ch4_interaction_modeling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from dataclasses import dataclass\n",
    "from typing import OrderedDict\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy_data = pd.DataFrame().assign(\n",
    "    x1=np.random.uniform(0, 450, 300)\n",
    ").assign(\n",
    "    x2=lambda df: df.x1.map(\n",
    "        lambda x: 500 - x\n",
    "    ).map(\n",
    "        lambda x: x - np.random.uniform(0,200)\n",
    "    )\n",
    ").pipe(\n",
    "    lambda df: df[df.x1>0]\n",
    ").pipe(\n",
    "    lambda df: df[df.x2>0]\n",
    ").pipe(\n",
    "    lambda df: df[:100]\n",
    ").assign(\n",
    "    x1=lambda df: df.x1.map(round).map(lambda x: x*10),\n",
    "    x2=lambda df: df.x2.map(round).map(lambda x: x*10)\n",
    ").assign(\n",
    "    interaction=lambda df: df.x1*df.x2\n",
    ").assign(\n",
    "    y=lambda df: 0.2*df.x1 + 0.2*df.x2 + 0.1*df.interaction\n",
    ").assign(\n",
    "    y=lambda df: df.y.map(round),\n",
    "    y_s=lambda df: (df.y - df.y.min())\n",
    ").assign(\n",
    "    y_s=lambda df: (df.y_s/df.y_s.max())*100\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>interaction</th>\n",
       "      <th>y</th>\n",
       "      <th>y_s</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>840</td>\n",
       "      <td>3500</td>\n",
       "      <td>2940000</td>\n",
       "      <td>294868</td>\n",
       "      <td>47.516982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1000</td>\n",
       "      <td>3190</td>\n",
       "      <td>3190000</td>\n",
       "      <td>319838</td>\n",
       "      <td>51.635826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>720</td>\n",
       "      <td>2340</td>\n",
       "      <td>1684800</td>\n",
       "      <td>169092</td>\n",
       "      <td>26.770014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3740</td>\n",
       "      <td>1130</td>\n",
       "      <td>4226200</td>\n",
       "      <td>423594</td>\n",
       "      <td>68.750557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3360</td>\n",
       "      <td>1010</td>\n",
       "      <td>3393600</td>\n",
       "      <td>340234</td>\n",
       "      <td>55.000181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>2110</td>\n",
       "      <td>2510</td>\n",
       "      <td>5296100</td>\n",
       "      <td>530534</td>\n",
       "      <td>86.390494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>2800</td>\n",
       "      <td>2150</td>\n",
       "      <td>6020000</td>\n",
       "      <td>602990</td>\n",
       "      <td>98.342235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>1280</td>\n",
       "      <td>3670</td>\n",
       "      <td>4697600</td>\n",
       "      <td>470750</td>\n",
       "      <td>76.529020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114</th>\n",
       "      <td>1000</td>\n",
       "      <td>3500</td>\n",
       "      <td>3500000</td>\n",
       "      <td>350900</td>\n",
       "      <td>56.759556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>350</td>\n",
       "      <td>3010</td>\n",
       "      <td>1053500</td>\n",
       "      <td>106022</td>\n",
       "      <td>16.366510</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       x1    x2  interaction       y        y_s\n",
       "0     840  3500      2940000  294868  47.516982\n",
       "1    1000  3190      3190000  319838  51.635826\n",
       "3     720  2340      1684800  169092  26.770014\n",
       "4    3740  1130      4226200  423594  68.750557\n",
       "5    3360  1010      3393600  340234  55.000181\n",
       "..    ...   ...          ...     ...        ...\n",
       "111  2110  2510      5296100  530534  86.390494\n",
       "112  2800  2150      6020000  602990  98.342235\n",
       "113  1280  3670      4697600  470750  76.529020\n",
       "114  1000  3500      3500000  350900  56.759556\n",
       "115   350  3010      1053500  106022  16.366510\n",
       "\n",
       "[100 rows x 5 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = dummy_data[[\"x1\", \"x2\", \"interaction\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = dummy_data.y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/a13771/.venv/local3.7/lib/python3.7/site-packages/sklearn/linear_model/base.py:485: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  linalg.lstsq(X, y)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.2, 0.2, 0.1])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy_data.to_csv('interaction_dummies.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1169cbe10>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dummy_data.plot.scatter(x=\"x1\", y=\"x2\", s=dummy_data.y_s, figsize=(16,16), xlim=[0,5000], ylim=[0,5000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.savefig('interaction_dat.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>interaction</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>840</td>\n",
       "      <td>3500</td>\n",
       "      <td>2940000</td>\n",
       "      <td>294868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1000</td>\n",
       "      <td>3190</td>\n",
       "      <td>3190000</td>\n",
       "      <td>319838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>720</td>\n",
       "      <td>2340</td>\n",
       "      <td>1684800</td>\n",
       "      <td>169092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3740</td>\n",
       "      <td>1130</td>\n",
       "      <td>4226200</td>\n",
       "      <td>423594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3360</td>\n",
       "      <td>1010</td>\n",
       "      <td>3393600</td>\n",
       "      <td>340234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>2110</td>\n",
       "      <td>2510</td>\n",
       "      <td>5296100</td>\n",
       "      <td>530534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>2800</td>\n",
       "      <td>2150</td>\n",
       "      <td>6020000</td>\n",
       "      <td>602990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>1280</td>\n",
       "      <td>3670</td>\n",
       "      <td>4697600</td>\n",
       "      <td>470750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>1000</td>\n",
       "      <td>3500</td>\n",
       "      <td>3500000</td>\n",
       "      <td>350900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>350</td>\n",
       "      <td>3010</td>\n",
       "      <td>1053500</td>\n",
       "      <td>106022</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      x1    x2  interaction       y\n",
       "0    840  3500      2940000  294868\n",
       "1   1000  3190      3190000  319838\n",
       "2    720  2340      1684800  169092\n",
       "3   3740  1130      4226200  423594\n",
       "4   3360  1010      3393600  340234\n",
       "..   ...   ...          ...     ...\n",
       "95  2110  2510      5296100  530534\n",
       "96  2800  2150      6020000  602990\n",
       "97  1280  3670      4697600  470750\n",
       "98  1000  3500      3500000  350900\n",
       "99   350  3010      1053500  106022\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.2 0.2 0.1]\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from sklearn.linear_model import LinearRegression\n",
    "data = pd.read_csv(\"interaction_dummies.csv\")[[\"x1\", \"x2\", \"y\"]]\n",
    "x, y = data.assign(\n",
    "    # 交互作用項のカラムを作成\n",
    "    x12=lambda df: df.x1 * df.x2\n",
    ").pipe(\n",
    "    # 説明変数と目的変数を抽出\n",
    "    lambda df: (df[[\"x1\", \"x2\", \"x12\"]], df.y)\n",
    ")\n",
    "model = LinearRegression()\n",
    "model.fit(x, y)\n",
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.2, 0.2, 0.1])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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