第6章『回帰分析』Pythonコード.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第6章『回帰分析』"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## p.101"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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     "end_time": "2019-04-14T17:29:26.133702Z",
     "start_time": "2019-04-14T17:29:25.326491Z"
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   },
   "outputs": [],
   "source": [
    "\"\"\" R自体に mtcarsというデータセットがビルトインされているが、Pythonではビルトインされていないので、今回はGithubに掲載されているmtcarsをインポートする。 \"\"\"\n",
    "\n",
    "import pandas as pd\n",
    "mtcars = pd.read_csv('https://gist.githubusercontent.com/ZeccaLehn/4e06d2575eb9589dbe8c365d61cb056c/raw/64f1660f38ef523b2a1a13be77b002b98665cdfe/mtcars.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:29:32.134619Z",
     "start_time": "2019-04-14T17:29:32.114802Z"
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   "outputs": [
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     "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>Unnamed: 0</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cyl</th>\n",
       "      <th>disp</th>\n",
       "      <th>hp</th>\n",
       "      <th>drat</th>\n",
       "      <th>wt</th>\n",
       "      <th>qsec</th>\n",
       "      <th>vs</th>\n",
       "      <th>am</th>\n",
       "      <th>gear</th>\n",
       "      <th>carb</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>160.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>22.8</td>\n",
       "      <td>4</td>\n",
       "      <td>108.0</td>\n",
       "      <td>93</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>21.4</td>\n",
       "      <td>6</td>\n",
       "      <td>258.0</td>\n",
       "      <td>110</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>18.7</td>\n",
       "      <td>8</td>\n",
       "      <td>360.0</td>\n",
       "      <td>175</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Unnamed: 0   mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  \\\n",
       "0          Mazda RX4  21.0    6  160.0  110  3.90  2.620  16.46   0   1     4   \n",
       "1      Mazda RX4 Wag  21.0    6  160.0  110  3.90  2.875  17.02   0   1     4   \n",
       "2         Datsun 710  22.8    4  108.0   93  3.85  2.320  18.61   1   1     4   \n",
       "3     Hornet 4 Drive  21.4    6  258.0  110  3.08  3.215  19.44   1   0     3   \n",
       "4  Hornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3   \n",
       "\n",
       "   carb  \n",
       "0     4  \n",
       "1     4  \n",
       "2     1  \n",
       "3     1  \n",
       "4     2  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mtcars.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## p.105"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    "ExecuteTime": {
     "end_time": "2019-04-14T17:30:10.481879Z",
     "start_time": "2019-04-14T17:30:10.462697Z"
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.718</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.709</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   76.51</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 25 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>9.38e-10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:38:34</td>     <th>  Log-Likelihood:    </th> <td> -82.105</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    32</td>      <th>  AIC:               </th> <td>   168.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    30</td>      <th>  BIC:               </th> <td>   171.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</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>   29.5999</td> <td>    1.230</td> <td>   24.070</td> <td> 0.000</td> <td>   27.088</td> <td>   32.111</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>disp</th>      <td>   -0.0412</td> <td>    0.005</td> <td>   -8.747</td> <td> 0.000</td> <td>   -0.051</td> <td>   -0.032</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.368</td> <th>  Durbin-Watson:     </th> <td>   1.250</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.186</td> <th>  Jarque-Bera (JB):  </th> <td>   3.049</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.719</td> <th>  Prob(JB):          </th> <td>   0.218</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.532</td> <th>  Cond. No.          </th> <td>    558.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                    mpg   R-squared:                       0.718\n",
       "Model:                            OLS   Adj. R-squared:                  0.709\n",
       "Method:                 Least Squares   F-statistic:                     76.51\n",
       "Date:                Sat, 25 Jan 2020   Prob (F-statistic):           9.38e-10\n",
       "Time:                        17:38:34   Log-Likelihood:                -82.105\n",
       "No. Observations:                  32   AIC:                             168.2\n",
       "Df Residuals:                      30   BIC:                             171.1\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     29.5999      1.230     24.070      0.000      27.088      32.111\n",
       "disp          -0.0412      0.005     -8.747      0.000      -0.051      -0.032\n",
       "==============================================================================\n",
       "Omnibus:                        3.368   Durbin-Watson:                   1.250\n",
       "Prob(Omnibus):                  0.186   Jarque-Bera (JB):                3.049\n",
       "Skew:                           0.719   Prob(JB):                        0.218\n",
       "Kurtosis:                       2.532   Cond. No.                         558.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\" Pythonでは、回帰分析の際には、sklearn.linear_model を利用する場合があるが、statmodelsの方が分析結果が一覧できる。 \"\"\"\n",
    "import statsmodels.formula.api as sm\n",
    "kaiki1 = sm.ols(formula='mpg ~ disp', data=mtcars)\n",
    "kaiki1_fitted = kaiki1.fit()\n",
    "kaiki1_fitted.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:30:13.360608Z",
     "start_time": "2019-04-14T17:30:13.355004Z"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.89220065, -2.20219093, -0.96308564,  1.62715468,  7.23054027])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.quantile(kaiki1_fitted.resid, [0, 0.25, 0.5, 0.75, 1]) # 四分位を出力"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:30:15.651873Z",
     "start_time": "2019-04-14T17:30:15.231826Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a19d5db10>"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.regplot(x='disp', y='mpg', data=mtcars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:30:39.105426Z",
     "start_time": "2019-04-14T17:30:39.097885Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    25.478343\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kaiki1_fitted.predict(pd.DataFrame({\"disp\": [100]})) # dispの値が100の場合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## p.108, 109"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:30:49.192222Z",
     "start_time": "2019-04-14T17:30:49.174576Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.760</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.743</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   45.81</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 25 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>1.06e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:38:34</td>     <th>  Log-Likelihood:    </th> <td> -79.573</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    32</td>      <th>  AIC:               </th> <td>   165.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    29</td>      <th>  BIC:               </th> <td>   169.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>   34.6610</td> <td>    2.547</td> <td>   13.609</td> <td> 0.000</td> <td>   29.452</td> <td>   39.870</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>disp</th>      <td>   -0.0206</td> <td>    0.010</td> <td>   -2.007</td> <td> 0.054</td> <td>   -0.042</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cyl</th>       <td>   -1.5873</td> <td>    0.712</td> <td>   -2.230</td> <td> 0.034</td> <td>   -3.043</td> <td>   -0.131</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.200</td> <th>  Durbin-Watson:     </th> <td>   1.596</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.202</td> <th>  Jarque-Bera (JB):  </th> <td>   2.660</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.701</td> <th>  Prob(JB):          </th> <td>   0.264</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.822</td> <th>  Cond. No.          </th> <td>1.27e+03</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, 1.27e+03. 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:                    mpg   R-squared:                       0.760\n",
       "Model:                            OLS   Adj. R-squared:                  0.743\n",
       "Method:                 Least Squares   F-statistic:                     45.81\n",
       "Date:                Sat, 25 Jan 2020   Prob (F-statistic):           1.06e-09\n",
       "Time:                        17:38:34   Log-Likelihood:                -79.573\n",
       "No. Observations:                  32   AIC:                             165.1\n",
       "Df Residuals:                      29   BIC:                             169.5\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     34.6610      2.547     13.609      0.000      29.452      39.870\n",
       "disp          -0.0206      0.010     -2.007      0.054      -0.042       0.000\n",
       "cyl           -1.5873      0.712     -2.230      0.034      -3.043      -0.131\n",
       "==============================================================================\n",
       "Omnibus:                        3.200   Durbin-Watson:                   1.596\n",
       "Prob(Omnibus):                  0.202   Jarque-Bera (JB):                2.660\n",
       "Skew:                           0.701   Prob(JB):                        0.264\n",
       "Kurtosis:                       2.822   Cond. No.                     1.27e+03\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, 1.27e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as sm\n",
    "kaiki2 = sm.ols(formula='mpg ~ disp + cyl', data=mtcars)\n",
    "kaiki2_fitted = kaiki2.fit()\n",
    "kaiki2_fitted.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:31:10.653356Z",
     "start_time": "2019-04-14T17:31:10.649514Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.42126787, -2.17223578, -0.63623117,  1.18986716,  7.05160883])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(kaiki2_fitted.resid, [0, 0.25, 0.5, 0.75, 1]) # 四分位を出力"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:31:14.648738Z",
     "start_time": "2019-04-14T17:31:14.643629Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     21.843953\n",
       "1     21.843953\n",
       "2     26.088855\n",
       "3     19.826756\n",
       "4     14.552672\n",
       "5     20.506016\n",
       "6     14.552672\n",
       "7     25.292268\n",
       "8     25.413712\n",
       "9     21.687517\n",
       "10    21.687517\n",
       "11    16.285814\n",
       "12    16.285814\n",
       "13    16.285814\n",
       "14    12.247305\n",
       "15    12.494309\n",
       "16    12.905982\n",
       "17    26.691956\n",
       "18    26.753706\n",
       "19    26.848391\n",
       "20    25.839793\n",
       "21    15.417185\n",
       "22    15.705356\n",
       "23    14.758509\n",
       "24    13.729327\n",
       "25    26.685780\n",
       "26    25.835676\n",
       "27    26.354384\n",
       "28    14.737925\n",
       "29    22.152707\n",
       "30    15.767107\n",
       "31    25.821268\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kaiki2_fitted.fittedvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:31:20.035211Z",
     "start_time": "2019-04-14T17:31:20.030244Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    -0.843953\n",
       "1    -0.843953\n",
       "2    -3.288855\n",
       "3     1.573244\n",
       "4     4.147328\n",
       "5    -2.406016\n",
       "6    -0.252672\n",
       "7    -0.892268\n",
       "8    -2.613712\n",
       "9    -2.487517\n",
       "10   -3.887517\n",
       "11    0.114186\n",
       "12    1.014186\n",
       "13   -1.085814\n",
       "14   -1.847305\n",
       "15   -2.094309\n",
       "16    1.794018\n",
       "17    5.708044\n",
       "18    3.646294\n",
       "19    7.051609\n",
       "20   -4.339793\n",
       "21    0.082815\n",
       "22   -0.505356\n",
       "23   -1.458509\n",
       "24    5.470673\n",
       "25    0.614220\n",
       "26    0.164324\n",
       "27    4.045616\n",
       "28    1.062075\n",
       "29   -2.452707\n",
       "30   -0.767107\n",
       "31   -4.421268\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kaiki2_fitted.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:31:27.088215Z",
     "start_time": "2019-04-14T17:31:27.076591Z"
    }
   },
   "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>mpg</th>\n",
       "      <th>kaiki2_fitted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.871531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kaiki2_fitted</th>\n",
       "      <td>0.871531</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    mpg  kaiki2_fitted\n",
       "mpg            1.000000       0.871531\n",
       "kaiki2_fitted  0.871531       1.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame({\n",
    "    \"mpg\": mtcars[\"mpg\"], \n",
    "    \"kaiki2_fitted\": kaiki2_fitted.fittedvalues\n",
    "}).corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:31:32.369733Z",
     "start_time": "2019-04-14T17:31:32.257521Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a1a213850>"
      ]
     },
     "execution_count": 12,
     "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": [
    "import matplotlib\n",
    "%matplotlib inline\n",
    "matplotlib.pyplot.scatter(mtcars[\"mpg\"], kaiki2_fitted.fittedvalues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:31:44.920485Z",
     "start_time": "2019-04-14T17:31:44.912208Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    15.78769\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kaiki2_fitted.predict(pd.DataFrame({\"disp\": [300.0,], \"cyl\": [8]})) # dispの値が300、cylが8の場合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## p.112"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:31:56.193866Z",
     "start_time": "2019-04-14T17:31:56.074711Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1., 10.,  8.,  5.,  4.,  1.,  3.]),\n",
       " array([-6., -4., -2.,  0.,  2.,  4.,  6.,  8.]),\n",
       " <a list of 7 Patch objects>)"
      ]
     },
     "execution_count": 14,
     "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": [
    "import matplotlib\n",
    "%matplotlib inline\n",
    "matplotlib.pyplot.hist(kaiki1_fitted.resid, range=(-6, 8), bins=7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:32:02.589917Z",
     "start_time": "2019-04-14T17:32:02.475045Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2., 7., 9., 8., 1., 4., 1.]),\n",
       " array([-6., -4., -2.,  0.,  2.,  4.,  6.,  8.]),\n",
       " <a list of 7 Patch objects>)"
      ]
     },
     "execution_count": 15,
     "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": [
    "import matplotlib\n",
    "%matplotlib inline\n",
    "# https://matplotlib.org/api/_as_gen/matplotlib.pyplot.hist.html\n",
    "matplotlib.pyplot.hist(kaiki2_fitted.resid, range=(-6, 8), bins=7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:32:07.769328Z",
     "start_time": "2019-04-14T17:32:07.757032Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.760</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.743</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   45.81</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 25 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>1.06e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:38:35</td>     <th>  Log-Likelihood:    </th> <td> -79.573</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    32</td>      <th>  AIC:               </th> <td>   165.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    29</td>      <th>  BIC:               </th> <td>   169.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>   34.6610</td> <td>    2.547</td> <td>   13.609</td> <td> 0.000</td> <td>   29.452</td> <td>   39.870</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>disp</th>      <td>   -0.0206</td> <td>    0.010</td> <td>   -2.007</td> <td> 0.054</td> <td>   -0.042</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cyl</th>       <td>   -1.5873</td> <td>    0.712</td> <td>   -2.230</td> <td> 0.034</td> <td>   -3.043</td> <td>   -0.131</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.200</td> <th>  Durbin-Watson:     </th> <td>   1.596</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.202</td> <th>  Jarque-Bera (JB):  </th> <td>   2.660</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.701</td> <th>  Prob(JB):          </th> <td>   0.264</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.822</td> <th>  Cond. No.          </th> <td>1.27e+03</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, 1.27e+03. 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:                    mpg   R-squared:                       0.760\n",
       "Model:                            OLS   Adj. R-squared:                  0.743\n",
       "Method:                 Least Squares   F-statistic:                     45.81\n",
       "Date:                Sat, 25 Jan 2020   Prob (F-statistic):           1.06e-09\n",
       "Time:                        17:38:35   Log-Likelihood:                -79.573\n",
       "No. Observations:                  32   AIC:                             165.1\n",
       "Df Residuals:                      29   BIC:                             169.5\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     34.6610      2.547     13.609      0.000      29.452      39.870\n",
       "disp          -0.0206      0.010     -2.007      0.054      -0.042       0.000\n",
       "cyl           -1.5873      0.712     -2.230      0.034      -3.043      -0.131\n",
       "==============================================================================\n",
       "Omnibus:                        3.200   Durbin-Watson:                   1.596\n",
       "Prob(Omnibus):                  0.202   Jarque-Bera (JB):                2.660\n",
       "Skew:                           0.701   Prob(JB):                        0.264\n",
       "Kurtosis:                       2.822   Cond. No.                     1.27e+03\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, 1.27e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kaiki2_fitted.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## p.115"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:32:22.555002Z",
     "start_time": "2019-04-14T17:32:22.543133Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.760</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.743</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   45.81</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 25 Jan 2020</td> <th>  Prob (F-statistic):</th> <td>1.06e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:38:35</td>     <th>  Log-Likelihood:    </th> <td> -79.573</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    32</td>      <th>  AIC:               </th> <td>   165.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    29</td>      <th>  BIC:               </th> <td>   169.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>   34.6610</td> <td>    2.547</td> <td>   13.609</td> <td> 0.000</td> <td>   29.452</td> <td>   39.870</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>disp</th>      <td>   -0.0206</td> <td>    0.010</td> <td>   -2.007</td> <td> 0.054</td> <td>   -0.042</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cyl</th>       <td>   -1.5873</td> <td>    0.712</td> <td>   -2.230</td> <td> 0.034</td> <td>   -3.043</td> <td>   -0.131</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.200</td> <th>  Durbin-Watson:     </th> <td>   1.596</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.202</td> <th>  Jarque-Bera (JB):  </th> <td>   2.660</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.701</td> <th>  Prob(JB):          </th> <td>   0.264</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.822</td> <th>  Cond. No.          </th> <td>1.27e+03</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, 1.27e+03. 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:                    mpg   R-squared:                       0.760\n",
       "Model:                            OLS   Adj. R-squared:                  0.743\n",
       "Method:                 Least Squares   F-statistic:                     45.81\n",
       "Date:                Sat, 25 Jan 2020   Prob (F-statistic):           1.06e-09\n",
       "Time:                        17:38:35   Log-Likelihood:                -79.573\n",
       "No. Observations:                  32   AIC:                             165.1\n",
       "Df Residuals:                      29   BIC:                             169.5\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     34.6610      2.547     13.609      0.000      29.452      39.870\n",
       "disp          -0.0206      0.010     -2.007      0.054      -0.042       0.000\n",
       "cyl           -1.5873      0.712     -2.230      0.034      -3.043      -0.131\n",
       "==============================================================================\n",
       "Omnibus:                        3.200   Durbin-Watson:                   1.596\n",
       "Prob(Omnibus):                  0.202   Jarque-Bera (JB):                2.660\n",
       "Skew:                           0.701   Prob(JB):                        0.264\n",
       "Kurtosis:                       2.822   Cond. No.                     1.27e+03\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, 1.27e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\" Pythonでは statmodelsのsummary()で95%信頼区間もt値も一括で出力される。 \"\"\"\n",
    "kaiki2_fitted.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## p.122, 123"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T17:32:37.159914Z",
     "start_time": "2019-04-14T17:32:37.156370Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "168.2093890987089\n",
      "165.14563701576952\n"
     ]
    }
   ],
   "source": [
    "\"\"\" Pythonでは statmodelsのsummary()でAICの値も他の情報とともに一括で出力される。 \"\"\"\n",
    "print(kaiki1_fitted.aic) # AICの値のみを取り出す\n",
    "print(kaiki2_fitted.aic) # AICの値のみを取り出す"
   ]
  }
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