【キカガク流】人工知能・機械学習 脱ブラックボックス講座 - 初級編 -

20180220_simple-linear-regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1, 2, 3]), array([ 2. ,  3.9,  6.1]))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = np.array([1, 2, 3])\n",
    "y = np.array([2, 3.9, 6.1])\n",
    "x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-1.,  0.,  1.]), array([-2. , -0.1,  2.1]))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# データの中心化\n",
    "xc = x - x.mean()\n",
    "yc = y - y.mean()\n",
    "xc, yc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation*}\n",
    "a = \\frac{ \\sum_{n=1}^N x_n y_n}{ \\sum_{n=1}^N x_n^2 }\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2. , -0. ,  2.1]), array([ 1.,  0.,  1.]))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xy = xc * yc\n",
    "xx = xc * xc\n",
    "xy, xx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0499999999999998"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = xy.sum() / xx.sum()\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>40.362</td>\n",
       "      <td>137500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>40.686</td>\n",
       "      <td>132500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>38.430</td>\n",
       "      <td>93000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        x         y\n",
       "0  40.362  137500.0\n",
       "1  40.686  132500.0\n",
       "2  38.430   93000.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('sample.csv')\n",
    "df.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = df['x']\n",
    "y = df['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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U7rbrKiobVC5pdEAnB+TNlHJJYHx0JHfisL2vHfhKMyWuNRuneIOq13cVvab1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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a6bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 横軸を x, 縦軸を y の散布図(scatter)をプロット\n",
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 単回帰分析の実装"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>37.622220</td>\n",
       "      <td>121065.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.087547</td>\n",
       "      <td>47174.009226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>29.418000</td>\n",
       "      <td>59000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>35.151000</td>\n",
       "      <td>90375.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>36.909000</td>\n",
       "      <td>104250.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>39.439500</td>\n",
       "      <td>147250.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>50.250000</td>\n",
       "      <td>250000.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x              y\n",
       "count  100.000000     100.000000\n",
       "mean    37.622220  121065.000000\n",
       "std      4.087547   47174.009226\n",
       "min     29.418000   59000.000000\n",
       "25%     35.151000   90375.000000\n",
       "50%     36.909000  104250.000000\n",
       "75%     39.439500  147250.000000\n",
       "max     50.250000  250000.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x        37.62222\n",
       "y    121065.00000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.73978</td>\n",
       "      <td>16435.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.06378</td>\n",
       "      <td>11435.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.80778</td>\n",
       "      <td>-28065.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x        y\n",
       "0  2.73978  16435.0\n",
       "1  3.06378  11435.0\n",
       "2  0.80778 -28065.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_c = df - df.mean()\n",
    "df_c.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.000000e+02</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.989520e-15</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.087547e+00</td>\n",
       "      <td>47174.009226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-8.204220e+00</td>\n",
       "      <td>-62065.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-2.471220e+00</td>\n",
       "      <td>-30690.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-7.132200e-01</td>\n",
       "      <td>-16815.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.817280e+00</td>\n",
       "      <td>26185.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.262778e+01</td>\n",
       "      <td>128935.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  x              y\n",
       "count  1.000000e+02     100.000000\n",
       "mean   1.989520e-15       0.000000\n",
       "std    4.087547e+00   47174.009226\n",
       "min   -8.204220e+00  -62065.000000\n",
       "25%   -2.471220e+00  -30690.000000\n",
       "50%   -7.132200e-01  -16815.000000\n",
       "75%    1.817280e+00   26185.000000\n",
       "max    1.262778e+01  128935.000000"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_c.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# データ抽出\n",
    "x = df_c['x']\n",
    "y = df_c['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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d12i9rTd00hLof/ud7Q1d0LPMTm9GK8FLqlsWeXRbHQQ+ERE/lfR6YJukLclrN0bEf0sf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118f5b400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 散布図\n",
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10069.022519284064"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = (x * y).sum() / (x * x).sum()\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SpRnXUdp0/QlzwHyGc26yc67NO54HLHfOHQQs944BPgsc5H2dB9wCyWADXAkcDRwFXJkK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\nEBGRwBQ8REQkMAUPEREJTMFDREQC+/9vk1Kl0JfS0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119277358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y, label='y')\n",
    "plt.plot(x, a * x, label='y_hat', color='red')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 予測値の計算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x        37.62222\n",
       "y    121065.00000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_new = 40\n",
    "mean = df.mean()\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23941.920365903276"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xc = x_new - mean['x']\n",
    "yc = a * xc\n",
    "yc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "145006.92036590326"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 元のスケールの予測値\n",
    "y_hat = a * xc + mean['y']\n",
    "y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 予測値を計算する関数の作成\n",
    "def predict(x):\n",
    "    # 定数項\n",
    "    a = 10069.022519284064\n",
    "    xm = 37.62222\n",
    "    ym = 121065.00000\n",
    "    # 中心化\n",
    "    xc = x - xm\n",
    "    # 予測値の計算\n",
    "    y_hat = a * xc + ym\n",
    "    return y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "145006.92036590326"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(40)"
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

sample.csv