practice_analysis_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "import statsmodels.api as sm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_excel('tomato_data_new.xlsx')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 8))\n",
    "plt.scatter(\n",
    "    data['fructose'],\n",
    "    data['OVERALL LIKING'],\n",
    "    c='black'\n",
    ")\n",
    "plt.xlabel(\"Amount of glucose\")\n",
    "plt.ylabel(\"Overall liking\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The linear model is: Y = 1.0533 + 0.89985X\n"
     ]
    }
   ],
   "source": [
    "X = data['fructose'].values.reshape(-1,1)\n",
    "y = data['OVERALL LIKING'].values.reshape(-1,1)\n",
    "reg = LinearRegression()\n",
    "reg.fit(X, y)\n",
    "print(\"The linear model is: Y = {:.5} + {:.5}X\".format(reg.intercept_[0], reg.coef_[0][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = reg.predict(X)\n",
    "plt.figure(figsize=(16, 8))\n",
    "plt.scatter(\n",
    "    data['fructose'],\n",
    "    data['OVERALL LIKING'],\n",
    "    c='black'\n",
    ")\n",
    "plt.plot(\n",
    "    data['fructose'],\n",
    "    predictions,\n",
    "    c='blue',\n",
    "    linewidth=2\n",
    ")\n",
    "plt.xlabel(\"fructose\")\n",
    "plt.ylabel(\"overall liking\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         OVERALL LIKING   R-squared:                       0.372\n",
      "Model:                            OLS   Adj. R-squared:                  0.365\n",
      "Method:                 Least Squares   F-statistic:                     51.58\n",
      "Date:                Thu, 03 Dec 2020   Prob (F-statistic):           2.20e-10\n",
      "Time:                        19:16:50   Log-Likelihood:                -255.10\n",
      "No. Observations:                  89   AIC:                             514.2\n",
      "Df Residuals:                      87   BIC:                             519.2\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.0533      1.859      0.567      0.572      -2.641       4.747\n",
      "fructose       0.8999      0.125      7.182      0.000       0.651       1.149\n",
      "==============================================================================\n",
      "Omnibus:                        0.424   Durbin-Watson:                   1.627\n",
      "Prob(Omnibus):                  0.809   Jarque-Bera (JB):                0.582\n",
      "Skew:                          -0.067   Prob(JB):                        0.747\n",
      "Kurtosis:                       2.627   Cond. No.                         60.7\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "X = data['fructose']\n",
    "y = data['OVERALL LIKING']\n",
    "X2 = sm.add_constant(X)\n",
    "est = sm.OLS(y, X2)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_pvals(column):\n",
    "    X = data[column]\n",
    "    y = data['OVERALL LIKING']\n",
    "    X2 = sm.add_constant(X)\n",
    "    est = sm.OLS(y, X2)\n",
    "    est2 = est.fit()\n",
    "    return est2.pvalues[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "compounds = data.columns[12:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "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>Compound</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>citric</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>malic acid</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>glucose</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fructose</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>glutamic acid</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>trans,trans-2,4-decadienal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>trans-2-heptenal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>trans-2-hexenal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>trans-2-pentenal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>trans-3-hexen-1-ol</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>69 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                      Compound\n",
       "0                       citric\n",
       "1                   malic acid\n",
       "2                      glucose\n",
       "3                     fructose\n",
       "4                glutamic acid\n",
       "..                         ...\n",
       "64  trans,trans-2,4-decadienal\n",
       "65            trans-2-heptenal\n",
       "66             trans-2-hexenal\n",
       "67            trans-2-pentenal\n",
       "68          trans-3-hexen-1-ol\n",
       "\n",
       "[69 rows x 1 columns]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_table = pd.DataFrame(compounds)\n",
    "p_table.columns = ['Compound']\n",
    "p_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_table['p_value'] = p_table['Compound'].apply(lambda x: find_pvals(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "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>Compound</th>\n",
       "      <th>p_value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fructose</td>\n",
       "      <td>2.204080e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>glucose</td>\n",
       "      <td>1.862785e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>sugar:acid</td>\n",
       "      <td>2.433092e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>4-carene</td>\n",
       "      <td>1.970898e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>glutamic acid</td>\n",
       "      <td>3.180658e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>benzaldehyde</td>\n",
       "      <td>4.746904e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>prenyl acetate</td>\n",
       "      <td>5.825625e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>phenylacetaldehyde</td>\n",
       "      <td>6.735268e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1-penten-3-one</td>\n",
       "      <td>9.139407e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>trans-2-pentenal</td>\n",
       "      <td>1.291881e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>hexyl acetate</td>\n",
       "      <td>1.684446e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>b-cyclocitral</td>\n",
       "      <td>1.808885e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>malic acid</td>\n",
       "      <td>1.868390e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>3-pentanone</td>\n",
       "      <td>1.955663e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>citric</td>\n",
       "      <td>4.176604e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>guaiacol</td>\n",
       "      <td>5.627783e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>benzyl cyanide</td>\n",
       "      <td>6.151207e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>citric:malic</td>\n",
       "      <td>6.798143e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>butyl acetate</td>\n",
       "      <td>7.136595e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2-ethylfuran</td>\n",
       "      <td>1.025498e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>b-damascenone</td>\n",
       "      <td>1.236224e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1-nitro-2-phenylethane</td>\n",
       "      <td>1.383554e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>methylsalicylate</td>\n",
       "      <td>1.500880e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>isobutyl acetate</td>\n",
       "      <td>1.716354e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>propyl acetate</td>\n",
       "      <td>1.863644e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2-methylbutyraldehyde</td>\n",
       "      <td>1.977535e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>benzothiazole</td>\n",
       "      <td>2.119469e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>cis-2-penten-1-ol</td>\n",
       "      <td>2.299936e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>benzyl alcohol</td>\n",
       "      <td>2.391749e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>3-methyl-2-butenal</td>\n",
       "      <td>2.608436e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2-methyl-2-butenal</td>\n",
       "      <td>2.763941e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>salicylaldehyde</td>\n",
       "      <td>2.809916e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>3-methyl-1-pentanol</td>\n",
       "      <td>3.198029e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2-phenyl ethanol</td>\n",
       "      <td>3.314932e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>6-methyl-5-hepten-2-one</td>\n",
       "      <td>3.374041e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>isopentyl acetate</td>\n",
       "      <td>3.561274e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>p-anisaldehyde</td>\n",
       "      <td>3.765282e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2-methylbutyl acetate</td>\n",
       "      <td>3.773462e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>cis-3-hexenyl acetate</td>\n",
       "      <td>4.174814e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>trans-2-heptenal</td>\n",
       "      <td>4.253217e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2-isobutylthiazole</td>\n",
       "      <td>4.293577e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>b-ionone</td>\n",
       "      <td>4.425644e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>nonyl aldehyde</td>\n",
       "      <td>4.714869e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>trans-3-hexen-1-ol</td>\n",
       "      <td>4.773268e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>eugenol</td>\n",
       "      <td>4.831898e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>trans-2-hexenal</td>\n",
       "      <td>4.945679e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>cis-3-hexen-1-ol</td>\n",
       "      <td>5.425692e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1-pentanol</td>\n",
       "      <td>5.542878e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>6-methyl-5-hepten-2-ol</td>\n",
       "      <td>5.848951e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>cis-3-hexenal</td>\n",
       "      <td>5.950461e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>isovaleric acid</td>\n",
       "      <td>6.226168e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1-octen-3-one</td>\n",
       "      <td>6.331345e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>heptaldehyde</td>\n",
       "      <td>7.151408e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>hexyl alcohol</td>\n",
       "      <td>7.173440e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2,5-dimethyl-4-hydroxy-3(2H)-furanone</td>\n",
       "      <td>7.457578e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>methional</td>\n",
       "      <td>7.498659e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>3-methyl-1-butanol</td>\n",
       "      <td>7.664034e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>isovaleronitrile</td>\n",
       "      <td>7.752500e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1-penten-3-ol</td>\n",
       "      <td>7.941330e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>cis-4-decenal</td>\n",
       "      <td>8.092179e-01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 Compound       p_value\n",
       "3                                fructose  2.204080e-10\n",
       "2                                 glucose  1.862785e-09\n",
       "6                              sugar:acid  2.433092e-05\n",
       "26                               4-carene  1.970898e-04\n",
       "4                           glutamic acid  3.180658e-04\n",
       "31                           benzaldehyde  4.746904e-04\n",
       "61                         prenyl acetate  5.825625e-03\n",
       "60                     phenylacetaldehyde  6.735268e-03\n",
       "12                         1-penten-3-one  9.139407e-03\n",
       "67                       trans-2-pentenal  1.291881e-02\n",
       "48                          hexyl acetate  1.684446e-02\n",
       "29                          b-cyclocitral  1.808885e-02\n",
       "1                              malic acid  1.868390e-02\n",
       "25                            3-pentanone  1.955663e-02\n",
       "0                                  citric  4.176604e-02\n",
       "45                               guaiacol  5.627783e-02\n",
       "34                         benzyl cyanide  6.151207e-02\n",
       "5                            citric:malic  6.798143e-02\n",
       "36                          butyl acetate  7.136595e-02\n",
       "15                           2-ethylfuran  1.025498e-01\n",
       "30                          b-damascenone  1.236224e-01\n",
       "7                  1-nitro-2-phenylethane  1.383554e-01\n",
       "56                       methylsalicylate  1.500880e-01\n",
       "50                       isobutyl acetate  1.716354e-01\n",
       "62                         propyl acetate  1.863644e-01\n",
       "20                  2-methylbutyraldehyde  1.977535e-01\n",
       "32                          benzothiazole  2.119469e-01\n",
       "37                      cis-2-penten-1-ol  2.299936e-01\n",
       "33                         benzyl alcohol  2.391749e-01\n",
       "24                     3-methyl-2-butenal  2.608436e-01\n",
       "18                     2-methyl-2-butenal  2.763941e-01\n",
       "63                        salicylaldehyde  2.809916e-01\n",
       "23                    3-methyl-1-pentanol  3.198029e-01\n",
       "21                       2-phenyl ethanol  3.314932e-01\n",
       "28                6-methyl-5-hepten-2-one  3.374041e-01\n",
       "51                      isopentyl acetate  3.561274e-01\n",
       "59                         p-anisaldehyde  3.765282e-01\n",
       "19                  2-methylbutyl acetate  3.773462e-01\n",
       "40                  cis-3-hexenyl acetate  4.174814e-01\n",
       "65                       trans-2-heptenal  4.253217e-01\n",
       "16                     2-isobutylthiazole  4.293577e-01\n",
       "35                               b-ionone  4.425644e-01\n",
       "58                         nonyl aldehyde  4.714869e-01\n",
       "68                     trans-3-hexen-1-ol  4.773268e-01\n",
       "42                                eugenol  4.831898e-01\n",
       "66                        trans-2-hexenal  4.945679e-01\n",
       "38                       cis-3-hexen-1-ol  5.425692e-01\n",
       "10                             1-pentanol  5.542878e-01\n",
       "27                 6-methyl-5-hepten-2-ol  5.848951e-01\n",
       "39                          cis-3-hexenal  5.950461e-01\n",
       "53                        isovaleric acid  6.226168e-01\n",
       "9                           1-octen-3-one  6.331345e-01\n",
       "46                           heptaldehyde  7.151408e-01\n",
       "49                          hexyl alcohol  7.173440e-01\n",
       "13  2,5-dimethyl-4-hydroxy-3(2H)-furanone  7.457578e-01\n",
       "55                              methional  7.498659e-01\n",
       "22                     3-methyl-1-butanol  7.664034e-01\n",
       "54                       isovaleronitrile  7.752500e-01\n",
       "11                          1-penten-3-ol  7.941330e-01\n",
       "41                          cis-4-decenal  8.092179e-01"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_table.sort_values(by = ['p_value']).head(60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "const       1.961040\n",
      "fructose    0.142079\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "SE = est2.HC3_se\n",
    "DF = "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([41., 37.,  8.,  0.,  0.,  0.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,\n",
       "         0.,  0.,  1.]),\n",
       " array([ 0.10204278,  1.2089423 ,  2.31584182,  3.42274134,  4.52964086,\n",
       "         5.63654038,  6.7434399 ,  7.85033942,  8.95723894, 10.06413846,\n",
       "        11.17103798, 12.2779375 , 13.38483702, 14.49173654, 15.59863606,\n",
       "        16.70553558, 17.8124351 ]),\n",
       " <a list of 16 Patch objects>)"
      ]
     },
     "execution_count": 82,
     "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": [
    "plt.hist(data['geranylacetone'], bins = 16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}