2. Linear Regression using Normal Method.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f6b12b34",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4aa6e640",
   "metadata": {},
   "outputs": [],
   "source": [
    "data=pd.read_csv('Sample data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d0ac2aa1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 25 entries, 0 to 24\n",
      "Data columns (total 2 columns):\n",
      " #   Column  Non-Null Count  Dtype\n",
      "---  ------  --------------  -----\n",
      " 0   x       25 non-null     int64\n",
      " 1   y       25 non-null     int64\n",
      "dtypes: int64(2)\n",
      "memory usage: 528.0 bytes\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f355b8aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>13.000000</td>\n",
       "      <td>13.080000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7.359801</td>\n",
       "      <td>7.788453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>13.000000</td>\n",
       "      <td>11.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>19.000000</td>\n",
       "      <td>20.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>25.000000</td>\n",
       "      <td>26.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               x          y\n",
       "count  25.000000  25.000000\n",
       "mean   13.000000  13.080000\n",
       "std     7.359801   7.788453\n",
       "min     1.000000   2.000000\n",
       "25%     7.000000   7.000000\n",
       "50%    13.000000  11.000000\n",
       "75%    19.000000  20.000000\n",
       "max    25.000000  26.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4ef9523d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>25</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>23</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "     x   y\n",
       "24  25  25\n",
       "10  11  16\n",
       "22  23  23\n",
       "3    4   4\n",
       "5    6   7"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.sample(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3f5ae110",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.isnull().values.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6ceb9fd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_mean = data['x'].mean()\n",
    "x_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b11446d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.08"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = data['y'].values\n",
    "\n",
    "y_mean = np.mean(Y)\n",
    "y_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "439b0ea3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rows=len(data['x'])\n",
    "rows = data.shape[0]\n",
    "rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6ec5a2a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "numer=0\n",
    "denom=0\n",
    "\n",
    "X = data['x'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "923d332a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Destiny\\AppData\\Local\\Temp\\ipykernel_3744\\839219221.py:8: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  m = numer/denom\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the slope: m\n",
    "\n",
    "for i in range(rows):\n",
    "    numer = numer + Y[i] - y_mean\n",
    "    denom = denom + X[i] - x_mean\n",
    "\n",
    "# slope: m = sum(yi - y)/sum(xi-x)\n",
    "m = numer/denom\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "812a29e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "denom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bb6066ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1   3\n",
      "2   4\n",
      "3   2\n",
      "4   4\n",
      "5   5\n",
      "6   7\n",
      "7   9\n",
      "8   5\n",
      "9   11\n",
      "10   8\n",
      "11   16\n",
      "12   9\n",
      "13   11\n",
      "14   12\n",
      "15   19\n",
      "16   15\n",
      "17   21\n",
      "18   8\n",
      "19   20\n",
      "20   20\n",
      "21   26\n",
      "22   18\n",
      "23   23\n",
      "24   26\n",
      "25   25\n",
      "Slope:0.963076923076923\n",
      "Slope: 0.963076923076923\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.963076923076923"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the slope: m\n",
    "\n",
    "for i in range(rows):\n",
    "    print(X[i],\" \",Y[i])\n",
    "    numer = numer + (X[i] - x_mean) * (Y[i] - y_mean)\n",
    "    denom = denom + (X[i] - x_mean) ** 2  # squared\n",
    "\n",
    "# slope: m = sum(yi - y)/sum(xi-x)\n",
    "m = numer/denom\n",
    "print(f'Slope:{m}')\n",
    "print(\"Slope:\",m)\n",
    "\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "37a0abee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5600000000000005"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Calculate intercept: c\n",
    "\n",
    "c = y_mean - m * x_mean\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a3f9cbbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  1.24242424,  1.48484848,  1.72727273,  1.96969697,\n",
       "        2.21212121,  2.45454545,  2.6969697 ,  2.93939394,  3.18181818,\n",
       "        3.42424242,  3.66666667,  3.90909091,  4.15151515,  4.39393939,\n",
       "        4.63636364,  4.87878788,  5.12121212,  5.36363636,  5.60606061,\n",
       "        5.84848485,  6.09090909,  6.33333333,  6.57575758,  6.81818182,\n",
       "        7.06060606,  7.3030303 ,  7.54545455,  7.78787879,  8.03030303,\n",
       "        8.27272727,  8.51515152,  8.75757576,  9.        ,  9.24242424,\n",
       "        9.48484848,  9.72727273,  9.96969697, 10.21212121, 10.45454545,\n",
       "       10.6969697 , 10.93939394, 11.18181818, 11.42424242, 11.66666667,\n",
       "       11.90909091, 12.15151515, 12.39393939, 12.63636364, 12.87878788,\n",
       "       13.12121212, 13.36363636, 13.60606061, 13.84848485, 14.09090909,\n",
       "       14.33333333, 14.57575758, 14.81818182, 15.06060606, 15.3030303 ,\n",
       "       15.54545455, 15.78787879, 16.03030303, 16.27272727, 16.51515152,\n",
       "       16.75757576, 17.        , 17.24242424, 17.48484848, 17.72727273,\n",
       "       17.96969697, 18.21212121, 18.45454545, 18.6969697 , 18.93939394,\n",
       "       19.18181818, 19.42424242, 19.66666667, 19.90909091, 20.15151515,\n",
       "       20.39393939, 20.63636364, 20.87878788, 21.12121212, 21.36363636,\n",
       "       21.60606061, 21.84848485, 22.09090909, 22.33333333, 22.57575758,\n",
       "       22.81818182, 23.06060606, 23.3030303 , 23.54545455, 23.78787879,\n",
       "       24.03030303, 24.27272727, 24.51515152, 24.75757576, 25.        ])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 25 data(rows) - for calculating m and c (like training data) \n",
    "\n",
    "# now we take random numbers in range for plotting line\n",
    "\n",
    "max_x = np.max(X)\n",
    "min_x = np.min(X)\n",
    "\n",
    "new_X = np.linspace(min_x, max_x, 100)\n",
    "new_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a131c1e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.52307692,  1.75655012,  1.99002331,  2.2234965 ,  2.4569697 ,\n",
       "        2.69044289,  2.92391608,  3.15738928,  3.39086247,  3.62433566,\n",
       "        3.85780886,  4.09128205,  4.32475524,  4.55822844,  4.79170163,\n",
       "        5.02517483,  5.25864802,  5.49212121,  5.72559441,  5.9590676 ,\n",
       "        6.19254079,  6.42601399,  6.65948718,  6.89296037,  7.12643357,\n",
       "        7.35990676,  7.59337995,  7.82685315,  8.06032634,  8.29379953,\n",
       "        8.52727273,  8.76074592,  8.99421911,  9.22769231,  9.4611655 ,\n",
       "        9.69463869,  9.92811189, 10.16158508, 10.39505828, 10.62853147,\n",
       "       10.86200466, 11.09547786, 11.32895105, 11.56242424, 11.79589744,\n",
       "       12.02937063, 12.26284382, 12.49631702, 12.72979021, 12.9632634 ,\n",
       "       13.1967366 , 13.43020979, 13.66368298, 13.89715618, 14.13062937,\n",
       "       14.36410256, 14.59757576, 14.83104895, 15.06452214, 15.29799534,\n",
       "       15.53146853, 15.76494172, 15.99841492, 16.23188811, 16.46536131,\n",
       "       16.6988345 , 16.93230769, 17.16578089, 17.39925408, 17.63272727,\n",
       "       17.86620047, 18.09967366, 18.33314685, 18.56662005, 18.80009324,\n",
       "       19.03356643, 19.26703963, 19.50051282, 19.73398601, 19.96745921,\n",
       "       20.2009324 , 20.43440559, 20.66787879, 20.90135198, 21.13482517,\n",
       "       21.36829837, 21.60177156, 21.83524476, 22.06871795, 22.30219114,\n",
       "       22.53566434, 22.76913753, 23.00261072, 23.23608392, 23.46955711,\n",
       "       23.7030303 , 23.9365035 , 24.16997669, 24.40344988, 24.63692308])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_Y = m * new_X + c\n",
    "new_Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b665edd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18ec0d8eda0>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(new_X, new_Y, color=\"red\", label='line')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f0f3d117",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y, color=\"orangered\", label=\"Data Points\")\n",
    "plt.xlabel(\"X Values\")\n",
    "plt.ylabel(\"Y Values\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c16a9b80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(new_X, new_Y, color=\"red\", label='Prediction line')\n",
    "\n",
    "plt.scatter(X, Y, color=\"orangered\", label=\"Actual Data Points\")\n",
    "plt.xlabel(\"X Values\")\n",
    "plt.ylabel(\"Y Values\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "283c1500",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "506bea2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8282313356497333"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# measure \n",
    "# calculating R-squared value for measuring goodness of our model\n",
    "\n",
    "sst = 0 # total sum of square\n",
    "ssr = 0\n",
    "\n",
    "for i in range(data.shape[0]):\n",
    "    y_pred = m * X[i] + c\n",
    "    \n",
    "    ssr = ssr + (Y[i] - y_pred) ** 2\n",
    "    sst = sst + (Y[i] - y_mean) ** 2\n",
    "    \n",
    "r2 = 1 - ssr/sst\n",
    "\n",
    "\n",
    "r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "35dd6dfb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8281a01",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}