D206 Final.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import requred packages and data to be cleaned\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "medical_data = pd.read_csv('medical_raw_data.csv',dtype={'CaseOrder':np.int64})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create index for dataset\n",
    "medical_data.rename(columns={'Unnamed: 0':'index'}, inplace=True)\n",
    "medical_data['index'] = pd.Series(range(0,10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "index                 False\n",
       "CaseOrder             False\n",
       "Customer_id           False\n",
       "Interaction           False\n",
       "UID                   False\n",
       "City                  False\n",
       "State                 False\n",
       "County                False\n",
       "Zip                   False\n",
       "Lat                   False\n",
       "Lng                   False\n",
       "Population            False\n",
       "Area                  False\n",
       "Timezone              False\n",
       "Job                   False\n",
       "Children               True\n",
       "Age                    True\n",
       "Education             False\n",
       "Employment            False\n",
       "Income                 True\n",
       "Marital               False\n",
       "Gender                False\n",
       "ReAdmis               False\n",
       "VitD_levels           False\n",
       "Doc_visits            False\n",
       "Full_meals_eaten      False\n",
       "VitD_supp             False\n",
       "Soft_drink             True\n",
       "Initial_admin         False\n",
       "HighBlood             False\n",
       "Stroke                False\n",
       "Complication_risk     False\n",
       "Overweight             True\n",
       "Arthritis             False\n",
       "Diabetes              False\n",
       "Hyperlipidemia        False\n",
       "BackPain              False\n",
       "Anxiety                True\n",
       "Allergic_rhinitis     False\n",
       "Reflux_esophagitis    False\n",
       "Asthma                False\n",
       "Services              False\n",
       "Initial_days           True\n",
       "TotalCharge           False\n",
       "Additional_charges    False\n",
       "Item1                 False\n",
       "Item2                 False\n",
       "Item3                 False\n",
       "Item4                 False\n",
       "Item5                 False\n",
       "Item6                 False\n",
       "Item7                 False\n",
       "Item8                 False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#check for nulls in data\n",
    "medical_data.isnull().any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Children</th>\n",
       "      <th>Age</th>\n",
       "      <th>Income</th>\n",
       "      <th>Soft_drink</th>\n",
       "      <th>Overweight</th>\n",
       "      <th>Anxiety</th>\n",
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       "      <td>No</td>\n",
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       "      <td>No</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1209.56</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.254807</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Children   Age    Income Soft_drink  Overweight  Anxiety  Initial_days\n",
       "0       1.0  53.0  86575.93        NaN         0.0      1.0     10.585770\n",
       "1       3.0  51.0  46805.99         No         1.0      NaN     15.129562\n",
       "2       3.0  53.0  14370.14         No         1.0      NaN      4.772177\n",
       "3       0.0  78.0  39741.49         No         0.0      NaN      1.714879\n",
       "4       NaN  22.0   1209.56        Yes         0.0      0.0      1.254807"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#isolate columns with null to prep for cleaning\n",
    "md_null = medical_data[['Children','Age','Income','Soft_drink','Overweight','Anxiety','Initial_days']]\n",
    "md_null.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fill numerical columns to better perform analysis\n",
    "medical_data = medical_data.fillna(medical_data.median())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fill categorical null values\n",
    "medical_data['Soft_drink'] = medical_data['Soft_drink'].fillna(medical_data['Soft_drink'].mode()[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "index                 False\n",
       "CaseOrder             False\n",
       "Customer_id           False\n",
       "Interaction           False\n",
       "UID                   False\n",
       "City                  False\n",
       "State                 False\n",
       "County                False\n",
       "Zip                   False\n",
       "Lat                   False\n",
       "Lng                   False\n",
       "Population            False\n",
       "Area                  False\n",
       "Timezone              False\n",
       "Job                   False\n",
       "Children              False\n",
       "Age                   False\n",
       "Education             False\n",
       "Employment            False\n",
       "Income                False\n",
       "Marital               False\n",
       "Gender                False\n",
       "ReAdmis               False\n",
       "VitD_levels           False\n",
       "Doc_visits            False\n",
       "Full_meals_eaten      False\n",
       "VitD_supp             False\n",
       "Soft_drink            False\n",
       "Initial_admin         False\n",
       "HighBlood             False\n",
       "Stroke                False\n",
       "Complication_risk     False\n",
       "Overweight            False\n",
       "Arthritis             False\n",
       "Diabetes              False\n",
       "Hyperlipidemia        False\n",
       "BackPain              False\n",
       "Anxiety               False\n",
       "Allergic_rhinitis     False\n",
       "Reflux_esophagitis    False\n",
       "Asthma                False\n",
       "Services              False\n",
       "Initial_days          False\n",
       "TotalCharge           False\n",
       "Additional_charges    False\n",
       "Item1                 False\n",
       "Item2                 False\n",
       "Item3                 False\n",
       "Item4                 False\n",
       "Item5                 False\n",
       "Item6                 False\n",
       "Item7                 False\n",
       "Item8                 False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#verify all nulls are filled\n",
    "medical_data.isnull().any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#check for duplicates that my skew analysis\n",
    "medical_data.duplicated().any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#perform z score of income variable and create new variable\n",
    "medical_data['Incomez'] = stats.zscore(medical_data['Income'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#isolate outlers to new variable\n",
    "medical_outliers = medical_data.query('Incomez > 3 | Incomez < -3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "      <td>Waban</td>\n",
       "      <td>MA</td>\n",
       "      <td>Middlesex</td>\n",
       "      <td>2468</td>\n",
       "      <td>42.32731</td>\n",
       "      <td>...</td>\n",
       "      <td>4204.826360</td>\n",
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       "      <td>d0ee6d98-4a9c-4898-a53a-20ee31b4d641</td>\n",
       "      <td>1b18c3313b8d62a4a4487ca693eb4926</td>\n",
       "      <td>Lynn Haven</td>\n",
       "      <td>FL</td>\n",
       "      <td>Bay</td>\n",
       "      <td>32444</td>\n",
       "      <td>30.23936</td>\n",
       "      <td>...</td>\n",
       "      <td>14397.946210</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
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       "      <td>4</td>\n",
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       "      <td>3.757416</td>\n",
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       "      <td>a624688f58099e7d62202790b73110b0</td>\n",
       "      <td>West Bloomfield</td>\n",
       "      <td>MI</td>\n",
       "      <td>Oakland</td>\n",
       "      <td>48322</td>\n",
       "      <td>42.54215</td>\n",
       "      <td>...</td>\n",
       "      <td>11058.380500</td>\n",
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       "      <td>2d1201d5070a453860cf425de074ccb8</td>\n",
       "      <td>Cynthiana</td>\n",
       "      <td>IN</td>\n",
       "      <td>Posey</td>\n",
       "      <td>47612</td>\n",
       "      <td>38.19303</td>\n",
       "      <td>...</td>\n",
       "      <td>3968.532959</td>\n",
       "      <td>4</td>\n",
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       "      <td>Asbury</td>\n",
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       "      <td>Greenbrier</td>\n",
       "      <td>24916</td>\n",
       "      <td>37.83127</td>\n",
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       "      <td>9609.241091</td>\n",
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       "      <td>4.583966</td>\n",
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       "      <td>9863</td>\n",
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       "      <td>2f7fda4c-c3b5-4b7b-b0a1-ae51f8149f2e</td>\n",
       "      <td>f2a735c2db8d0c5c824c77dfd94e59fb</td>\n",
       "      <td>Pittsburgh</td>\n",
       "      <td>PA</td>\n",
       "      <td>Allegheny</td>\n",
       "      <td>15260</td>\n",
       "      <td>40.44329</td>\n",
       "      <td>...</td>\n",
       "      <td>9175.406982</td>\n",
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       "      <td>8ae790d973df20db7ac404159105c640</td>\n",
       "      <td>Honolulu</td>\n",
       "      <td>HI</td>\n",
       "      <td>Honolulu</td>\n",
       "      <td>96814</td>\n",
       "      <td>21.29398</td>\n",
       "      <td>...</td>\n",
       "      <td>8171.843436</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
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       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>3.979006</td>\n",
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       "    <tr>\n",
       "      <th>9910</th>\n",
       "      <td>9910</td>\n",
       "      <td>9911</td>\n",
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       "      <td>8deaec35-fb84-4d70-9331-3e3180a6cb19</td>\n",
       "      <td>0d25d0100e92724a5ca84b47578761d8</td>\n",
       "      <td>Saint Clair Shores</td>\n",
       "      <td>MI</td>\n",
       "      <td>Macomb</td>\n",
       "      <td>48081</td>\n",
       "      <td>42.49507</td>\n",
       "      <td>...</td>\n",
       "      <td>22281.115980</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>3.226905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9955</th>\n",
       "      <td>9955</td>\n",
       "      <td>9956</td>\n",
       "      <td>K984015</td>\n",
       "      <td>9ab96ccd-b2b0-4351-b9e0-df752a189975</td>\n",
       "      <td>a746aa6e32f770c8dde8dc6eb24aadcc</td>\n",
       "      <td>Blanch</td>\n",
       "      <td>NC</td>\n",
       "      <td>Caswell</td>\n",
       "      <td>27212</td>\n",
       "      <td>36.46059</td>\n",
       "      <td>...</td>\n",
       "      <td>9189.087049</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3.331227</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>180 rows × 54 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      index  CaseOrder Customer_id                           Interaction  \\\n",
       "30       30         31      D54890  81693046-dc24-4c84-8d60-dac8a9271438   \n",
       "36       36         37     X589810  71d5c53b-382f-4bfb-ba89-a5cc8f79b09a   \n",
       "58       58         59     H786242  d0ee6d98-4a9c-4898-a53a-20ee31b4d641   \n",
       "63       63         64     R430894  7cdcd202-f475-4bbc-8ce2-eef9eb1a38eb   \n",
       "77       77         78     G903269  28275f93-aa0c-4311-ac14-2637d45023cf   \n",
       "...     ...        ...         ...                                   ...   \n",
       "9742   9742       9743     M714824  91573992-4e09-444a-abfa-1fa92f5fb187   \n",
       "9862   9862       9863     S984639  2f7fda4c-c3b5-4b7b-b0a1-ae51f8149f2e   \n",
       "9906   9906       9907     E416766  be658e42-e0d5-45ed-a259-4943a4e3c808   \n",
       "9910   9910       9911     T760129  8deaec35-fb84-4d70-9331-3e3180a6cb19   \n",
       "9955   9955       9956     K984015  9ab96ccd-b2b0-4351-b9e0-df752a189975   \n",
       "\n",
       "                                   UID                City State      County  \\\n",
       "30    342d672cea7e6882f63e8fb3e0076cb1             Niotaze    KS  Chautauqua   \n",
       "36    9c7c5a7430801f7e9c6af38d7ba79fd2               Waban    MA   Middlesex   \n",
       "58    1b18c3313b8d62a4a4487ca693eb4926          Lynn Haven    FL         Bay   \n",
       "63    a624688f58099e7d62202790b73110b0     West Bloomfield    MI     Oakland   \n",
       "77    2d1201d5070a453860cf425de074ccb8           Cynthiana    IN       Posey   \n",
       "...                                ...                 ...   ...         ...   \n",
       "9742  eaa46570bf4ec55c7652c48c4982b0c3              Asbury    WV  Greenbrier   \n",
       "9862  f2a735c2db8d0c5c824c77dfd94e59fb          Pittsburgh    PA   Allegheny   \n",
       "9906  8ae790d973df20db7ac404159105c640            Honolulu    HI    Honolulu   \n",
       "9910  0d25d0100e92724a5ca84b47578761d8  Saint Clair Shores    MI      Macomb   \n",
       "9955  a746aa6e32f770c8dde8dc6eb24aadcc              Blanch    NC     Caswell   \n",
       "\n",
       "        Zip       Lat  ...  Additional_charges  Item1 Item2 Item3 Item4  \\\n",
       "30    67355  37.03392  ...        13907.967640      3     2     5     3   \n",
       "36     2468  42.32731  ...         4204.826360      4     4     5     5   \n",
       "58    32444  30.23936  ...        14397.946210      3     3     3     4   \n",
       "63    48322  42.54215  ...        11058.380500      4     5     4     5   \n",
       "77    47612  38.19303  ...         3968.532959      4     4     4     3   \n",
       "...     ...       ...  ...                 ...    ...   ...   ...   ...   \n",
       "9742  24916  37.83127  ...         9609.241091      3     3     2     3   \n",
       "9862  15260  40.44329  ...         9175.406982      5     4     3     4   \n",
       "9906  96814  21.29398  ...         8171.843436      3     3     5     4   \n",
       "9910  48081  42.49507  ...        22281.115980      4     6     3     6   \n",
       "9955  27212  36.46059  ...         9189.087049      4     4     4     2   \n",
       "\n",
       "      Item5  Item6 Item7 Item8   Incomez  \n",
       "30        3      3     3     5  5.120796  \n",
       "36        1      3     5     5  3.344178  \n",
       "58        4      5     4     4  3.757416  \n",
       "63        3      4     4     2  3.593346  \n",
       "77        5      4     2     4  3.850233  \n",
       "...     ...    ...   ...   ...       ...  \n",
       "9742      4      4     4     4  4.583966  \n",
       "9862      3      4     5     4  3.290696  \n",
       "9906      3      4     4     4  3.979006  \n",
       "9910      2      5     6     4  3.226905  \n",
       "9955      5      3     3     2  3.331227  \n",
       "\n",
       "[180 rows x 54 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medical_outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# At this point, due to amount of outliers there must be a convsersation to determine if they must be\n",
    "# dropped of if the outliers are permissable in the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#export file to csv\n",
    "medical_data.to_csv('medical_data_clean.csv', index = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create dataframe to perform PCA\n",
    "\n",
    "md_pca = medical_data[['Income', 'Age', 'Children','Population','VitD_levels', \n",
    "                                 'Doc_visits','Full_meals_eaten','VitD_supp','Initial_days',\n",
    "                                'TotalCharge','Additional_charges']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#normalize data \n",
    "\n",
    "md_normal = (md_pca - md_pca.mean())/md_pca.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create pca\n",
    "pca = PCA(n_components=md_pca.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca.fit(md_normal)\n",
    "medical_pca = pd.DataFrame(pca.transform(md_normal),\n",
    "columns=['PC1','PC2','PC3','PC4','PC5','PC6','PC7','PC8','PC9', 'PC10','PC11'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3OGZWIHK5VTUTyL6X8VZStlPJ9yI3AKcDk4FzJE3uUG09cBlwTRfaXg3MiYgaYE6ybbvpi8fvy8CyEr73wNJ8h2JmBSKXxKGIeGfS6ohoA0pyaDcVqI+I5RGxDbgTmJ5dISLWRcRcoOPLk3bWdjpwW7J+G3BmDrHYDgzZo4zPH7cvD7ywlgUNG/IdjpkVgFwSx3JJl0kqTT6XA7m87GgMkD3tXENSloudtR0ZEasBkuWIzg4g6SJJdZLqGhsbczxt/3TBseMZukcp17jXYWY5yCVxXAwcDawk8wv8SOCiHNqpk7LopKy722YqR9wUEbURUVtdXd2Vpv1OVUUpF390In9e2sjTK9bnOxwz6+VyeapqXUScHREjImJkRHw6ItblcOwGYFzW9lhgVY5x7aztWkmjAZJlLrHYLpz7kfFUV5VzzQNLyLozaWb2Prk8VVUt6WuSbpI0q/2Tw7HnAjWSJkgqA84G7s0xrp21vReYkazPAH6X4zFtJyrLirl02n48vWI9j730er7DMbNeLJcvuX8HPAb8CWjN9cAR0SLpUuB+oBiYFRHPS7o42X+jpFFAHTAIaJN0BTA5Ipo6a5sc+lvAXZIuBF4Fzso1Jtu5s6eO46Y/L+fcWU8zfGA5owaXM2pQJaMHVzBqcAWjBlW8uz64gj3KcvnnY2Z9jXZ1W0LSsxExpWfCSUdtbW3U1dXlO4yCUL9uM39YsJo1Tc2s2biF1RubWdPUzIa33z9r4KCKEkYPrnwnqYwa/N7EMnpQJYMqS5A6+8rKzHo7SfMiorZjeS5/Mv6XpDMiYnYKcVkvs9+IgVx+cs37yrdsa2VtU3OSSDIJZe3G5ncSywurm3h981Y6/h1SWVrM6MEVjMzqrby7nUk6wwaUUVTk5GJWKHJJHJcDX5O0lcx4CwEREYNSjcx6lcqyYsYPH8D44QN2WGd7axvrNm19t6eSfFY3ZZZPrVjP2qZmWtrem11Ki8WIqkxSGVJZyqDKUgZXljKoooRByfagilIGVZYk5ZmyqvISJxyzPNhl4oiIqp4IxApfaXERY4ZUMmZI5Q7rtLUFr7+1NZNQ2pNL07tJZk1TM0vWbqJpy3Y2bW15Xw8mmwRV5SVZiSZZVpZkrb8/4bSvV5QW+Taa2W7I6dvN5H1QNUBFe1lE/DmtoKzvKirK9C5GVFVw8Nid121rCzZtbaFpy3Y2btlOU/N2mrZktjPr7eXv1ln++maatrSwcct2tmzf+bMcpcV6J4lUlhVTVlJEWXERZSVFlJcUvWc7s95eR1llRZSVFL9n+52272v//n0lxZ692QrPLhOHpM+TuV01FngWOAp4Ajgx1cis3ysqyvxiH1xZ+p5BPbna1tLGpub3J5f2BNS+vnHLdpq3tbKttY2tLW1sam7hjZY2trW2sa0l+XRY7y4lRWJgRQkDy0uoqiilqqKEQR22qypKGZiUv7Nd/t71Yt+ysx6U63ccRwBPRsQ0SQcA30w3LLMPrqykiGEDyxk2sLxbjxsRO0wqWzsmmWR7e5KUOrZp3t7K5q0tbGpuYVPzdjY1t7BqQzObtm5Pylpobdv1gMwBZcVZiaaEgVlJqGOiqaoooaq8hPLSIkqKiigpFqXFRZQUJctiUVJURGmxKMkqd3KydrkkjuaIaJaEpPKIeFHSpNQjM+ulJFFeUkx5SXHq54oImrdnek6bOiSYzc0tNLWvb323fFNzpjfV8Obb79Rv3v7Be0kSlBZlEkjnyaaTxJOVmIqL9J6ykiJRXFSULJPtrPLSDtvvqZfEUJJdXtx5vfZzl5cUMX7YAD9Q0Q1ySRwNkoYAvwUelPQmub86xMw+AElUlhVTWVbc+ds8c7S9tY3NSVJp781sbWmjpbWN7a1BS1sbrW2RWW9tY3tbZtnSGmxvyyyzy9vbtLRGh/U2WtqSZVK+Zfu7+1vaj9sWtLbFu8vWtne228vS8PW/PpDPH7dvKsfuT3J5quoTyeo3JD0MDAbuSzUqM+tWpcVFDB1QxtABZfkOJScRHRLLO8skwbS2l7UlyWjX9X7y2ApufHQZnzlyHyrL0u8t9mU7TBySBiWv/tgzq3hhshxIZhImM7NuJyW3orrx9/uwgeWcdeMT3PHUK+51fEA7exbw58lyHpn3SXVcmpkVjCPG78nRE4fxH39eTvMuHtW2ndth4oiIjykzOuqjEbFvREzIXvZgjGZm3eLyk2po3LSVXzz9ar5DKWg7HX2UTBn7mx6KxcwsVUfuO4wjJ+zJjY8uc6/jA8hl2OqTko5IPRIzsx5w+ck1rG3ayi/nvrbrytapXBLHNOAJScskLZC0UNKCtAMzM0vDR/YdxtTxezLzkWVsbXGvY3fkkjhOByaSecXI3wAfS5ZmZgVHEpedVMOapmbuqmvIdzgFKZc5x1+JiFeALUBkfczMCtIx+w3j8H2GMvPhevc6dkMuc45/XNJLwArgUeBl4I8px2VmlhpJXH5SDas2NvPree51dFUut6r+hcwbcZdGxATgJOAvqUZlZpay42qGM2XcEH788DK2tXTfG4/7g1wSx/aIeAMoklQUEQ8DU3I5uKTTJC2RVC/p6k72S9L1yf4Fkg5LyidJejbr0yTpimTfNyStzNp3Rs5Xa2aWkMTlJ9ewcsMW7pnvXkdX5PKSww2SBgKPAXdIWge07KqRpGLgBuAUoAGYK+neiHghq9rpZCaIqgGOBGYCR0bEEpLklBxnJe8dT/L9iLgmh9jNzHbohP2rOWTsYH70cD1/e/hYSj2xVk5y+Sn9GRhCZl6O+4Bl5PZU1VSgPiKWR8Q24E5geoc604HbI+NJYIik0R3qnAQsS76gNzPrNu1PWDW8uYXfPLMy3+EUjFwSh4D7gUfIvNzwl8mtq10ZA2SPsGlIyrpa52zgFx3KLk1ubc1KprU1M9stJx4wgg+PGcwND9fT0o2zO/ZluTyO+82IOAi4BNgLeFTSn3I4dmezpXR8jHendSSVAR8HfpW1fyaZcSVTgNXAtZ2eXLpIUp2kusbGxhzCNbP+qL3X8cobb/PbZz3VUC66ckNvHbAGeANymlOmAd4zVfRY3j8B1K7qnA7Mj4i17QURsTYiWiOiDbiZzC2x94mImyKiNiJqq6urcwjXzPqrkw8cweTRg/jRQy+515GDXMZxfEnSI8AcYDjwhYg4OIdjzwVqJE1Ieg5nA/d2qHMvcG7ydNVRwMaIWJ21/xw63Kbq8B3IJ4BFOcRiZrZD7b2Ol994m98vcK9jV3J5qmof4IqIeLYrB46IFkmXkvl+pBiYFRHPS7o42X8jMBs4A6gH3gbOb28vaQ8yT2R9scOhvyNpCplbWi93st/MrMtOnTySA0ZV8cOH6vn4IWMo9tzkO6TMm9P7ttra2qir89xTZrZzf1y4mi/dMZ/rzp7C9Ckdn9PpfyTNi4jajuV+aNnMLPFXB41i0shMr6O1re//Ub27nDjMzBJFReIrJ+1H/brNzF64etcN+iknDjOzLGd8aDQ1Iwbyw4deos29jk45cZiZZSkqEpeeuB9L127mvufX5DucXsmJw8ysg48dvBcTqwdw/Rz3OjrjxGFm1kFxkfjKiTW8uGYTD7zgXkdHThxmZp342MGjmTB8ANfNqXevowMnDjOzTpQUF3HptP1YvLqJPy1eu+sG/YgTh5nZDkyfshf7DNuD6+a8RH8YLJ0rJw4zsx0oKS7ikmn78fyqJuYsXpfvcHoNJw4zs534xKFjGLdnJdc/5F5HOycOM7OdKE2+61jQsJFHlnhuH3DiMDPbpf9x2FjGDKnkB/6uA3DiMDPbpdLku47nXtvAo0vd63DiMDPLwScPz/Q6/ISVE4eZWU7KSor40gkTeebVDTxe/3q+w8krJw4zsxydVTuW0YMruO5P/bvX4cRhZpaj8pJivnTCROpeeZMnlr2R73DyxonDzKwLPlU7jpGDyvnBnJfyHUreOHGYmXVBRWkxF390Ik+vWN9vex2pJg5Jp0laIqle0tWd7Jek65P9CyQdlrXvZUkLJT0rqS6rfE9JD0p6KVkOTfMazMw6Omfq3lRXlXN9P+11pJY4JBUDNwCnA5OBcyRN7lDtdKAm+VwEzOywf1pETImI2qyyq4E5EVEDzEm2zcx6THuv44nlb/D0ivX5DqfHpdnjmArUR8TyiNgG3AlM71BnOnB7ZDwJDJE0ehfHnQ7clqzfBpzZjTGbmeXk01P3ZvjAcq6bszTfofS4NBPHGOC1rO2GpCzXOgE8IGmepIuy6oyMiNUAyXJEZyeXdJGkOkl1jY0e6Wlm3auyrJgvHr8vf6l/g7qX+1evI83EoU7KOj74vLM6x0TEYWRuZ10i6fiunDwiboqI2oiora6u7kpTM7OcfOaovRk2oIzr+tl3HWkmjgZgXNb2WGBVrnUion25DvgNmVtfAGvbb2clS78k38zyYo+yEi46fl8ee+l15r/6Zr7D6TFpJo65QI2kCZLKgLOBezvUuRc4N3m66ihgY0SsljRAUhWApAHAqcCirDYzkvUZwO9SvAYzs5367FH7sOeAMq77U//pdaSWOCKiBbgUuB9YDNwVEc9LuljSxUm12cByoB64GfhyUj4SeFzSc8DTwB8i4r5k37eAUyS9BJySbJuZ5cWA8hI+f9wEHl3ayLOvbch3OD1C/eF9K7W1tVFXV7frimZmu2Hz1haO/fZDHLb3UGadd0S+w+k2kuZ1GA4BeOS4mdkHNrC8hM8fO4GHXlzHgoYN+Q4ndU4cZmbdYMbR4xlcWdovRpM7cZiZdYOqilIuPHYCf1q8jkUrN+Y7nFQ5cZiZdZMZR4+nqqKkz/c6nDjMzLrJ4MpSLjhmAg+8sJYXVjXlO5zUOHGYmXWjC46ZQFV5CT98qO/2Opw4zMy60eA9SjnvmPH8cdEaXlzTN3sdThxmZt3swmMnMLC8hB/Oqc93KKlw4jAz62ZD9ihjxtH7MHvRapau3ZTvcLqdE4eZWQouPHZfKkuL+eFDfa/X4cRhZpaCPQeUce5HxvNfC1ZRv65v9TqcOMzMUvKF4yZQUVLM9x5cSl96L6ATh5lZSoYNLOdLJ0xk9sI1/PiRZfkOp9uU5DsAM7O+7NJp+7G8cTPfvX8J1VXlfKp23K4b9XJOHGZmKSoqEt/55CG88dY2/vGehQwbUMZJB47Md1gfiG9VmZmlrKykiJmfPZzJowdxyc/nF/w0s04cZmY9YGB5CbPOO4KRgyq44Na51K/bnO+QdpsTh5lZD6muKuf2C6ZSUiRmzHqatU3N+Q5ptzhxmJn1oH2GDeCW86ay4e1tzJj1NBu3bM93SF3mxGFm1sM+PHYwN37ucOrXbeai2+to3t6a75C6JNXEIek0SUsk1Uu6upP9knR9sn+BpMOS8nGSHpa0WNLzki7PavMNSSslPZt8zkjzGszM0nBcTTXXnHUIT61Yz5V3PUtrW+EMEEztcVxJxcANwClAAzBX0r0R8UJWtdOBmuRzJDAzWbYAX42I+ZKqgHmSHsxq+/2IuCat2M3MesKZh47h9c1b+X9/WEz1wOf5xscPQlK+w9qlNMdxTAXqI2I5gKQ7gelAduKYDtwembH4T0oaIml0RKwGVgNExCZJi4ExHdqamRW8zx+3L2ubmrn5sRWMGFTBJdP2y3dIu5TmraoxwGtZ2w1JWZfqSBoPHAo8lVV8aXJra5akoZ2dXNJFkuok1TU2Nu7mJZiZpe8fTz+QM6fsxXfvX8Kv6l7bdYM8SzNxdNbf6ngTb6d1JA0E7gauiIj2qbRmAhOBKWR6Jdd2dvKIuCkiaiOitrq6uouhm5n1nPbR5cfVDOfqexby0Itr8x3STqWZOBqA7JeyjAVW5VpHUimZpHFHRNzTXiEi1kZEa0S0ATeTuSVmZlbQ2keXHzi6ii/fMZ9nevHo8jQTx1ygRtIESWXA2cC9HercC5ybPF11FLAxIlYr8+3QT4HFEfG97AaSRmdtfgJYlN4lmJn1nIHlJdxy3lRGVGVGly9r7J2jy1NLHBHRAlwK3A8sBu6KiOclXSzp4qTabGA5UE+m9/DlpPwY4HPAiZ08dvsdSQslLQCmAX+X1jWYmfW09tHlxUXi3J/2ztHl6kuTi+xIbW1t1NXV5TsMM7OcLWzYyP+86Qn2GTaAX37xKAZVlPZ4DJLmRURtx3KPHDcz64U+PHYwN372cF5au4mLbq9ja0vvGV3uxGFm1ksdv39mdPmTy9dz5S+fo62XjC73RE5mZr3YmYeOoXHTVv519mKqq8r557+ZnPfR5U4cZma93BeOz4wu/8njKxgxqJwvn5Df0eVOHGZmBeBrZxxI4+atfOe+JVQPLOesPM5d7sRhZlYAiorEdz95CG9s3sbV9yxk+MByph0wIj+x5OWsZmbWZWUlRdz4ufyPLnfiMDMrIO2jy6uryrng1rksz8PocicOM7MC0z66vEji3FlPs66HR5c7cZiZFaDxwwdwy/lHsP6tbcy4ZS5NzT03d7kTh5lZgTp47JB3Rpd/8fZ5PTa63InDzKyAHb9/Nd8962CeWP4GV97VM6PL/TiumVmB+8ShY2nctJV/m/0i1QPTH13uxGFm1gd84bh9Wdu0lZ8+voKRgyr40gkTUzuXE4eZWR8giX8640AaN23l2/e9SHVVOZ88fGwq53LiMDPrI4qKxDVnHcL6t7bxD3cvYNjAMqZN6v7R5f5y3MysD8nMXX4YB4yq4ss/m8+zr23o9nM4cZiZ9TFVFaXcev5UascPZXBl988c6FtVZmZ9UHVVOf954ZGpHDvVHoek0yQtkVQv6epO9kvS9cn+BZIO21VbSXtKelDSS8lyaJrXYGZm75Va4pBUDNwAnA5MBs6RNLlDtdOBmuRzETAzh7ZXA3MiogaYk2ybmVkPSbPHMRWoj4jlEbENuBOY3qHOdOD2yHgSGCJp9C7aTgduS9ZvA85M8RrMzKyDNBPHGOC1rO2GpCyXOjtrOzIiVgMky06fNZN0kaQ6SXWNjY27fRFmZvZeaSaOzsa7d3yJyo7q5NJ2pyLipoiojYja6urqrjQ1M7OdSDNxNADZk+KOBVblWGdnbdcmt7NIluu6MWYzM9uFNBPHXKBG0gRJZcDZwL0d6twLnJs8XXUUsDG5/bSztvcCM5L1GcDvUrwGMzPrILVxHBHRIulS4H6gGJgVEc9LujjZfyMwGzgDqAfeBs7fWdvk0N8C7pJ0IfAqcFZa12BmZu+niPTf3Z5vkhqBV3az+XDg9W4MpxD4mvsHX3P/8EGueZ+IeN+XxP0icXwQkuoiojbfcfQkX3P/4GvuH9K4Zr+ryszMusSJw8zMusSJY9duyncAeeBr7h98zf1Dt1+zv+MwM7MucY/DzMy6xInDzMy6xIljJ3Y1n0hfI2mcpIclLZb0vKTL8x1TT5BULOkZSf+V71h6gqQhkn4t6cXkv/VH8h1T2iT9XfJvepGkX0iqyHdM3U3SLEnrJC3KKktl/iInjh3IcT6RvqYF+GpEHAgcBVzSD64Z4HJgcb6D6EHXAfdFxAHAIfTxa5c0BrgMqI2ID5F5G8XZ+Y0qFbcCp3UoS2X+IieOHctlPpE+JSJWR8T8ZH0TmV8oHV+F36dIGgv8NfCTfMfSEyQNAo4HfgoQEdsiYkNeg+oZJUClpBJgD97/wtWCFxF/BtZ3KE5l/iInjh3LZT6RPkvSeOBQ4Kk8h5K2HwD/C2jLcxw9ZV+gEbgluT33E0kD8h1UmiJiJXANmXfbrSbzMtUH8htVj8lp/qKucuLYsQ88J0ihkjQQuBu4IiKa8h1PWiR9DFgXEfPyHUsPKgEOA2ZGxKHAW/Tx6ZeT+/rTgQnAXsAASZ/Nb1SFzYljx3KZT6TPkVRKJmncERH35DuelB0DfFzSy2RuRZ4o6Wf5DSl1DUBDRLT3JH9NJpH0ZScDKyKiMSK2A/cAR+c5pp6SyvxFThw7lst8In2KJJG59704Ir6X73jSFhH/GBFjI2I8mf++D0VEn/5LNCLWAK9JmpQUnQS8kMeQesKrwFGS9kj+jZ9EH38gIEsq8xelNh9HodvFnCB91THA54CFkp5Nyr4WEbPzF5Kl4CvAHckfRMtJ5sHpqyLiKUm/BuaTeXLwGfrgq0ck/QI4ARguqQH4Z1Kav8ivHDEzsy7xrSozM+sSJw4zM+sSJw4zM+sSJw4zM+sSJw4zM+sSJw6zXkTSFZL26OFzfkPSVT15TitsThxmvcsVZF7CVxCU4d8j/Yz/g1tBk3SupAWSnpP0n0nZPpLmJOVzJO2dlN8qaWYy58hySR9N5jBYLOnWrGNulnStpPlJ++qkfIqkJ5Pj/qZ9bgNJj0j6tqSnJS2VdFxSXizpu5LmJm2+mJSfkLRpnxPjjuQX8GVk3qX0sKSHO7nWlyV9M4lroaQDkvL39BiSOSfGJ58XkxcZLkrOc7KkvyTzM0zNOvwhkh5Kyr+Qday/z4r/m0nZ+ORn9mMyg+qyX81j/YAThxUsSQcB/wScGBGHkJlXA+BHwO0RcTBwB3B9VrOhwInA3wG/B74PHAR8WNKUpM4AYH5EHAY8SmYELsDtwD8kx12YVQ5QEhFTyfQY2ssvJPMm1iOAI4AvSJqQ7Ds0qTuZzBtrj4mI68m8D21aREzbwWW/nsQ1E8jl9tJ+ZObfOBg4APg0cGzS9mtZ9Q4m83r5jwD/R9Jekk4FashMMTAFOFzS8Un9SWR+xodGxCs5xGF9iBOHFbITgV9HxOsAEdE+F8FHgJ8n6/9J5hdlu99H5nUJC4G1EbEwItqA54HxSZ024JfJ+s+AYyUNBoZExKNJ+W1k5rVo1/5CyHlZxzkVODd5fctTwDAyv4gBno6IhuTcz2a12ZXOzrMzKzpc45ys689u/7uI2JL8LB8mkyxOTT7PkOlZHJAV/ysR8WSOMVsf43dVWSETub3qPrvO1mTZlrXevr2j/x9yOUf7sVqzjiPgKxFxf3ZFSSd0OHd2m905Twvv/SOwopP68N5r7ni9Ha8xyMT/7xHxH9k7krla3soxXuuD3OOwQjYH+JSkYZCZXzkp/2/enRr0M8DjXTxuEfDJZP3TwOMRsRF4s/37CzIvg3y0s8ZZ7ge+lLyqHkn75zBp0iagqovxvkzyanRJh5GZd6KrpkuqSH6WJ5B5O/T9wAXKzM+CpDGSumUiICts7nFYwYqI5yX9K/CopFYyt1TOIzO/9CxJf09mtruuvv31LeAgSfOAjcD/TMpnADcmj8vm8lbZn5C5HTQ/eZ13I7ueuvMm4I+SVu/ke46O7ubdW2JzgaU5tsv2NPAHYG/gXyJiFbBK0oHAE5nw2Qx8lkxvx/oxvx3XrANJmyNiYL7jMOutfKvKzMy6xD0OMzPrEvc4zMysS5w4zMysS5w4zMysS5w4zMysS5w4zMysS/4/cAp23qCj//cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Scree Plot\n",
    "\n",
    "plt.plot(pca.explained_variance_ratio_)\n",
    "plt.xlabel('component number')\n",
    "plt.ylabel('variance')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Check eigenvalues with plot\n",
    "cov_matrix = np.dot(md_normal.T, md_normal) / md_pca.shape[0]\n",
    "eigenvalues = [np.dot(eigenvector.T, np.dot(cov_matrix, eigenvector)) for eigenvector in pca.components_]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": [
    "#plot PCA with eigenvalues\n",
    "plt.plot(eigenvalues)\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('eigenvalues')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>PC4</th>\n",
       "      <th>PC5</th>\n",
       "      <th>PC6</th>\n",
       "      <th>PC7</th>\n",
       "      <th>PC8</th>\n",
       "      <th>PC9</th>\n",
       "      <th>PC10</th>\n",
       "      <th>PC11</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Income</th>\n",
       "      <td>-0.006752</td>\n",
       "      <td>-0.005251</td>\n",
       "      <td>0.153074</td>\n",
       "      <td>0.616374</td>\n",
       "      <td>0.311451</td>\n",
       "      <td>-0.335112</td>\n",
       "      <td>-0.300179</td>\n",
       "      <td>0.544926</td>\n",
       "      <td>-0.013092</td>\n",
       "      <td>-0.007175</td>\n",
       "      <td>-0.001110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>0.082864</td>\n",
       "      <td>0.700979</td>\n",
       "      <td>0.022122</td>\n",
       "      <td>-0.024594</td>\n",
       "      <td>-0.014242</td>\n",
       "      <td>0.004057</td>\n",
       "      <td>-0.015265</td>\n",
       "      <td>0.021947</td>\n",
       "      <td>-0.013605</td>\n",
       "      <td>-0.706598</td>\n",
       "      <td>-0.016378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Children</th>\n",
       "      <td>0.004317</td>\n",
       "      <td>0.011313</td>\n",
       "      <td>0.143266</td>\n",
       "      <td>-0.055997</td>\n",
       "      <td>0.886958</td>\n",
       "      <td>0.143675</td>\n",
       "      <td>0.277871</td>\n",
       "      <td>-0.246596</td>\n",
       "      <td>-0.175343</td>\n",
       "      <td>-0.009117</td>\n",
       "      <td>-0.002495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Population</th>\n",
       "      <td>0.020665</td>\n",
       "      <td>-0.027059</td>\n",
       "      <td>0.503288</td>\n",
       "      <td>0.011591</td>\n",
       "      <td>-0.021264</td>\n",
       "      <td>0.545865</td>\n",
       "      <td>0.154957</td>\n",
       "      <td>0.292515</td>\n",
       "      <td>0.580765</td>\n",
       "      <td>-0.010910</td>\n",
       "      <td>-0.001653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VitD_levels</th>\n",
       "      <td>0.540348</td>\n",
       "      <td>-0.052702</td>\n",
       "      <td>-0.291242</td>\n",
       "      <td>0.267669</td>\n",
       "      <td>-0.069801</td>\n",
       "      <td>0.088197</td>\n",
       "      <td>0.467136</td>\n",
       "      <td>0.136248</td>\n",
       "      <td>-0.052233</td>\n",
       "      <td>-0.022902</td>\n",
       "      <td>0.544146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Doc_visits</th>\n",
       "      <td>-0.005261</td>\n",
       "      <td>0.012735</td>\n",
       "      <td>0.175200</td>\n",
       "      <td>0.626217</td>\n",
       "      <td>-0.179293</td>\n",
       "      <td>0.406584</td>\n",
       "      <td>-0.216578</td>\n",
       "      <td>-0.529823</td>\n",
       "      <td>-0.227726</td>\n",
       "      <td>-0.005734</td>\n",
       "      <td>-0.000223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Full_meals_eaten</th>\n",
       "      <td>-0.009232</td>\n",
       "      <td>0.036620</td>\n",
       "      <td>-0.552477</td>\n",
       "      <td>0.164779</td>\n",
       "      <td>0.232029</td>\n",
       "      <td>-0.009004</td>\n",
       "      <td>-0.227679</td>\n",
       "      <td>-0.277955</td>\n",
       "      <td>0.695041</td>\n",
       "      <td>-0.009578</td>\n",
       "      <td>-0.001451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VitD_supp</th>\n",
       "      <td>0.033956</td>\n",
       "      <td>0.010585</td>\n",
       "      <td>0.424363</td>\n",
       "      <td>0.159845</td>\n",
       "      <td>-0.126951</td>\n",
       "      <td>-0.621369</td>\n",
       "      <td>0.382618</td>\n",
       "      <td>-0.391081</td>\n",
       "      <td>0.302515</td>\n",
       "      <td>-0.005007</td>\n",
       "      <td>-0.001481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Initial_days</th>\n",
       "      <td>0.446482</td>\n",
       "      <td>-0.073483</td>\n",
       "      <td>0.316693</td>\n",
       "      <td>-0.315722</td>\n",
       "      <td>0.093118</td>\n",
       "      <td>-0.098170</td>\n",
       "      <td>-0.587201</td>\n",
       "      <td>-0.162090</td>\n",
       "      <td>0.047716</td>\n",
       "      <td>-0.005801</td>\n",
       "      <td>0.451201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalCharge</th>\n",
       "      <td>0.702192</td>\n",
       "      <td>-0.078146</td>\n",
       "      <td>-0.023420</td>\n",
       "      <td>0.003262</td>\n",
       "      <td>0.002286</td>\n",
       "      <td>0.005498</td>\n",
       "      <td>-0.016139</td>\n",
       "      <td>0.002566</td>\n",
       "      <td>-0.012083</td>\n",
       "      <td>0.021002</td>\n",
       "      <td>-0.706662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Additional_charges</th>\n",
       "      <td>0.083549</td>\n",
       "      <td>0.701314</td>\n",
       "      <td>0.024091</td>\n",
       "      <td>-0.004444</td>\n",
       "      <td>-0.000739</td>\n",
       "      <td>0.011600</td>\n",
       "      <td>-0.003667</td>\n",
       "      <td>0.020986</td>\n",
       "      <td>0.001742</td>\n",
       "      <td>0.706623</td>\n",
       "      <td>0.025865</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         PC1       PC2       PC3       PC4       PC5  \\\n",
       "Income             -0.006752 -0.005251  0.153074  0.616374  0.311451   \n",
       "Age                 0.082864  0.700979  0.022122 -0.024594 -0.014242   \n",
       "Children            0.004317  0.011313  0.143266 -0.055997  0.886958   \n",
       "Population          0.020665 -0.027059  0.503288  0.011591 -0.021264   \n",
       "VitD_levels         0.540348 -0.052702 -0.291242  0.267669 -0.069801   \n",
       "Doc_visits         -0.005261  0.012735  0.175200  0.626217 -0.179293   \n",
       "Full_meals_eaten   -0.009232  0.036620 -0.552477  0.164779  0.232029   \n",
       "VitD_supp           0.033956  0.010585  0.424363  0.159845 -0.126951   \n",
       "Initial_days        0.446482 -0.073483  0.316693 -0.315722  0.093118   \n",
       "TotalCharge         0.702192 -0.078146 -0.023420  0.003262  0.002286   \n",
       "Additional_charges  0.083549  0.701314  0.024091 -0.004444 -0.000739   \n",
       "\n",
       "                         PC6       PC7       PC8       PC9      PC10      PC11  \n",
       "Income             -0.335112 -0.300179  0.544926 -0.013092 -0.007175 -0.001110  \n",
       "Age                 0.004057 -0.015265  0.021947 -0.013605 -0.706598 -0.016378  \n",
       "Children            0.143675  0.277871 -0.246596 -0.175343 -0.009117 -0.002495  \n",
       "Population          0.545865  0.154957  0.292515  0.580765 -0.010910 -0.001653  \n",
       "VitD_levels         0.088197  0.467136  0.136248 -0.052233 -0.022902  0.544146  \n",
       "Doc_visits          0.406584 -0.216578 -0.529823 -0.227726 -0.005734 -0.000223  \n",
       "Full_meals_eaten   -0.009004 -0.227679 -0.277955  0.695041 -0.009578 -0.001451  \n",
       "VitD_supp          -0.621369  0.382618 -0.391081  0.302515 -0.005007 -0.001481  \n",
       "Initial_days       -0.098170 -0.587201 -0.162090  0.047716 -0.005801  0.451201  \n",
       "TotalCharge         0.005498 -0.016139  0.002566 -0.012083  0.021002 -0.706662  \n",
       "Additional_charges  0.011600 -0.003667  0.020986  0.001742  0.706623  0.025865  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#output loadings to components\n",
    "loadings = pd.DataFrame(pca.components_.T,\n",
    "columns = ['PC1','PC2','PC3','PC4','PC5','PC6','PC7','PC8','PC9', 'PC10','PC11'],\n",
    "index = md_pca.columns)\n",
    "loadings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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