",
       "       'below_ground_ratio', 'is_seattle', 'top_5_district', 'Spring',\n",
       "       'Winter'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictors.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>price_100k</td>    <th>  R-squared:         </th> <td>   0.723</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.722</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1433.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 09 Jul 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:31:33</td>     <th>  Log-Likelihood:    </th> <td> -31441.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 17094</td>      <th>  AIC:               </th> <td>6.295e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 17062</td>      <th>  BIC:               </th> <td>6.319e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    31</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>          <td>   27.1604</td> <td>    2.044</td> <td>   13.289</td> <td> 0.000</td> <td>   23.154</td> <td>   31.166</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>           <td>   -0.1211</td> <td>    0.017</td> <td>   -6.992</td> <td> 0.000</td> <td>   -0.155</td> <td>   -0.087</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th>          <td>    0.2793</td> <td>    0.028</td> <td>    9.859</td> <td> 0.000</td> <td>    0.224</td> <td>    0.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_living</th>        <td>    0.0014</td> <td>  3.1e-05</td> <td>   43.849</td> <td> 0.000</td> <td>    0.001</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_lot</th>            <td>    0.0482</td> <td>    0.017</td> <td>    2.754</td> <td> 0.006</td> <td>    0.014</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waterfront</th>         <td>    4.8166</td> <td>    0.169</td> <td>   28.543</td> <td> 0.000</td> <td>    4.486</td> <td>    5.147</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>yr_of_last_update</th>  <td>   -0.0139</td> <td>    0.001</td> <td>  -20.671</td> <td> 0.000</td> <td>   -0.015</td> <td>   -0.013</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>below_ground_ratio</th> <td>   -0.3800</td> <td>    0.053</td> <td>   -7.231</td> <td> 0.000</td> <td>   -0.483</td> <td>   -0.277</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>is_seattle</th>         <td>    2.1047</td> <td>    0.037</td> <td>   57.569</td> <td> 0.000</td> <td>    2.033</td> <td>    2.176</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>top_5_district</th>     <td>    1.8094</td> <td>    0.030</td> <td>   59.695</td> <td> 0.000</td> <td>    1.750</td> <td>    1.869</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Spring</th>             <td>    0.2767</td> <td>    0.032</td> <td>    8.607</td> <td> 0.000</td> <td>    0.214</td> <td>    0.340</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Summer</th>             <td>    0.0262</td> <td>    0.032</td> <td>    0.810</td> <td> 0.418</td> <td>   -0.037</td> <td>    0.090</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Winter</th>             <td>    0.0703</td> <td>    0.037</td> <td>    1.895</td> <td> 0.058</td> <td>   -0.002</td> <td>    0.143</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_1h</th>          <td>   -0.0031</td> <td>    0.047</td> <td>   -0.067</td> <td> 0.947</td> <td>   -0.095</td> <td>    0.089</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_2</th>           <td>   -0.2617</td> <td>    0.039</td> <td>   -6.637</td> <td> 0.000</td> <td>   -0.339</td> <td>   -0.184</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_2h</th>          <td>    0.2624</td> <td>    0.150</td> <td>    1.750</td> <td> 0.080</td> <td>   -0.031</td> <td>    0.556</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_3</th>           <td>   -0.0305</td> <td>    0.087</td> <td>   -0.352</td> <td> 0.725</td> <td>   -0.201</td> <td>    0.140</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_3h</th>          <td>   -0.1524</td> <td>    0.882</td> <td>   -0.173</td> <td> 0.863</td> <td>   -1.881</td> <td>    1.576</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_4</th>            <td>   -0.5704</td> <td>    1.565</td> <td>   -0.365</td> <td> 0.715</td> <td>   -3.637</td> <td>    2.497</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_5</th>            <td>   -0.6333</td> <td>    1.529</td> <td>   -0.414</td> <td> 0.679</td> <td>   -3.630</td> <td>    2.364</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_6</th>            <td>   -0.5888</td> <td>    1.526</td> <td>   -0.386</td> <td> 0.700</td> <td>   -3.579</td> <td>    2.401</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_7</th>            <td>    0.0190</td> <td>    1.526</td> <td>    0.012</td> <td> 0.990</td> <td>   -2.971</td> <td>    3.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_8</th>            <td>    0.8375</td> <td>    1.526</td> <td>    0.549</td> <td> 0.583</td> <td>   -2.154</td> <td>    3.829</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_9</th>            <td>    2.0868</td> <td>    1.527</td> <td>    1.367</td> <td> 0.172</td> <td>   -0.906</td> <td>    5.079</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_10</th>           <td>    3.3062</td> <td>    1.528</td> <td>    2.164</td> <td> 0.030</td> <td>    0.312</td> <td>    6.301</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_11</th>           <td>    4.6901</td> <td>    1.531</td> <td>    3.064</td> <td> 0.002</td> <td>    1.690</td> <td>    7.690</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_12</th>           <td>    7.0178</td> <td>    1.544</td> <td>    4.544</td> <td> 0.000</td> <td>    3.991</td> <td>   10.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_13</th>           <td>    9.2811</td> <td>    2.159</td> <td>    4.299</td> <td> 0.000</td> <td>    5.049</td> <td>   13.513</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_2</th>             <td>   -0.0801</td> <td>    0.346</td> <td>   -0.231</td> <td> 0.817</td> <td>   -0.759</td> <td>    0.599</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_3</th>             <td>    0.2067</td> <td>    0.321</td> <td>    0.645</td> <td> 0.519</td> <td>   -0.422</td> <td>    0.835</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_4</th>             <td>    0.4852</td> <td>    0.321</td> <td>    1.513</td> <td> 0.130</td> <td>   -0.143</td> <td>    1.114</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_5</th>             <td>    0.8998</td> <td>    0.323</td> <td>    2.790</td> <td> 0.005</td> <td>    0.268</td> <td>    1.532</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>5653.548</td> <th>  Durbin-Watson:     </th> <td>   2.005</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>35979.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 1.441</td>  <th>  Prob(JB):          </th> <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 9.497</td>  <th>  Cond. No.          </th> <td>1.28e+06</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.28e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             price_100k   R-squared:                       0.723\n",
       "Model:                            OLS   Adj. R-squared:                  0.722\n",
       "Method:                 Least Squares   F-statistic:                     1433.\n",
       "Date:                Thu, 09 Jul 2020   Prob (F-statistic):               0.00\n",
       "Time:                        12:31:33   Log-Likelihood:                -31441.\n",
       "No. Observations:               17094   AIC:                         6.295e+04\n",
       "Df Residuals:                   17062   BIC:                         6.319e+04\n",
       "Df Model:                          31                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================\n",
       "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "Intercept             27.1604      2.044     13.289      0.000      23.154      31.166\n",
       "bedrooms              -0.1211      0.017     -6.992      0.000      -0.155      -0.087\n",
       "bathrooms              0.2793      0.028      9.859      0.000       0.224       0.335\n",
       "sqft_living            0.0014    3.1e-05     43.849      0.000       0.001       0.001\n",
       "log_lot                0.0482      0.017      2.754      0.006       0.014       0.082\n",
       "waterfront             4.8166      0.169     28.543      0.000       4.486       5.147\n",
       "yr_of_last_update     -0.0139      0.001    -20.671      0.000      -0.015      -0.013\n",
       "below_ground_ratio    -0.3800      0.053     -7.231      0.000      -0.483      -0.277\n",
       "is_seattle             2.1047      0.037     57.569      0.000       2.033       2.176\n",
       "top_5_district         1.8094      0.030     59.695      0.000       1.750       1.869\n",
       "Spring                 0.2767      0.032      8.607      0.000       0.214       0.340\n",
       "Summer                 0.0262      0.032      0.810      0.418      -0.037       0.090\n",
       "Winter                 0.0703      0.037      1.895      0.058      -0.002       0.143\n",
       "floors_1h             -0.0031      0.047     -0.067      0.947      -0.095       0.089\n",
       "floors_2              -0.2617      0.039     -6.637      0.000      -0.339      -0.184\n",
       "floors_2h              0.2624      0.150      1.750      0.080      -0.031       0.556\n",
       "floors_3              -0.0305      0.087     -0.352      0.725      -0.201       0.140\n",
       "floors_3h             -0.1524      0.882     -0.173      0.863      -1.881       1.576\n",
       "grade_4               -0.5704      1.565     -0.365      0.715      -3.637       2.497\n",
       "grade_5               -0.6333      1.529     -0.414      0.679      -3.630       2.364\n",
       "grade_6               -0.5888      1.526     -0.386      0.700      -3.579       2.401\n",
       "grade_7                0.0190      1.526      0.012      0.990      -2.971       3.009\n",
       "grade_8                0.8375      1.526      0.549      0.583      -2.154       3.829\n",
       "grade_9                2.0868      1.527      1.367      0.172      -0.906       5.079\n",
       "grade_10               3.3062      1.528      2.164      0.030       0.312       6.301\n",
       "grade_11               4.6901      1.531      3.064      0.002       1.690       7.690\n",
       "grade_12               7.0178      1.544      4.544      0.000       3.991      10.045\n",
       "grade_13               9.2811      2.159      4.299      0.000       5.049      13.513\n",
       "cond_2                -0.0801      0.346     -0.231      0.817      -0.759       0.599\n",
       "cond_3                 0.2067      0.321      0.645      0.519      -0.422       0.835\n",
       "cond_4                 0.4852      0.321      1.513      0.130      -0.143       1.114\n",
       "cond_5                 0.8998      0.323      2.790      0.005       0.268       1.532\n",
       "==============================================================================\n",
       "Omnibus:                     5653.548   Durbin-Watson:                   2.005\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            35979.009\n",
       "Skew:                           1.441   Prob(JB):                         0.00\n",
       "Kurtosis:                       9.497   Cond. No.                     1.28e+06\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.28e+06. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outcome = 'price_100k'\n",
    "predictors = reg_df2.drop('price_100k', axis=1)\n",
    "pred_sum = '+'.join(predictors.columns)\n",
    "formula = outcome + '~' + pred_sum\n",
    "model = ols(formula=formula, data=reg_df2).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Normality check for residuals with QQ plot\n",
    "resid1 = model.resid\n",
    "fig = sm.graphics.qqplot(resid1, dist=stats.norm, line='45', fit=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('F statistic', 1.036604823912329), ('p-value', 0.04858643950891584)]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gq_test(reg_df2, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same as above but set dummy var reference variable as middle value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>price_100k</th>\n",
       "      <th>is_seattle</th>\n",
       "      <th>top_5_district</th>\n",
       "      <th>Spring</th>\n",
       "      <th>Summer</th>\n",
       "      <th>Winter</th>\n",
       "      <th>floors_1</th>\n",
       "      <th>floors_1h</th>\n",
       "      <th>floors_2h</th>\n",
       "      <th>floors_3</th>\n",
       "      <th>floors_3h</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
       "      <td>3470</td>\n",
       "      <td>9.392912</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1978</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.990</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>4.500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1959</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  waterfront  condition  grade  \\\n",
       "0         5       2.50         3470  9.392912         0.0          3      8   \n",
       "1         5       2.75         2990  8.911934         0.0          3      8   \n",
       "2         4       2.75         2900  8.764053         0.0          3      7   \n",
       "3         3       2.50         2620  9.979847         0.0          3      7   \n",
       "4         3       1.50         1770  9.753130         0.0          3      8   \n",
       "\n",
       "   yr_of_last_update  below_ground_ratio  price_100k  is_seattle  \\\n",
       "0               1978            0.000000       5.990         0.0   \n",
       "1               1996            0.000000       4.985         0.0   \n",
       "2               1970            0.421569       4.500         1.0   \n",
       "3               1992            0.000000       6.720         0.0   \n",
       "4               1959            0.525862       4.500         0.0   \n",
       "\n",
       "   top_5_district  Spring  Summer  Winter  floors_1  floors_1h  floors_2h  \\\n",
       "0             1.0       1       0       0         0          0          0   \n",
       "1             0.0       0       1       0         0          0          0   \n",
       "2             0.0       0       0       1         0          0          0   \n",
       "3             1.0       1       0       0         0          0          0   \n",
       "4             1.0       1       0       0         1          0          0   \n",
       "\n",
       "   floors_3  floors_3h  \n",
       "0         0          0  \n",
       "1         0          0  \n",
       "2         0          0  \n",
       "3         0          0  \n",
       "4         0          0  "
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Floors\n",
    "reg_df3 = reg_df\n",
    "floors = pd.get_dummies(reg_df3['floors'], prefix='floors')\n",
    "reg_df3 = pd.concat([reg_df3, floors], axis=1)\n",
    "reg_df3.drop('floors', axis=1, inplace=True)\n",
    "\n",
    "#Drop floor 2 to make it ref var\n",
    "reg_df3.drop('floors_2.0', axis=1, inplace=True)\n",
    "\n",
    "#Rename floors so no decimal in column name\n",
    "reg_df3.rename(columns={'floors_1.0':'floors_1', 'floors_1.5':'floors_1h','floors_2.0':'floors_2','floors_2.5':'floors_2h','floors_3.0':'floors_3','floors_3.5':'floors_3h'}, inplace=True)\n",
    "\n",
    "reg_df3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>condition</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>price_100k</th>\n",
       "      <th>is_seattle</th>\n",
       "      <th>...</th>\n",
       "      <th>grade_3</th>\n",
       "      <th>grade_4</th>\n",
       "      <th>grade_5</th>\n",
       "      <th>grade_6</th>\n",
       "      <th>grade_8</th>\n",
       "      <th>grade_9</th>\n",
       "      <th>grade_10</th>\n",
       "      <th>grade_11</th>\n",
       "      <th>grade_12</th>\n",
       "      <th>grade_13</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
       "      <td>3470</td>\n",
       "      <td>9.392912</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1978</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.990</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
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       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>4</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>4.500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
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       "      <th>4</th>\n",
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       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1959</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  waterfront  condition  \\\n",
       "0         5       2.50         3470  9.392912         0.0          3   \n",
       "1         5       2.75         2990  8.911934         0.0          3   \n",
       "2         4       2.75         2900  8.764053         0.0          3   \n",
       "3         3       2.50         2620  9.979847         0.0          3   \n",
       "4         3       1.50         1770  9.753130         0.0          3   \n",
       "\n",
       "   yr_of_last_update  below_ground_ratio  price_100k  is_seattle  ...  \\\n",
       "0               1978            0.000000       5.990         0.0  ...   \n",
       "1               1996            0.000000       4.985         0.0  ...   \n",
       "2               1970            0.421569       4.500         1.0  ...   \n",
       "3               1992            0.000000       6.720         0.0  ...   \n",
       "4               1959            0.525862       4.500         0.0  ...   \n",
       "\n",
       "   grade_3  grade_4  grade_5  grade_6  grade_8  grade_9  grade_10  grade_11  \\\n",
       "0        0        0        0        0        1        0         0         0   \n",
       "1        0        0        0        0        1        0         0         0   \n",
       "2        0        0        0        0        0        0         0         0   \n",
       "3        0        0        0        0        0        0         0         0   \n",
       "4        0        0        0        0        1        0         0         0   \n",
       "\n",
       "   grade_12  grade_13  \n",
       "0         0         0  \n",
       "1         0         0  \n",
       "2         0         0  \n",
       "3         0         0  \n",
       "4         0         0  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Grade - Data in master table ranges from 3-13\n",
    "grade = pd.get_dummies(reg_df3['grade'], prefix='grade')\n",
    "reg_df3 = pd.concat([reg_df3, grade], axis=1)\n",
    "\n",
    "#Drop Grade 7 (average grade) to make ref var\n",
    "reg_df3.drop('grade_7', axis=1, inplace=True)\n",
    "\n",
    "reg_df3.drop('grade', axis=1, inplace=True)\n",
    "reg_df3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>cond_4</th>\n",
       "      <th>cond_5</th>\n",
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       "      <td>8.911934</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>8.764053</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1970</td>\n",
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       "      <td>4.500</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2620</td>\n",
       "      <td>9.979847</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1992</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.720</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1770</td>\n",
       "      <td>9.753130</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1959</td>\n",
       "      <td>0.525862</td>\n",
       "      <td>4.500</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 32 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  waterfront  yr_of_last_update  \\\n",
       "0         5       2.50         3470  9.392912         0.0               1978   \n",
       "1         5       2.75         2990  8.911934         0.0               1996   \n",
       "2         4       2.75         2900  8.764053         0.0               1970   \n",
       "3         3       2.50         2620  9.979847         0.0               1992   \n",
       "4         3       1.50         1770  9.753130         0.0               1959   \n",
       "\n",
       "   below_ground_ratio  price_100k  is_seattle  top_5_district  ...  grade_8  \\\n",
       "0            0.000000       5.990         0.0             1.0  ...        1   \n",
       "1            0.000000       4.985         0.0             0.0  ...        1   \n",
       "2            0.421569       4.500         1.0             0.0  ...        0   \n",
       "3            0.000000       6.720         0.0             1.0  ...        0   \n",
       "4            0.525862       4.500         0.0             1.0  ...        1   \n",
       "\n",
       "   grade_9  grade_10  grade_11  grade_12  grade_13  cond_1  cond_2  cond_4  \\\n",
       "0        0         0         0         0         0       0       0       0   \n",
       "1        0         0         0         0         0       0       0       0   \n",
       "2        0         0         0         0         0       0       0       0   \n",
       "3        0         0         0         0         0       0       0       0   \n",
       "4        0         0         0         0         0       0       0       0   \n",
       "\n",
       "   cond_5  \n",
       "0       0  \n",
       "1       0  \n",
       "2       0  \n",
       "3       0  \n",
       "4       0  \n",
       "\n",
       "[5 rows x 32 columns]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Condition \n",
    "condition = pd.get_dummies(reg_df3['condition'], prefix='cond')\n",
    "reg_df3 = pd.concat([reg_df3, condition], axis=1)\n",
    "\n",
    "#Drop Condition 3 (average cond) to make ref var\n",
    "reg_df3.drop('cond_3', axis=1, inplace=True)\n",
    "\n",
    "reg_df3.drop('condition', axis=1, inplace=True)\n",
    "reg_df3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>price_100k</td>    <th>  R-squared:         </th> <td>   0.723</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.722</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1433.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 09 Jul 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:31:39</td>     <th>  Log-Likelihood:    </th> <td> -31441.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 17094</td>      <th>  AIC:               </th> <td>6.295e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 17062</td>      <th>  BIC:               </th> <td>6.319e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    31</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>          <td>   27.1244</td> <td>    1.362</td> <td>   19.916</td> <td> 0.000</td> <td>   24.455</td> <td>   29.794</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>           <td>   -0.1211</td> <td>    0.017</td> <td>   -6.992</td> <td> 0.000</td> <td>   -0.155</td> <td>   -0.087</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th>          <td>    0.2793</td> <td>    0.028</td> <td>    9.859</td> <td> 0.000</td> <td>    0.224</td> <td>    0.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_living</th>        <td>    0.0014</td> <td>  3.1e-05</td> <td>   43.849</td> <td> 0.000</td> <td>    0.001</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_lot</th>            <td>    0.0482</td> <td>    0.017</td> <td>    2.754</td> <td> 0.006</td> <td>    0.014</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waterfront</th>         <td>    4.8166</td> <td>    0.169</td> <td>   28.543</td> <td> 0.000</td> <td>    4.486</td> <td>    5.147</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>yr_of_last_update</th>  <td>   -0.0139</td> <td>    0.001</td> <td>  -20.671</td> <td> 0.000</td> <td>   -0.015</td> <td>   -0.013</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>below_ground_ratio</th> <td>   -0.3800</td> <td>    0.053</td> <td>   -7.231</td> <td> 0.000</td> <td>   -0.483</td> <td>   -0.277</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>is_seattle</th>         <td>    2.1047</td> <td>    0.037</td> <td>   57.569</td> <td> 0.000</td> <td>    2.033</td> <td>    2.176</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>top_5_district</th>     <td>    1.8094</td> <td>    0.030</td> <td>   59.695</td> <td> 0.000</td> <td>    1.750</td> <td>    1.869</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Spring</th>             <td>    0.2767</td> <td>    0.032</td> <td>    8.607</td> <td> 0.000</td> <td>    0.214</td> <td>    0.340</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Summer</th>             <td>    0.0262</td> <td>    0.032</td> <td>    0.810</td> <td> 0.418</td> <td>   -0.037</td> <td>    0.090</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Winter</th>             <td>    0.0703</td> <td>    0.037</td> <td>    1.895</td> <td> 0.058</td> <td>   -0.002</td> <td>    0.143</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_1</th>           <td>    0.2617</td> <td>    0.039</td> <td>    6.637</td> <td> 0.000</td> <td>    0.184</td> <td>    0.339</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_1h</th>          <td>    0.2586</td> <td>    0.054</td> <td>    4.822</td> <td> 0.000</td> <td>    0.153</td> <td>    0.364</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_2h</th>          <td>    0.5242</td> <td>    0.147</td> <td>    3.575</td> <td> 0.000</td> <td>    0.237</td> <td>    0.812</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_3</th>           <td>    0.2312</td> <td>    0.078</td> <td>    2.966</td> <td> 0.003</td> <td>    0.078</td> <td>    0.384</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_3h</th>          <td>    0.1093</td> <td>    0.881</td> <td>    0.124</td> <td> 0.901</td> <td>   -1.617</td> <td>    1.836</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_3</th>            <td>   -0.0190</td> <td>    1.526</td> <td>   -0.012</td> <td> 0.990</td> <td>   -3.009</td> <td>    2.971</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_4</th>            <td>   -0.5894</td> <td>    0.352</td> <td>   -1.673</td> <td> 0.094</td> <td>   -1.280</td> <td>    0.101</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_5</th>            <td>   -0.6524</td> <td>    0.115</td> <td>   -5.693</td> <td> 0.000</td> <td>   -0.877</td> <td>   -0.428</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_6</th>            <td>   -0.6079</td> <td>    0.045</td> <td>  -13.593</td> <td> 0.000</td> <td>   -0.696</td> <td>   -0.520</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_8</th>            <td>    0.8185</td> <td>    0.032</td> <td>   25.328</td> <td> 0.000</td> <td>    0.755</td> <td>    0.882</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_9</th>            <td>    2.0677</td> <td>    0.049</td> <td>   41.935</td> <td> 0.000</td> <td>    1.971</td> <td>    2.164</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_10</th>           <td>    3.2872</td> <td>    0.071</td> <td>   46.314</td> <td> 0.000</td> <td>    3.148</td> <td>    3.426</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_11</th>           <td>    4.6711</td> <td>    0.117</td> <td>   40.093</td> <td> 0.000</td> <td>    4.443</td> <td>    4.899</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_12</th>           <td>    6.9987</td> <td>    0.235</td> <td>   29.725</td> <td> 0.000</td> <td>    6.537</td> <td>    7.460</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_13</th>           <td>    9.2620</td> <td>    1.527</td> <td>    6.067</td> <td> 0.000</td> <td>    6.270</td> <td>   12.254</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_1</th>             <td>   -0.2067</td> <td>    0.321</td> <td>   -0.645</td> <td> 0.519</td> <td>   -0.835</td> <td>    0.422</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_2</th>             <td>   -0.2868</td> <td>    0.138</td> <td>   -2.084</td> <td> 0.037</td> <td>   -0.557</td> <td>   -0.017</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_4</th>             <td>    0.2784</td> <td>    0.030</td> <td>    9.397</td> <td> 0.000</td> <td>    0.220</td> <td>    0.337</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_5</th>             <td>    0.6931</td> <td>    0.048</td> <td>   14.566</td> <td> 0.000</td> <td>    0.600</td> <td>    0.786</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>5653.548</td> <th>  Durbin-Watson:     </th> <td>   2.005</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>35979.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 1.441</td>  <th>  Prob(JB):          </th> <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 9.497</td>  <th>  Cond. No.          </th> <td>3.83e+05</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.83e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             price_100k   R-squared:                       0.723\n",
       "Model:                            OLS   Adj. R-squared:                  0.722\n",
       "Method:                 Least Squares   F-statistic:                     1433.\n",
       "Date:                Thu, 09 Jul 2020   Prob (F-statistic):               0.00\n",
       "Time:                        12:31:39   Log-Likelihood:                -31441.\n",
       "No. Observations:               17094   AIC:                         6.295e+04\n",
       "Df Residuals:                   17062   BIC:                         6.319e+04\n",
       "Df Model:                          31                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================\n",
       "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "Intercept             27.1244      1.362     19.916      0.000      24.455      29.794\n",
       "bedrooms              -0.1211      0.017     -6.992      0.000      -0.155      -0.087\n",
       "bathrooms              0.2793      0.028      9.859      0.000       0.224       0.335\n",
       "sqft_living            0.0014    3.1e-05     43.849      0.000       0.001       0.001\n",
       "log_lot                0.0482      0.017      2.754      0.006       0.014       0.082\n",
       "waterfront             4.8166      0.169     28.543      0.000       4.486       5.147\n",
       "yr_of_last_update     -0.0139      0.001    -20.671      0.000      -0.015      -0.013\n",
       "below_ground_ratio    -0.3800      0.053     -7.231      0.000      -0.483      -0.277\n",
       "is_seattle             2.1047      0.037     57.569      0.000       2.033       2.176\n",
       "top_5_district         1.8094      0.030     59.695      0.000       1.750       1.869\n",
       "Spring                 0.2767      0.032      8.607      0.000       0.214       0.340\n",
       "Summer                 0.0262      0.032      0.810      0.418      -0.037       0.090\n",
       "Winter                 0.0703      0.037      1.895      0.058      -0.002       0.143\n",
       "floors_1               0.2617      0.039      6.637      0.000       0.184       0.339\n",
       "floors_1h              0.2586      0.054      4.822      0.000       0.153       0.364\n",
       "floors_2h              0.5242      0.147      3.575      0.000       0.237       0.812\n",
       "floors_3               0.2312      0.078      2.966      0.003       0.078       0.384\n",
       "floors_3h              0.1093      0.881      0.124      0.901      -1.617       1.836\n",
       "grade_3               -0.0190      1.526     -0.012      0.990      -3.009       2.971\n",
       "grade_4               -0.5894      0.352     -1.673      0.094      -1.280       0.101\n",
       "grade_5               -0.6524      0.115     -5.693      0.000      -0.877      -0.428\n",
       "grade_6               -0.6079      0.045    -13.593      0.000      -0.696      -0.520\n",
       "grade_8                0.8185      0.032     25.328      0.000       0.755       0.882\n",
       "grade_9                2.0677      0.049     41.935      0.000       1.971       2.164\n",
       "grade_10               3.2872      0.071     46.314      0.000       3.148       3.426\n",
       "grade_11               4.6711      0.117     40.093      0.000       4.443       4.899\n",
       "grade_12               6.9987      0.235     29.725      0.000       6.537       7.460\n",
       "grade_13               9.2620      1.527      6.067      0.000       6.270      12.254\n",
       "cond_1                -0.2067      0.321     -0.645      0.519      -0.835       0.422\n",
       "cond_2                -0.2868      0.138     -2.084      0.037      -0.557      -0.017\n",
       "cond_4                 0.2784      0.030      9.397      0.000       0.220       0.337\n",
       "cond_5                 0.6931      0.048     14.566      0.000       0.600       0.786\n",
       "==============================================================================\n",
       "Omnibus:                     5653.548   Durbin-Watson:                   2.005\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            35979.009\n",
       "Skew:                           1.441   Prob(JB):                         0.00\n",
       "Kurtosis:                       9.497   Cond. No.                     3.83e+05\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.83e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outcome = 'price_100k'\n",
    "predictors = reg_df3.drop('price_100k', axis=1)\n",
    "pred_sum = '+'.join(predictors.columns)\n",
    "formula = outcome + '~' + pred_sum\n",
    "model = ols(formula=formula, data=reg_df3).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Normality check for residuals with QQ plot\n",
    "resid1 = model.resid\n",
    "fig = sm.graphics.qqplot(resid1, dist=stats.norm, line='45', fit=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('F statistic', 1.0366048239123289), ('p-value', 0.04858643950896008)]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gq_test(reg_df3, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make Predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following steps in \"Polynomial Regression\" lecture.  Redoing model using OLS()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>log_lot</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>yr_of_last_update</th>\n",
       "      <th>below_ground_ratio</th>\n",
       "      <th>is_seattle</th>\n",
       "      <th>top_5_district</th>\n",
       "      <th>Spring</th>\n",
       "      <th>...</th>\n",
       "      <th>grade_8</th>\n",
       "      <th>grade_9</th>\n",
       "      <th>grade_10</th>\n",
       "      <th>grade_11</th>\n",
       "      <th>grade_12</th>\n",
       "      <th>grade_13</th>\n",
       "      <th>cond_1</th>\n",
       "      <th>cond_2</th>\n",
       "      <th>cond_4</th>\n",
       "      <th>cond_5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2.50</td>\n",
       "      <td>3470</td>\n",
       "      <td>9.392912</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1978</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2990</td>\n",
       "      <td>8.911934</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1996</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>2.75</td>\n",
       "      <td>2900</td>\n",
       "      <td>8.764053</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1970</td>\n",
       "      <td>0.421569</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living   log_lot  waterfront  yr_of_last_update  \\\n",
       "0         5       2.50         3470  9.392912         0.0               1978   \n",
       "1         5       2.75         2990  8.911934         0.0               1996   \n",
       "2         4       2.75         2900  8.764053         0.0               1970   \n",
       "\n",
       "   below_ground_ratio  is_seattle  top_5_district  Spring  ...  grade_8  \\\n",
       "0            0.000000         0.0             1.0       1  ...        1   \n",
       "1            0.000000         0.0             0.0       0  ...        1   \n",
       "2            0.421569         1.0             0.0       0  ...        0   \n",
       "\n",
       "   grade_9  grade_10  grade_11  grade_12  grade_13  cond_1  cond_2  cond_4  \\\n",
       "0        0         0         0         0         0       0       0       0   \n",
       "1        0         0         0         0         0       0       0       0   \n",
       "2        0         0         0         0         0       0       0       0   \n",
       "\n",
       "   cond_5  \n",
       "0       0  \n",
       "1       0  \n",
       "2       0  \n",
       "\n",
       "[3 rows x 31 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0    5.990\n",
       "1    4.985\n",
       "2    4.500\n",
       "Name: price_100k, dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = reg_df3['price_100k']\n",
    "independent_variables = list(predictors.columns)\n",
    "X = reg_df3[independent_variables]\n",
    "display(X.head(3), y.head(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>price_100k</td>    <th>  R-squared:         </th> <td>   0.723</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.722</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1433.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 09 Jul 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:31:44</td>     <th>  Log-Likelihood:    </th> <td> -31441.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 17094</td>      <th>  AIC:               </th> <td>6.295e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 17062</td>      <th>  BIC:               </th> <td>6.319e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    31</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>              <td>   27.1244</td> <td>    1.362</td> <td>   19.916</td> <td> 0.000</td> <td>   24.455</td> <td>   29.794</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>           <td>   -0.1211</td> <td>    0.017</td> <td>   -6.992</td> <td> 0.000</td> <td>   -0.155</td> <td>   -0.087</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th>          <td>    0.2793</td> <td>    0.028</td> <td>    9.859</td> <td> 0.000</td> <td>    0.224</td> <td>    0.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_living</th>        <td>    0.0014</td> <td>  3.1e-05</td> <td>   43.849</td> <td> 0.000</td> <td>    0.001</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_lot</th>            <td>    0.0482</td> <td>    0.017</td> <td>    2.754</td> <td> 0.006</td> <td>    0.014</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waterfront</th>         <td>    4.8166</td> <td>    0.169</td> <td>   28.543</td> <td> 0.000</td> <td>    4.486</td> <td>    5.147</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>yr_of_last_update</th>  <td>   -0.0139</td> <td>    0.001</td> <td>  -20.671</td> <td> 0.000</td> <td>   -0.015</td> <td>   -0.013</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>below_ground_ratio</th> <td>   -0.3800</td> <td>    0.053</td> <td>   -7.231</td> <td> 0.000</td> <td>   -0.483</td> <td>   -0.277</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>is_seattle</th>         <td>    2.1047</td> <td>    0.037</td> <td>   57.569</td> <td> 0.000</td> <td>    2.033</td> <td>    2.176</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>top_5_district</th>     <td>    1.8094</td> <td>    0.030</td> <td>   59.695</td> <td> 0.000</td> <td>    1.750</td> <td>    1.869</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Spring</th>             <td>    0.2767</td> <td>    0.032</td> <td>    8.607</td> <td> 0.000</td> <td>    0.214</td> <td>    0.340</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Summer</th>             <td>    0.0262</td> <td>    0.032</td> <td>    0.810</td> <td> 0.418</td> <td>   -0.037</td> <td>    0.090</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Winter</th>             <td>    0.0703</td> <td>    0.037</td> <td>    1.895</td> <td> 0.058</td> <td>   -0.002</td> <td>    0.143</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_1</th>           <td>    0.2617</td> <td>    0.039</td> <td>    6.637</td> <td> 0.000</td> <td>    0.184</td> <td>    0.339</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_1h</th>          <td>    0.2586</td> <td>    0.054</td> <td>    4.822</td> <td> 0.000</td> <td>    0.153</td> <td>    0.364</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_2h</th>          <td>    0.5242</td> <td>    0.147</td> <td>    3.575</td> <td> 0.000</td> <td>    0.237</td> <td>    0.812</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_3</th>           <td>    0.2312</td> <td>    0.078</td> <td>    2.966</td> <td> 0.003</td> <td>    0.078</td> <td>    0.384</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors_3h</th>          <td>    0.1093</td> <td>    0.881</td> <td>    0.124</td> <td> 0.901</td> <td>   -1.617</td> <td>    1.836</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_3</th>            <td>   -0.0190</td> <td>    1.526</td> <td>   -0.012</td> <td> 0.990</td> <td>   -3.009</td> <td>    2.971</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_4</th>            <td>   -0.5894</td> <td>    0.352</td> <td>   -1.673</td> <td> 0.094</td> <td>   -1.280</td> <td>    0.101</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_5</th>            <td>   -0.6524</td> <td>    0.115</td> <td>   -5.693</td> <td> 0.000</td> <td>   -0.877</td> <td>   -0.428</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_6</th>            <td>   -0.6079</td> <td>    0.045</td> <td>  -13.593</td> <td> 0.000</td> <td>   -0.696</td> <td>   -0.520</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_8</th>            <td>    0.8185</td> <td>    0.032</td> <td>   25.328</td> <td> 0.000</td> <td>    0.755</td> <td>    0.882</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_9</th>            <td>    2.0677</td> <td>    0.049</td> <td>   41.935</td> <td> 0.000</td> <td>    1.971</td> <td>    2.164</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_10</th>           <td>    3.2872</td> <td>    0.071</td> <td>   46.314</td> <td> 0.000</td> <td>    3.148</td> <td>    3.426</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_11</th>           <td>    4.6711</td> <td>    0.117</td> <td>   40.093</td> <td> 0.000</td> <td>    4.443</td> <td>    4.899</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_12</th>           <td>    6.9987</td> <td>    0.235</td> <td>   29.725</td> <td> 0.000</td> <td>    6.537</td> <td>    7.460</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade_13</th>           <td>    9.2620</td> <td>    1.527</td> <td>    6.067</td> <td> 0.000</td> <td>    6.270</td> <td>   12.254</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_1</th>             <td>   -0.2067</td> <td>    0.321</td> <td>   -0.645</td> <td> 0.519</td> <td>   -0.835</td> <td>    0.422</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_2</th>             <td>   -0.2868</td> <td>    0.138</td> <td>   -2.084</td> <td> 0.037</td> <td>   -0.557</td> <td>   -0.017</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_4</th>             <td>    0.2784</td> <td>    0.030</td> <td>    9.397</td> <td> 0.000</td> <td>    0.220</td> <td>    0.337</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cond_5</th>             <td>    0.6931</td> <td>    0.048</td> <td>   14.566</td> <td> 0.000</td> <td>    0.600</td> <td>    0.786</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>5653.548</td> <th>  Durbin-Watson:     </th> <td>   2.005</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>35979.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 1.441</td>  <th>  Prob(JB):          </th> <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 9.497</td>  <th>  Cond. No.          </th> <td>3.83e+05</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.83e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             price_100k   R-squared:                       0.723\n",
       "Model:                            OLS   Adj. R-squared:                  0.722\n",
       "Method:                 Least Squares   F-statistic:                     1433.\n",
       "Date:                Thu, 09 Jul 2020   Prob (F-statistic):               0.00\n",
       "Time:                        12:31:44   Log-Likelihood:                -31441.\n",
       "No. Observations:               17094   AIC:                         6.295e+04\n",
       "Df Residuals:                   17062   BIC:                         6.319e+04\n",
       "Df Model:                          31                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================\n",
       "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "const                 27.1244      1.362     19.916      0.000      24.455      29.794\n",
       "bedrooms              -0.1211      0.017     -6.992      0.000      -0.155      -0.087\n",
       "bathrooms              0.2793      0.028      9.859      0.000       0.224       0.335\n",
       "sqft_living            0.0014    3.1e-05     43.849      0.000       0.001       0.001\n",
       "log_lot                0.0482      0.017      2.754      0.006       0.014       0.082\n",
       "waterfront             4.8166      0.169     28.543      0.000       4.486       5.147\n",
       "yr_of_last_update     -0.0139      0.001    -20.671      0.000      -0.015      -0.013\n",
       "below_ground_ratio    -0.3800      0.053     -7.231      0.000      -0.483      -0.277\n",
       "is_seattle             2.1047      0.037     57.569      0.000       2.033       2.176\n",
       "top_5_district         1.8094      0.030     59.695      0.000       1.750       1.869\n",
       "Spring                 0.2767      0.032      8.607      0.000       0.214       0.340\n",
       "Summer                 0.0262      0.032      0.810      0.418      -0.037       0.090\n",
       "Winter                 0.0703      0.037      1.895      0.058      -0.002       0.143\n",
       "floors_1               0.2617      0.039      6.637      0.000       0.184       0.339\n",
       "floors_1h              0.2586      0.054      4.822      0.000       0.153       0.364\n",
       "floors_2h              0.5242      0.147      3.575      0.000       0.237       0.812\n",
       "floors_3               0.2312      0.078      2.966      0.003       0.078       0.384\n",
       "floors_3h              0.1093      0.881      0.124      0.901      -1.617       1.836\n",
       "grade_3               -0.0190      1.526     -0.012      0.990      -3.009       2.971\n",
       "grade_4               -0.5894      0.352     -1.673      0.094      -1.280       0.101\n",
       "grade_5               -0.6524      0.115     -5.693      0.000      -0.877      -0.428\n",
       "grade_6               -0.6079      0.045    -13.593      0.000      -0.696      -0.520\n",
       "grade_8                0.8185      0.032     25.328      0.000       0.755       0.882\n",
       "grade_9                2.0677      0.049     41.935      0.000       1.971       2.164\n",
       "grade_10               3.2872      0.071     46.314      0.000       3.148       3.426\n",
       "grade_11               4.6711      0.117     40.093      0.000       4.443       4.899\n",
       "grade_12               6.9987      0.235     29.725      0.000       6.537       7.460\n",
       "grade_13               9.2620      1.527      6.067      0.000       6.270      12.254\n",
       "cond_1                -0.2067      0.321     -0.645      0.519      -0.835       0.422\n",
       "cond_2                -0.2868      0.138     -2.084      0.037      -0.557      -0.017\n",
       "cond_4                 0.2784      0.030      9.397      0.000       0.220       0.337\n",
       "cond_5                 0.6931      0.048     14.566      0.000       0.600       0.786\n",
       "==============================================================================\n",
       "Omnibus:                     5653.548   Durbin-Watson:                   2.005\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            35979.009\n",
       "Skew:                           1.441   Prob(JB):                         0.00\n",
       "Kurtosis:                       9.497   Cond. No.                     3.83e+05\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.83e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "Xconst = sm.add_constant(X)\n",
    "\n",
    "model = sm.OLS(y, Xconst, hasconst= True)\n",
    "\n",
    "fitted_model = model.fit()\n",
    "\n",
    "fitted_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Find predictions\n",
    "y_predict = fitted_model.predict(Xconst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1,\n",
       " 'bedrooms',\n",
       " 'bathrooms',\n",
       " 'sqft_living',\n",
       " 'log_lot',\n",
       " 'waterfront',\n",
       " 'yr_of_last_update',\n",
       " 'below_ground_ratio',\n",
       " 'is_seattle',\n",
       " 'top_5_district',\n",
       " 'Spring',\n",
       " 'Summer',\n",
       " 'Winter',\n",
       " 'floors_1',\n",
       " 'floors_1h',\n",
       " 'floors_2h',\n",
       " 'floors_3',\n",
       " 'floors_3h',\n",
       " 'grade_3',\n",
       " 'grade_4',\n",
       " 'grade_5',\n",
       " 'grade_6',\n",
       " 'grade_8',\n",
       " 'grade_9',\n",
       " 'grade_10',\n",
       " 'grade_11',\n",
       " 'grade_12',\n",
       " 'grade_13',\n",
       " 'cond_1',\n",
       " 'cond_2',\n",
       " 'cond_4',\n",
       " 'cond_5']"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array_columns = independent_variables\n",
    "array_columns.insert(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Function to find index based on column name\n",
    "def find_index(col_name, array_2d):\n",
    "    x = 0\n",
    "    for i in array_2d[0]:\n",
    "        if i == col_name:\n",
    "            return x\n",
    "        else:\n",
    "            x += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Better User Input Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_home_stats(df, col_names, fit_model, seattle=0, top_dist=0, spring=0):\n",
    "    #Known variables given as inputs\n",
    "    \n",
    "    # Insignificant - Summer, Winter, floors_3h, grade_3, grade_4, cond_1\n",
    "    \n",
    "    empty_values = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
    "    prediction_values = np.array([col_names, empty_values])\n",
    "    \n",
    "\n",
    "    \n",
    "    #Floors\n",
    "    floor_num = input(\"Number of floors ('1' for one floor, '1h' for 1.5 floors): \")\n",
    "    floor_str = 'floors_' + str(floor_num)\n",
    "    prediction_values[1][find_index(floor_str, prediction_values)] = 1\n",
    "    \n",
    "    #Bedrooms\n",
    "    bed_num = input(\"Number of bedrooms (whole number): \")\n",
    "    prediction_values[1][find_index('bedrooms', prediction_values)] = bed_num\n",
    "    \n",
    "    #Bathrooms\n",
    "    bath_num = input(\"Number of bathrooms: \")\n",
    "    prediction_values[1][find_index('bathrooms', prediction_values)] = bath_num\n",
    "    \n",
    "    #Waterfront\n",
    "    wf = input(\"Is your house on the waterfront? (1 for yes, 0 for no): \")\n",
    "    prediction_values[1][find_index('waterfront', prediction_values)] = wf\n",
    "    \n",
    "    #Square feet\n",
    "    sqft = input(\"Total square feet: \")\n",
    "    prediction_values[1][find_index('sqft_living', prediction_values)] = sqft\n",
    "    \n",
    "    #Grade\n",
    "    grade_num = input(\"House grade(whole number 3-13): \")\n",
    "    grade_str = 'grade_' + str(grade_num)\n",
    "    prediction_values[1][find_index(grade_str, prediction_values)] = 1\n",
    "    \n",
    "    #Condition\n",
    "    cond_num = input(\"House condition (whole number 1-5): \")\n",
    "    cond_str = 'cond_' + str(cond_num)\n",
    "    prediction_values[1][find_index(cond_str, prediction_values)] = 1\n",
    "    \n",
    "    \n",
    "    #Set values for vars known from location/date\n",
    "    prediction_values[1][find_index('is_seattle', prediction_values)] = seattle\n",
    "    prediction_values[1][find_index('top_5_district', prediction_values)] = top_dist\n",
    "    prediction_values[1][find_index('Spring', prediction_values)] = spring\n",
    "    \n",
    "    # Set values for unknown variables as median - log_lot, below_ground_ratio, yr_of_last_update\n",
    "    prediction_values[1][find_index('log_lot', prediction_values)] = df['log_lot'].median()\n",
    "    prediction_values[1][find_index('below_ground_ratio', prediction_values)] = df['below_ground_ratio'].median()\n",
    "    prediction_values[1][find_index('yr_of_last_update', prediction_values)] = df['yr_of_last_update'].median()\n",
    "    \n",
    "    \n",
    "    #Get values only in array\n",
    "    prediction_input = prediction_values[1].astype(float)\n",
    "    \n",
    "    #Calculate intervals\n",
    "    intervals = fit_model.get_prediction(prediction_input)\n",
    "    bounds = intervals.summary_frame(alpha=0.05)\n",
    "    \n",
    "    #Format and print\n",
    "    # Shows the bounds for true average value of a home of this type\n",
    "    lower_bound = bounds['mean_ci_lower'][0] * 100000\n",
    "    upper_bound = bounds['mean_ci_upper'][0] * 100000\n",
    "    print('Your house is worth between ' + \"${:,.0f}\".format(lower_bound) + ' and ' \"${:,.0f}\".format(upper_bound) + '!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ADD ALL POSSIBLE SIGNIFICANT OPTIONS HERE - OTHERS WONT BE ALLOWED & WILL STAY 0\n",
    "# Insignificant - Summer, Winter, floors_3h, grade_3, grade_4, cond_1\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Number of floors ('1' for one floor, '1h' for 1.5 floors):  1h\n",
      "Number of bedrooms (whole number):  3\n",
      "Number of bathrooms:  2.5\n",
      "Is your house on the waterfront? (1 for yes, 0 for no):  1\n",
      "Total square feet:  1000\n",
      "House grade(whole number 3-13):  8\n",
      "House condition (whole number 1-5):  4\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your house is worth between $778,687 and $849,751!\n"
     ]
    }
   ],
   "source": [
    "#Ex 3 bed, 1000 ft, wf, 2.5 br, gr8, cond4, 1h floors, spring\n",
    "get_home_stats(reg_df3, array_columns, fitted_model, seattle=0, top_dist=0, spring=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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