Decision Tree Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing the libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.formula.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>cap-shape</th>\n",
       "      <th>cap-surface</th>\n",
       "      <th>cap-color</th>\n",
       "      <th>bruises</th>\n",
       "      <th>odor</th>\n",
       "      <th>gill-attachment</th>\n",
       "      <th>gill-spacing</th>\n",
       "      <th>gill-size</th>\n",
       "      <th>gill-color</th>\n",
       "      <th>...</th>\n",
       "      <th>stalk-surface-below-ring</th>\n",
       "      <th>stalk-color-above-ring</th>\n",
       "      <th>stalk-color-below-ring</th>\n",
       "      <th>veil-type</th>\n",
       "      <th>veil-color</th>\n",
       "      <th>ring-number</th>\n",
       "      <th>ring-type</th>\n",
       "      <th>spore-print-color</th>\n",
       "      <th>population</th>\n",
       "      <th>habitat</th>\n",
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       "      <td>m</td>\n",
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       "      <th>3</th>\n",
       "      <td>p</td>\n",
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       "      <td>w</td>\n",
       "      <td>t</td>\n",
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       "      <td>o</td>\n",
       "      <td>p</td>\n",
       "      <td>k</td>\n",
       "      <td>s</td>\n",
       "      <td>u</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>e</td>\n",
       "      <td>x</td>\n",
       "      <td>s</td>\n",
       "      <td>g</td>\n",
       "      <td>f</td>\n",
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       "      <td>w</td>\n",
       "      <td>p</td>\n",
       "      <td>w</td>\n",
       "      <td>o</td>\n",
       "      <td>e</td>\n",
       "      <td>n</td>\n",
       "      <td>a</td>\n",
       "      <td>g</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 23 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  class cap-shape cap-surface cap-color bruises odor gill-attachment  \\\n",
       "0     p         x           s         n       t    p               f   \n",
       "1     e         x           s         y       t    a               f   \n",
       "2     e         b           s         w       t    l               f   \n",
       "3     p         x           y         w       t    p               f   \n",
       "4     e         x           s         g       f    n               f   \n",
       "\n",
       "  gill-spacing gill-size gill-color  ... stalk-surface-below-ring  \\\n",
       "0            c         n          k  ...                        s   \n",
       "1            c         b          k  ...                        s   \n",
       "2            c         b          n  ...                        s   \n",
       "3            c         n          n  ...                        s   \n",
       "4            w         b          k  ...                        s   \n",
       "\n",
       "  stalk-color-above-ring stalk-color-below-ring veil-type veil-color  \\\n",
       "0                      w                      w         p          w   \n",
       "1                      w                      w         p          w   \n",
       "2                      w                      w         p          w   \n",
       "3                      w                      w         p          w   \n",
       "4                      w                      w         p          w   \n",
       "\n",
       "  ring-number ring-type spore-print-color population habitat  \n",
       "0           o         p                 k          s       u  \n",
       "1           o         p                 n          n       g  \n",
       "2           o         p                 n          n       m  \n",
       "3           o         p                 k          s       u  \n",
       "4           o         e                 n          a       g  \n",
       "\n",
       "[5 rows x 23 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset=pd.read_csv('mushrooms.csv') \n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th>cap-color</th>\n",
       "      <th>bruises</th>\n",
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       "      <th>veil-color</th>\n",
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       "      <th>spore-print-color</th>\n",
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       "      <td>v</td>\n",
       "      <td>d</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>4208</td>\n",
       "      <td>3656</td>\n",
       "      <td>3244</td>\n",
       "      <td>2284</td>\n",
       "      <td>4748</td>\n",
       "      <td>3528</td>\n",
       "      <td>7914</td>\n",
       "      <td>6812</td>\n",
       "      <td>5612</td>\n",
       "      <td>1728</td>\n",
       "      <td>...</td>\n",
       "      <td>4936</td>\n",
       "      <td>4464</td>\n",
       "      <td>4384</td>\n",
       "      <td>8124</td>\n",
       "      <td>7924</td>\n",
       "      <td>7488</td>\n",
       "      <td>3968</td>\n",
       "      <td>2388</td>\n",
       "      <td>4040</td>\n",
       "      <td>3148</td>\n",
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       "<p>4 rows × 23 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       class cap-shape cap-surface cap-color bruises  odor gill-attachment  \\\n",
       "count   8124      8124        8124      8124    8124  8124            8124   \n",
       "unique     2         6           4        10       2     9               2   \n",
       "top        e         x           y         n       f     n               f   \n",
       "freq    4208      3656        3244      2284    4748  3528            7914   \n",
       "\n",
       "       gill-spacing gill-size gill-color  ... stalk-surface-below-ring  \\\n",
       "count          8124      8124       8124  ...                     8124   \n",
       "unique            2         2         12  ...                        4   \n",
       "top               c         b          b  ...                        s   \n",
       "freq           6812      5612       1728  ...                     4936   \n",
       "\n",
       "       stalk-color-above-ring stalk-color-below-ring veil-type veil-color  \\\n",
       "count                    8124                   8124      8124       8124   \n",
       "unique                      9                      9         1          4   \n",
       "top                         w                      w         p          w   \n",
       "freq                     4464                   4384      8124       7924   \n",
       "\n",
       "       ring-number ring-type spore-print-color population habitat  \n",
       "count         8124      8124              8124       8124    8124  \n",
       "unique           3         5                 9          6       7  \n",
       "top              o         p                 w          v       d  \n",
       "freq          7488      3968              2388       4040    3148  \n",
       "\n",
       "[4 rows x 23 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>cap-shape</th>\n",
       "      <th>cap-surface</th>\n",
       "      <th>cap-color</th>\n",
       "      <th>bruises</th>\n",
       "      <th>odor</th>\n",
       "      <th>gill-attachment</th>\n",
       "      <th>gill-spacing</th>\n",
       "      <th>gill-size</th>\n",
       "      <th>gill-color</th>\n",
       "      <th>...</th>\n",
       "      <th>stalk-surface-below-ring</th>\n",
       "      <th>stalk-color-above-ring</th>\n",
       "      <th>stalk-color-below-ring</th>\n",
       "      <th>veil-type</th>\n",
       "      <th>veil-color</th>\n",
       "      <th>ring-number</th>\n",
       "      <th>ring-type</th>\n",
       "      <th>spore-print-color</th>\n",
       "      <th>population</th>\n",
       "      <th>habitat</th>\n",
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      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [class, cap-shape, cap-surface, cap-color, bruises, odor, gill-attachment, gill-spacing, gill-size, gill-color, stalk-shape, stalk-root, stalk-surface-above-ring, stalk-surface-below-ring, stalk-color-above-ring, stalk-color-below-ring, veil-type, veil-color, ring-number, ring-type, spore-print-color, population, habitat]\n",
       "Index: []\n",
       "\n",
       "[0 rows x 23 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# verify that there are no null columns in the dataset\n",
    "dataset[dataset.isnull().any(axis=1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = dataset['class']\n",
    "x = dataset.drop(['class'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  cap-shape cap-surface cap-color bruises odor gill-attachment gill-spacing  \\\n",
      "0         x           s         n       t    p               f            c   \n",
      "1         x           s         y       t    a               f            c   \n",
      "2         b           s         w       t    l               f            c   \n",
      "3         x           y         w       t    p               f            c   \n",
      "4         x           s         g       f    n               f            w   \n",
      "\n",
      "  gill-size gill-color stalk-shape  ... stalk-surface-below-ring  \\\n",
      "0         n          k           e  ...                        s   \n",
      "1         b          k           e  ...                        s   \n",
      "2         b          n           e  ...                        s   \n",
      "3         n          n           e  ...                        s   \n",
      "4         b          k           t  ...                        s   \n",
      "\n",
      "  stalk-color-above-ring stalk-color-below-ring veil-type veil-color  \\\n",
      "0                      w                      w         p          w   \n",
      "1                      w                      w         p          w   \n",
      "2                      w                      w         p          w   \n",
      "3                      w                      w         p          w   \n",
      "4                      w                      w         p          w   \n",
      "\n",
      "  ring-number ring-type spore-print-color population habitat  \n",
      "0           o         p                 k          s       u  \n",
      "1           o         p                 n          n       g  \n",
      "2           o         p                 n          n       m  \n",
      "3           o         p                 k          s       u  \n",
      "4           o         e                 n          a       g  \n",
      "\n",
      "[5 rows x 22 columns]\n"
     ]
    }
   ],
   "source": [
    "print(x.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    p\n",
      "1    e\n",
      "2    e\n",
      "3    p\n",
      "4    e\n",
      "Name: class, dtype: object\n"
     ]
    }
   ],
   "source": [
    "print(y.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 1 0 0 0 0 1 0]\n"
     ]
    }
   ],
   "source": [
    "# use LabelEncoder to replace purchased (dependent variable) with 0 and 1 \n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "y= LabelEncoder().fit_transform(y)\n",
    "print(y[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   cap-shape_b  cap-shape_c  cap-shape_f  cap-shape_k  cap-shape_s  \\\n",
      "0            0            0            0            0            0   \n",
      "1            0            0            0            0            0   \n",
      "2            1            0            0            0            0   \n",
      "3            0            0            0            0            0   \n",
      "4            0            0            0            0            0   \n",
      "\n",
      "   cap-shape_x  cap-surface_f  cap-surface_g  cap-surface_s  cap-surface_y  \\\n",
      "0            1              0              0              1              0   \n",
      "1            1              0              0              1              0   \n",
      "2            0              0              0              1              0   \n",
      "3            1              0              0              0              1   \n",
      "4            1              0              0              1              0   \n",
      "\n",
      "   ...  population_s  population_v  population_y  habitat_d  habitat_g  \\\n",
      "0  ...             1             0             0          0          0   \n",
      "1  ...             0             0             0          0          1   \n",
      "2  ...             0             0             0          0          0   \n",
      "3  ...             1             0             0          0          0   \n",
      "4  ...             0             0             0          0          1   \n",
      "\n",
      "   habitat_l  habitat_m  habitat_p  habitat_u  habitat_w  \n",
      "0          0          0          0          1          0  \n",
      "1          0          0          0          0          0  \n",
      "2          0          1          0          0          0  \n",
      "3          0          0          0          1          0  \n",
      "4          0          0          0          0          0  \n",
      "\n",
      "[5 rows x 117 columns]\n"
     ]
    }
   ],
   "source": [
    "x = pd.get_dummies(x)\n",
    "print(x.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Splitting the dataset into training and test set  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.3,random_state = 0) # func returns train and test data. It takes dataset and then split size test_size =0.3 means 30% data is for test and rest for training and random_state \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      cap-shape_b  cap-shape_c  cap-shape_f  cap-shape_k  cap-shape_s  \\\n",
      "5314            0            0            0            0            0   \n",
      "2075            0            0            0            0            0   \n",
      "5165            0            0            1            0            0   \n",
      "1155            1            0            0            0            0   \n",
      "4448            0            0            0            0            0   \n",
      "\n",
      "      cap-shape_x  cap-surface_f  cap-surface_g  cap-surface_s  cap-surface_y  \\\n",
      "5314            1              0              0              1              0   \n",
      "2075            1              0              0              1              0   \n",
      "5165            0              0              0              1              0   \n",
      "1155            0              0              0              0              1   \n",
      "4448            1              0              0              0              1   \n",
      "\n",
      "      ...  population_s  population_v  population_y  habitat_d  habitat_g  \\\n",
      "5314  ...             0             1             0          0          1   \n",
      "2075  ...             0             0             0          0          0   \n",
      "5165  ...             1             0             0          0          1   \n",
      "1155  ...             1             0             0          0          0   \n",
      "4448  ...             0             0             1          0          1   \n",
      "\n",
      "      habitat_l  habitat_m  habitat_p  habitat_u  habitat_w  \n",
      "5314          0          0          0          0          0  \n",
      "2075          0          1          0          0          0  \n",
      "5165          0          0          0          0          0  \n",
      "1155          0          1          0          0          0  \n",
      "4448          0          0          0          0          0  \n",
      "\n",
      "[5 rows x 117 columns]\n"
     ]
    }
   ],
   "source": [
    "print(x_train.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      cap-shape_b  cap-shape_c  cap-shape_f  cap-shape_k  cap-shape_s  \\\n",
      "380             0            0            0            0            0   \n",
      "3641            0            0            1            0            0   \n",
      "273             0            0            0            0            0   \n",
      "1029            0            0            0            0            0   \n",
      "684             0            0            0            0            0   \n",
      "\n",
      "      cap-shape_x  cap-surface_f  cap-surface_g  cap-surface_s  cap-surface_y  \\\n",
      "380             1              0              0              0              1   \n",
      "3641            0              0              0              0              1   \n",
      "273             1              0              0              0              1   \n",
      "1029            1              0              0              1              0   \n",
      "684             1              1              0              0              0   \n",
      "\n",
      "      ...  population_s  population_v  population_y  habitat_d  habitat_g  \\\n",
      "380   ...             1             0             0          0          0   \n",
      "3641  ...             0             0             1          1          0   \n",
      "273   ...             0             0             0          0          0   \n",
      "1029  ...             0             0             0          0          1   \n",
      "684   ...             0             1             0          1          0   \n",
      "\n",
      "      habitat_l  habitat_m  habitat_p  habitat_u  habitat_w  \n",
      "380           0          0          0          1          0  \n",
      "3641          0          0          0          0          0  \n",
      "273           0          1          0          0          0  \n",
      "1029          0          0          0          0          0  \n",
      "684           0          0          0          0          0  \n",
      "\n",
      "[5 rows x 117 columns]\n"
     ]
    }
   ],
   "source": [
    "print(x_test.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 1 0 1 0 1 0 0 1]\n"
     ]
    }
   ],
   "source": [
    "print(y_train[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 0 0 0 1 1 0 1]\n"
     ]
    }
   ],
   "source": [
    "print(y_test[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Build Model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(random_state=0)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor \n",
    "regressor = DecisionTreeRegressor(random_state = 0)\n",
    "regressor.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred= regressor.predict(x_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluate Model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score, mean_absolute_error, mean_squared_error, confusion_matrix, classification_report\n",
    "r2_score(y_test,y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(y_test,y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(y_test,y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the decision tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(196.94117647058823, 203.85, 'X[27] <= 0.5\\nmse = 0.25\\nsamples = 5686\\nvalue = 0.484'),\n",
       " Text(118.16470588235295, 176.67000000000002, 'X[53] <= 0.5\\nmse = 0.14\\nsamples = 3203\\nvalue = 0.831'),\n",
       " Text(78.7764705882353, 149.49, 'X[55] <= 0.5\\nmse = 0.064\\nsamples = 2831\\nvalue = 0.931'),\n",
       " Text(59.082352941176474, 122.31, 'X[25] <= 0.5\\nmse = 0.023\\nsamples = 2698\\nvalue = 0.977'),\n",
       " Text(39.38823529411765, 95.13, 'X[22] <= 0.5\\nmse = 0.01\\nsamples = 2663\\nvalue = 0.989'),\n",
       " Text(19.694117647058825, 67.94999999999999, 'mse = 0.0\\nsamples = 2635\\nvalue = 1.0'),\n",
       " Text(59.082352941176474, 67.94999999999999, 'mse = 0.0\\nsamples = 28\\nvalue = 0.0'),\n",
       " Text(78.7764705882353, 95.13, 'mse = 0.0\\nsamples = 35\\nvalue = 0.0'),\n",
       " Text(98.47058823529412, 122.31, 'mse = 0.0\\nsamples = 133\\nvalue = 0.0'),\n",
       " Text(157.5529411764706, 149.49, 'X[71] <= 0.5\\nmse = 0.07\\nsamples = 372\\nvalue = 0.075'),\n",
       " Text(137.85882352941178, 122.31, 'mse = 0.0\\nsamples = 28\\nvalue = 1.0'),\n",
       " Text(177.24705882352941, 122.31, 'mse = 0.0\\nsamples = 344\\nvalue = 0.0'),\n",
       " Text(275.71764705882356, 176.67000000000002, 'X[100] <= 0.5\\nmse = 0.034\\nsamples = 2483\\nvalue = 0.035'),\n",
       " Text(256.02352941176474, 149.49, 'X[63] <= 0.5\\nmse = 0.015\\nsamples = 2432\\nvalue = 0.015'),\n",
       " Text(216.63529411764708, 122.31, 'X[7] <= 0.5\\nmse = 0.003\\nsamples = 2391\\nvalue = 0.003'),\n",
       " Text(196.94117647058823, 95.13, 'X[1] <= 0.5\\nmse = 0.001\\nsamples = 2388\\nvalue = 0.001'),\n",
       " Text(177.24705882352941, 67.94999999999999, 'X[36] <= 0.5\\nmse = 0.001\\nsamples = 2387\\nvalue = 0.001'),\n",
       " Text(157.5529411764706, 40.77000000000001, 'mse = 0.0\\nsamples = 2246\\nvalue = 0.0'),\n",
       " Text(196.94117647058823, 40.77000000000001, 'X[105] <= 0.5\\nmse = 0.014\\nsamples = 141\\nvalue = 0.014'),\n",
       " Text(177.24705882352941, 13.590000000000003, 'mse = 0.0\\nsamples = 139\\nvalue = 0.0'),\n",
       " Text(216.63529411764708, 13.590000000000003, 'mse = 0.0\\nsamples = 2\\nvalue = 1.0'),\n",
       " Text(216.63529411764708, 67.94999999999999, 'mse = 0.0\\nsamples = 1\\nvalue = 1.0'),\n",
       " Text(236.3294117647059, 95.13, 'mse = 0.0\\nsamples = 3\\nvalue = 1.0'),\n",
       " Text(295.4117647058824, 122.31, 'X[109] <= 0.5\\nmse = 0.196\\nsamples = 41\\nvalue = 0.732'),\n",
       " Text(275.71764705882356, 95.13, 'mse = 0.0\\nsamples = 30\\nvalue = 1.0'),\n",
       " Text(315.1058823529412, 95.13, 'mse = 0.0\\nsamples = 11\\nvalue = 0.0'),\n",
       " Text(295.4117647058824, 149.49, 'mse = 0.0\\nsamples = 51\\nvalue = 1.0')]"
      ]
     },
     "execution_count": 20,
     "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": [
    "from sklearn.tree import plot_tree\n",
    "plot_tree(regressor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\r\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n",
       "<!-- Generated by graphviz version 2.44.1 (20200629.0846)\r\n",
       " -->\r\n",
       "<!-- Title: Tree Pages: 1 -->\r\n",
       "<svg width=\"910pt\" height=\"789pt\"\r\n",
       " viewBox=\"0.00 0.00 909.50 789.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 785)\">\r\n",
       "<title>Tree</title>\r\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-785 905.5,-785 905.5,4 -4,4\"/>\r\n",
       "<!-- 0 -->\r\n",
       "<g id=\"node1\" class=\"node\">\r\n",
       "<title>0</title>\r\n",
       "<polygon fill=\"none\" stroke=\"black\" points=\"623,-781 519,-781 519,-713 623,-713 623,-781\"/>\r\n",
       "<text text-anchor=\"middle\" x=\"571\" y=\"-765.8\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">X[27] &lt;= 0.5</text>\r\n",
       "<text text-anchor=\"middle\" x=\"571\" y=\"-750.8\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">mse = 0.25</text>\r\n",
       "<text text-anchor=\"middle\" x=\"571\" y=\"-735.8\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">samples = 5686</text>\r\n",
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      "text/plain": [
       "<graphviz.files.Source at 0x1ddfc76eb50>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz # Refer to https://forum.graphviz.org/t/new-simplified-installation-procedure-on-windows/224\n",
    "from sklearn import tree\n",
    "dot_data = tree.export_graphviz(regressor)\n",
    "graph = graphviz.Source(dot_data)\n",
    "graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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