notebooks/T4 - 5 - Linear Regression - Problemas con la regresión lineal.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# El tratamiento de las variables categóricas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"../datasets/ecom-expense/Ecom Expense.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Transaction ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Items</th>\n",
       "      <th>Monthly Income</th>\n",
       "      <th>Transaction Time</th>\n",
       "      <th>Record</th>\n",
       "      <th>Gender</th>\n",
       "      <th>City Tier</th>\n",
       "      <th>Total Spend</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>TXN001</td>\n",
       "      <td>42</td>\n",
       "      <td>10</td>\n",
       "      <td>7313</td>\n",
       "      <td>627.668127</td>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>4198.385084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>TXN002</td>\n",
       "      <td>24</td>\n",
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       "      <td>17747</td>\n",
       "      <td>126.904567</td>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>4134.976648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>TXN003</td>\n",
       "      <td>47</td>\n",
       "      <td>11</td>\n",
       "      <td>22845</td>\n",
       "      <td>873.469701</td>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>5166.614455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>TXN004</td>\n",
       "      <td>50</td>\n",
       "      <td>11</td>\n",
       "      <td>18552</td>\n",
       "      <td>380.219428</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7784.447676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>TXN005</td>\n",
       "      <td>60</td>\n",
       "      <td>2</td>\n",
       "      <td>14439</td>\n",
       "      <td>403.374223</td>\n",
       "      <td>2</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>3254.160485</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "  Transaction ID  Age    Items   Monthly Income  Transaction Time  Record  \\\n",
       "0         TXN001    42       10            7313        627.668127       5   \n",
       "1         TXN002    24        8           17747        126.904567       3   \n",
       "2         TXN003    47       11           22845        873.469701       2   \n",
       "3         TXN004    50       11           18552        380.219428       7   \n",
       "4         TXN005    60        2           14439        403.374223       2   \n",
       "\n",
       "   Gender City Tier  Total Spend  \n",
       "0  Female    Tier 1  4198.385084  \n",
       "1  Female    Tier 2  4134.976648  \n",
       "2    Male    Tier 2  5166.614455  \n",
       "3  Female    Tier 1  7784.447676  \n",
       "4  Female    Tier 2  3254.160485  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy_gender = pd.get_dummies(df[\"Gender\"], prefix = \"Gender\")\n",
    "dummy_city_tier = pd.get_dummies(df[\"City Tier\"], prefix = \"City\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gender_Female</th>\n",
       "      <th>Gender_Male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <th>2</th>\n",
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       "      <th>3</th>\n",
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       "      <th>4</th>\n",
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      ],
      "text/plain": [
       "   Gender_Female  Gender_Male\n",
       "0              1            0\n",
       "1              1            0\n",
       "2              0            1\n",
       "3              1            0\n",
       "4              1            0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_gender.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>City_Tier 1</th>\n",
       "      <th>City_Tier 2</th>\n",
       "      <th>City_Tier 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>3</th>\n",
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      ],
      "text/plain": [
       "   City_Tier 1  City_Tier 2  City_Tier 3\n",
       "0            1            0            0\n",
       "1            0            1            0\n",
       "2            0            1            0\n",
       "3            1            0            0\n",
       "4            0            1            0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_city_tier.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Transaction ID',\n",
       " 'Age ',\n",
       " ' Items ',\n",
       " 'Monthly Income',\n",
       " 'Transaction Time',\n",
       " 'Record',\n",
       " 'Gender',\n",
       " 'City Tier',\n",
       " 'Total Spend']"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "column_names = df.columns.values.tolist()\n",
    "column_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Monthly Income</th>\n",
       "      <th>Transaction Time</th>\n",
       "      <th>Record</th>\n",
       "      <th>Gender</th>\n",
       "      <th>City Tier</th>\n",
       "      <th>Total Spend</th>\n",
       "      <th>Gender_Female</th>\n",
       "      <th>Gender_Male</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>TXN001</td>\n",
       "      <td>42</td>\n",
       "      <td>10</td>\n",
       "      <td>7313</td>\n",
       "      <td>627.668127</td>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>4198.385084</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>126.904567</td>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>4134.976648</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>11</td>\n",
       "      <td>22845</td>\n",
       "      <td>873.469701</td>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>5166.614455</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>TXN004</td>\n",
       "      <td>50</td>\n",
       "      <td>11</td>\n",
       "      <td>18552</td>\n",
       "      <td>380.219428</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7784.447676</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>TXN005</td>\n",
       "      <td>60</td>\n",
       "      <td>2</td>\n",
       "      <td>14439</td>\n",
       "      <td>403.374223</td>\n",
       "      <td>2</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>3254.160485</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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      ],
      "text/plain": [
       "  Transaction ID  Age    Items   Monthly Income  Transaction Time  Record  \\\n",
       "0         TXN001    42       10            7313        627.668127       5   \n",
       "1         TXN002    24        8           17747        126.904567       3   \n",
       "2         TXN003    47       11           22845        873.469701       2   \n",
       "3         TXN004    50       11           18552        380.219428       7   \n",
       "4         TXN005    60        2           14439        403.374223       2   \n",
       "\n",
       "   Gender City Tier  Total Spend  Gender_Female  Gender_Male  \n",
       "0  Female    Tier 1  4198.385084              1            0  \n",
       "1  Female    Tier 2  4134.976648              1            0  \n",
       "2    Male    Tier 2  5166.614455              0            1  \n",
       "3  Female    Tier 1  7784.447676              1            0  \n",
       "4  Female    Tier 2  3254.160485              1            0  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new = df[column_names].join(dummy_gender)\n",
    "column_names = df_new.columns.values.tolist()\n",
    "df_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "      <td>11</td>\n",
       "      <td>22845</td>\n",
       "      <td>873.469701</td>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>5166.614455</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <th>3</th>\n",
       "      <td>TXN004</td>\n",
       "      <td>50</td>\n",
       "      <td>11</td>\n",
       "      <td>18552</td>\n",
       "      <td>380.219428</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7784.447676</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>TXN005</td>\n",
       "      <td>60</td>\n",
       "      <td>2</td>\n",
       "      <td>14439</td>\n",
       "      <td>403.374223</td>\n",
       "      <td>2</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>3254.160485</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Transaction ID  Age    Items   Monthly Income  Transaction Time  Record  \\\n",
       "0         TXN001    42       10            7313        627.668127       5   \n",
       "1         TXN002    24        8           17747        126.904567       3   \n",
       "2         TXN003    47       11           22845        873.469701       2   \n",
       "3         TXN004    50       11           18552        380.219428       7   \n",
       "4         TXN005    60        2           14439        403.374223       2   \n",
       "\n",
       "   Gender City Tier  Total Spend  Gender_Female  Gender_Male  City_Tier 1  \\\n",
       "0  Female    Tier 1  4198.385084              1            0            1   \n",
       "1  Female    Tier 2  4134.976648              1            0            0   \n",
       "2    Male    Tier 2  5166.614455              0            1            0   \n",
       "3  Female    Tier 1  7784.447676              1            0            1   \n",
       "4  Female    Tier 2  3254.160485              1            0            0   \n",
       "\n",
       "   City_Tier 2  City_Tier 3  \n",
       "0            0            0  \n",
       "1            1            0  \n",
       "2            1            0  \n",
       "3            0            0  \n",
       "4            1            0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new = df_new[column_names].join(dummy_city_tier)\n",
    "df_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_cols = [\"Monthly Income\", \"Transaction Time\", \n",
    "                \"Gender_Female\", \"Gender_Male\", \n",
    "                \"City_Tier 1\", \"City_Tier 2\", \"City_Tier 3\",\n",
    "                \"Record\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df_new[feature_cols]\n",
    "Y = df_new[\"Total Spend\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-79.41713030137362\n",
      "[ 1.47538980e-01  1.54946125e-01 -1.31025013e+02  1.31025013e+02\n",
      "  7.67643260e+01  5.51389743e+01 -1.31903300e+02  7.72233446e+02]\n"
     ]
    }
   ],
   "source": [
    "print(lm.intercept_)\n",
    "print(lm.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Monthly Income', 0.14753898049205738),\n",
       " ('Transaction Time', 0.15494612549589545),\n",
       " ('Gender_Female', -131.02501325554567),\n",
       " ('Gender_Male', 131.0250132555456),\n",
       " ('City_Tier 1', 76.76432601049527),\n",
       " ('City_Tier 2', 55.138974309232474),\n",
       " ('City_Tier 3', -131.9033003197278),\n",
       " ('Record', 772.2334457445648)]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(zip(feature_cols, lm.coef_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9179923586131016"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El modelo puede ser escrito como:\n",
    "* Total_Spend = -79.41713030137362 + 'Monthly Income'* 0.14753898049205738 + 'Transaction Time'* 0.15494612549589545+'Gender_Female'* -131.02501325554567 + 'Gender_Male'* 131.0250132555456+'City_Tier 1'* 76.76432601049527 + 'City_Tier 2'* 55.138974309232474 + 'City_Tier 3'* -131.9033003197278+'Record'* 772.2334457445648\n",
    "    * Si es hombre y vive en CT1: Total_Spend = 128.37220896466724 + 'Monthly Income'* 0.14753898049205738 + 'Transaction Time'* 0.15494612549589545+'Record'* 772.2334457445648\n",
    "    * Si es hombre y vive en CT2: Total_Spend = 106.74685726340445 + 'Monthly Income'* 0.14753898049205738 + 'Transaction Time'* 0.15494612549589545 +'Record'* 772.2334457445648\n",
    "    * Si es hombre y vive en CT3: Total_Spend = -80.29541736555583 + 'Monthly Income'* 0.14753898049205738 + 'Transaction Time'* 0.15494612549589545+'Record'* 772.2334457445648\n",
    "    * Si es mujer y vive en CT1: Total_Spend = -79.41713030137362 + 'Monthly Income'* 0.14753898049205738 + 'Transaction Time'* 0.15494612549589545 - 131.0250132555456+ 76.76432601049527 +'Record'* 772.2334457445648\n",
    "    * Si es mujer y vive en CT2: Total_Spend = -79.41713030137362 + 'Monthly Income'* 0.14753898049205738 + 'Transaction Time'* 0.15494612549589545 - 131.0250132555456+ 55.138974309232474  +'Record'* 772.2334457445648\n",
    "    * Si es mujer y vive en CT3: Total_Spend = -79.41713030137362 + 'Monthly Income'* 0.14753898049205738 + 'Transaction Time'* 0.15494612549589545 - 131.0250132555456-131.9033003197278 +'Record'* 772.2334457445648"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-80.29541736555583"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " -79.41713030137362 + 131.0250132555456-131.9033003197278"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_new[\"prediction\"] = -79.41713030137362 + df_new['Monthly Income']*0.14753898049205738 + df_new['Transaction Time']* 0.15494612549589545+ df_new['Gender_Female'] * (-131.02501325554567) + df_new['Gender_Male'] * 131.0250132555456+ df_new['City_Tier 1']* 76.76432601049527 +  df_new['City_Tier 2']* 55.138974309232474 + df_new['City_Tier 3']* (-131.9033003197278)+ df_new['Record']* 772.2334457445648"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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>Transaction ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Items</th>\n",
       "      <th>Monthly Income</th>\n",
       "      <th>Transaction Time</th>\n",
       "      <th>Record</th>\n",
       "      <th>Gender</th>\n",
       "      <th>City Tier</th>\n",
       "      <th>Total Spend</th>\n",
       "      <th>Gender_Female</th>\n",
       "      <th>Gender_Male</th>\n",
       "      <th>City_Tier 1</th>\n",
       "      <th>City_Tier 2</th>\n",
       "      <th>City_Tier 3</th>\n",
       "      <th>prediction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>TXN001</td>\n",
       "      <td>42</td>\n",
       "      <td>10</td>\n",
       "      <td>7313</td>\n",
       "      <td>627.668127</td>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>4198.385084</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4903.696720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>TXN002</td>\n",
       "      <td>24</td>\n",
       "      <td>8</td>\n",
       "      <td>17747</td>\n",
       "      <td>126.904567</td>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>4134.976648</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4799.434826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>TXN003</td>\n",
       "      <td>47</td>\n",
       "      <td>11</td>\n",
       "      <td>22845</td>\n",
       "      <td>873.469701</td>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>5166.614455</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>5157.082504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>TXN004</td>\n",
       "      <td>50</td>\n",
       "      <td>11</td>\n",
       "      <td>18552</td>\n",
       "      <td>380.219428</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7784.447676</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8068.012996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>TXN005</td>\n",
       "      <td>60</td>\n",
       "      <td>2</td>\n",
       "      <td>14439</td>\n",
       "      <td>403.374223</td>\n",
       "      <td>2</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>3254.160485</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3581.980335</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Transaction ID  Age    Items   Monthly Income  Transaction Time  Record  \\\n",
       "0         TXN001    42       10            7313        627.668127       5   \n",
       "1         TXN002    24        8           17747        126.904567       3   \n",
       "2         TXN003    47       11           22845        873.469701       2   \n",
       "3         TXN004    50       11           18552        380.219428       7   \n",
       "4         TXN005    60        2           14439        403.374223       2   \n",
       "\n",
       "   Gender City Tier  Total Spend  Gender_Female  Gender_Male  City_Tier 1  \\\n",
       "0  Female    Tier 1  4198.385084              1            0            1   \n",
       "1  Female    Tier 2  4134.976648              1            0            0   \n",
       "2    Male    Tier 2  5166.614455              0            1            0   \n",
       "3  Female    Tier 1  7784.447676              1            0            1   \n",
       "4  Female    Tier 2  3254.160485              1            0            0   \n",
       "\n",
       "   City_Tier 2  City_Tier 3   prediction  \n",
       "0            0            0  4903.696720  \n",
       "1            1            0  4799.434826  \n",
       "2            1            0  5157.082504  \n",
       "3            0            0  8068.012996  \n",
       "4            1            0  3581.980335  "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "SSD = np.sum((df_new[\"prediction\"] - df_new[\"Total Spend\"])**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1517733985.3408163"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "RSE = np.sqrt(SSD/(len(df_new)-len(feature_cols)-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "803.1318809818165"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales_mean=np.mean(df_new[\"Total Spend\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6163.176415976714"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sales_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "error = RSE/sales_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.031135680294161"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eliminar variables dummy redundantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "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>Gender_Male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender_Male\n",
       "0            0\n",
       "1            0\n",
       "2            1\n",
       "3            0\n",
       "4            0"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_gender = pd.get_dummies(df[\"Gender\"], prefix=\"Gender\").iloc[:,1:]\n",
    "dummy_gender.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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>City_Tier 2</th>\n",
       "      <th>City_Tier 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   City_Tier 2  City_Tier 3\n",
       "0            0            0\n",
       "1            1            0\n",
       "2            1            0\n",
       "3            0            0\n",
       "4            1            0"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_city_tier = pd.get_dummies(df[\"City Tier\"], prefix=\"City\").iloc[:,1:]\n",
    "dummy_city_tier.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "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",
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Transaction ID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Items</th>\n",
       "      <th>Monthly Income</th>\n",
       "      <th>Transaction Time</th>\n",
       "      <th>Record</th>\n",
       "      <th>Gender</th>\n",
       "      <th>City Tier</th>\n",
       "      <th>Total Spend</th>\n",
       "      <th>Gender_Male</th>\n",
       "      <th>City_Tier 2</th>\n",
       "      <th>City_Tier 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>TXN001</td>\n",
       "      <td>42</td>\n",
       "      <td>10</td>\n",
       "      <td>7313</td>\n",
       "      <td>627.668127</td>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>4198.385084</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>TXN002</td>\n",
       "      <td>24</td>\n",
       "      <td>8</td>\n",
       "      <td>17747</td>\n",
       "      <td>126.904567</td>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>4134.976648</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>TXN003</td>\n",
       "      <td>47</td>\n",
       "      <td>11</td>\n",
       "      <td>22845</td>\n",
       "      <td>873.469701</td>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>5166.614455</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>TXN004</td>\n",
       "      <td>50</td>\n",
       "      <td>11</td>\n",
       "      <td>18552</td>\n",
       "      <td>380.219428</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7784.447676</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>TXN005</td>\n",
       "      <td>60</td>\n",
       "      <td>2</td>\n",
       "      <td>14439</td>\n",
       "      <td>403.374223</td>\n",
       "      <td>2</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>3254.160485</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Transaction ID  Age    Items   Monthly Income  Transaction Time  Record  \\\n",
       "0         TXN001    42       10            7313        627.668127       5   \n",
       "1         TXN002    24        8           17747        126.904567       3   \n",
       "2         TXN003    47       11           22845        873.469701       2   \n",
       "3         TXN004    50       11           18552        380.219428       7   \n",
       "4         TXN005    60        2           14439        403.374223       2   \n",
       "\n",
       "   Gender City Tier  Total Spend  Gender_Male  City_Tier 2  City_Tier 3  \n",
       "0  Female    Tier 1  4198.385084            0            0            0  \n",
       "1  Female    Tier 2  4134.976648            0            1            0  \n",
       "2    Male    Tier 2  5166.614455            1            1            0  \n",
       "3  Female    Tier 1  7784.447676            0            0            0  \n",
       "4  Female    Tier 2  3254.160485            0            1            0  "
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "column_names = df.columns.values.tolist()\n",
    "df_new = df[column_names].join(dummy_gender)\n",
    "column_names = df_new.columns.values.tolist()\n",
    "df_new = df_new[column_names].join(dummy_city_tier)\n",
    "df_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_cols = [\"Monthly Income\", \"Transaction Time\", \"Gender_Male\", \"City_Tier 2\", \"City_Tier 3\", \"Record\"]\n",
    "X = df_new[feature_cols]\n",
    "Y = df_new[\"Total Spend\"]\n",
    "lm = LinearRegression()\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-133.67781754642056\n"
     ]
    }
   ],
   "source": [
    "print(lm.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Monthly Income', 0.14753898049205744),\n",
       " ('Transaction Time', 0.15494612549589631),\n",
       " ('Gender_Male', 262.05002651109595),\n",
       " ('City_Tier 2', -21.62535170126296),\n",
       " ('City_Tier 3', -208.66762633022324),\n",
       " ('Record', 772.2334457445635)]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(zip(feature_cols, lm.coef_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9179923586131016"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coeficientes con todas las variables en el modelo\n",
    "* ('Monthly Income', 0.14753898049205738),\n",
    "* ('Transaction Time', 0.15494612549589545),\n",
    "* ('Gender_Female', -131.02501325554567),\n",
    "* ('Gender_Male', 131.0250132555456),\n",
    "* ('City_Tier 1', 76.76432601049527),\n",
    "* ('City_Tier 2', 55.138974309232474),\n",
    "* ('City_Tier 3', -131.9033003197278),\n",
    "* ('Record', 772.2334457445648)\n",
    " \n",
    " Coeficientes tras enmascarar las variables dummy pertinentes\n",
    "* 'Monthly Income', 0.14753898049205744),\n",
    "* ('Transaction Time', 0.15494612549589631),\n",
    "* ('Gender_Male', 262.05002651109595),\n",
    "* ('City_Tier 2', -21.62535170126296),\n",
    "* ('City_Tier 3', -208.66762633022324),\n",
    "* ('Record', 772.2334457445635)]\n",
    "\n",
    "Los cambios se reflejan en\n",
    "* Gender_Male: \n",
    "    * antes -> 131.02, \n",
    "    * después -> 262.05 = ( 131.02 - (-131.02))\n",
    "* Gender_Female: \n",
    "    * antes -> -131.02,\n",
    "    * después -> 0\n",
    "* CT1: \n",
    "    * antes -> 76.76,\n",
    "    * después -> 0\n",
    "* CT2: \n",
    "    * antes -> 55.13, \n",
    "    * después -> -21.62 = (55.13 - 76.76)\n",
    "* CT3: \n",
    "    * antes -> -131.90, \n",
    "    * después -> -208.66 = (-131.90 - 76.76)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformación de variables para conseguir una relación no lineal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model year</th>\n",
       "      <th>origin</th>\n",
       "      <th>car name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165.0</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration  \\\n",
       "0  18.0          8         307.0       130.0    3504          12.0   \n",
       "1  15.0          8         350.0       165.0    3693          11.5   \n",
       "2  18.0          8         318.0       150.0    3436          11.0   \n",
       "3  16.0          8         304.0       150.0    3433          12.0   \n",
       "4  17.0          8         302.0       140.0    3449          10.5   \n",
       "\n",
       "   model year  origin                   car name  \n",
       "0          70       1  chevrolet chevelle malibu  \n",
       "1          70       1          buick skylark 320  \n",
       "2          70       1         plymouth satellite  \n",
       "3          70       1              amc rebel sst  \n",
       "4          70       1                ford torino  "
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto = pd.read_csv(\"../datasets/auto/auto-mpg.csv\")\n",
    "data_auto.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(406, 9)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'CV vs MPG')"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a19a7b668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "data_auto[\"mpg\"] = data_auto[\"mpg\"].dropna()\n",
    "data_auto[\"horsepower\"] = data_auto[\"horsepower\"].dropna()\n",
    "plt.plot(data_auto[\"horsepower\"], data_auto[\"mpg\"], \"ro\")\n",
    "plt.xlabel(\"Caballos de Potencia\")\n",
    "plt.ylabel(\"Consumo (millas por galeón)\")\n",
    "plt.title(\"CV vs MPG\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modelo de regresión lineal\n",
    "* mpg = a + b * horsepower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data_auto[\"horsepower\"].fillna(data_auto[\"horsepower\"].mean())\n",
    "Y = data_auto[\"mpg\"].fillna(data_auto[\"mpg\"].mean())\n",
    "X_data = X[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm.fit(X_data,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.series.Series"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(X_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1b7ee978>]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1e7135f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.plot(X,Y, \"ro\")\n",
    "plt.plot(X, lm.predict(X_data), color=\"blue\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.574653340645025"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X_data, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10315.75196006092, 5.046879480825511, 23.51457286432162, 21.46277336163346)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SSD = np.sum((Y - lm.predict(X_data))**2)\n",
    "RSE = np.sqrt(SSD/(len(X_data)-1))\n",
    "y_mean = np.mean(Y)\n",
    "error = RSE/y_mean\n",
    "SSD, RSE, y_mean, error*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modelo de regresión cuadrático\n",
    "* mpg = a + b * horsepower^2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_data = X**2\n",
    "X_data = X_data[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm.fit(X_data, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4849887034823205"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X_data, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12490.350340501926, 5.553410772769817, 23.51457286432162, 23.6168898529981)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SSD = np.sum((Y - lm.predict(X_data))**2)\n",
    "RSE = np.sqrt(SSD/(len(X_data)-1))\n",
    "y_mean = np.mean(Y)\n",
    "error = RSE/y_mean\n",
    "SSD, RSE, y_mean, error*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modelo de regresión  lineal y cuadrático\n",
    "* mpg = a + b * horsepower + c * horsepower^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_data = poly.fit_transform(X[:,np.newaxis])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = linear_model.LinearRegression()\n",
    "lm.fit(X_data, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6439066584257469"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X_data, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.026192447080355"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        , -0.43404318,  0.00112615])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mpg = 55.026 -0.434 * hp + 0.00112615 * hp^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regresión de grado 2\n",
      "R2:0.6439066584257469\n",
      "55.026192447080355\n",
      "[ 0.         -0.43404318  0.00112615]\n",
      "SSD: 8636.180643524502, RSE: 4.61778115803654, Y_mean: 23.51457286432162, error: 19.63795466190689%\n",
      "Regresión de grado 3\n",
      "R2:0.6444678885560742\n",
      "58.44877411191809\n",
      "[ 0.00000000e+00 -5.27113167e-01  1.89736722e-03 -1.95723195e-06]\n",
      "SSD: 8622.569367428552, RSE: 4.614140736300908, Y_mean: 23.51457286432162, error: 19.622473106036676%\n",
      "Regresión de grado 4\n",
      "R2:0.6467674189704502\n",
      "40.096643850138875\n",
      "[ 0.00000000e+00  1.62563541e-01 -7.10892744e-03  4.65580255e-05\n",
      " -9.15840093e-08]\n",
      "SSD: 8566.799832491353, RSE: 4.5991947315797574, Y_mean: 23.51457286432162, error: 19.55891250126878%\n",
      "Regresión de grado 5\n",
      "R2:0.6547512490679683\n",
      "-40.693829800815294\n",
      "[ 0.00000000e+00  4.00021432e+00 -7.54801920e-02  6.19621368e-04\n",
      " -2.36220932e-06  3.41982976e-09]\n",
      "SSD: 8373.171390452659, RSE: 4.546921734577904, Y_mean: 23.51457286432162, error: 19.336612069517507%\n",
      "Regresión de grado 6\n",
      "R2:0.6572895595307906\n",
      "-157.06800537233534\n",
      "[ 0.00000000e+00  1.07623362e+01 -2.30128490e-01  2.40537374e-03\n",
      " -1.33773684e-05  3.79725580e-08 -4.32494610e-11]\n",
      "SSD: 8311.610824368023, RSE: 4.530176140354489, Y_mean: 23.51457286432162, error: 19.265398382923937%\n",
      "Regresión de grado 7\n",
      "R2:0.6538574297764823\n",
      "14.78101556705461\n",
      "[ 0.00000000e+00  1.14612741e-03  4.31542691e-02 -1.25404186e-03\n",
      "  1.46299381e-05 -8.50482922e-08  2.45097435e-10 -2.79311454e-13]\n",
      "SSD: 8394.848810282569, RSE: 4.552803724495941, Y_mean: 23.51457286432162, error: 19.361626301976575%\n",
      "Regresión de grado 8\n",
      "R2:0.651243218495551\n",
      "36.40672952320243\n",
      "[ 0.00000000e+00  4.43777164e-07  3.03135040e-06  8.84885484e-05\n",
      " -3.97067205e-06  5.47393601e-08 -3.43825957e-10  1.02689459e-12\n",
      " -1.18561693e-15]\n",
      "SSD: 8458.250166687194, RSE: 4.569963710228768, Y_mean: 23.51457286432162, error: 19.43460226386982%\n",
      "Regresión de grado 9\n",
      "R2:0.651053631916962\n",
      "39.46643472093898\n",
      "[ 0.00000000e+00 -7.79795260e-09 -1.27929387e-09 -6.48447884e-08\n",
      " -1.77132827e-06  3.55551206e-08 -3.00241201e-10  1.32278884e-12\n",
      " -3.04048282e-15  2.92448674e-18]\n",
      "SSD: 8462.848129493923, RSE: 4.571205673276188, Y_mean: 23.51457286432162, error: 19.439883937726222%\n",
      "Regresión de grado 10\n",
      "R2:0.6523570737818101\n",
      "38.44031944400909\n",
      "[ 0.00000000e+00 -1.18966016e-09 -9.07249391e-13 -2.72052174e-11\n",
      " -1.29822393e-09 -3.51557922e-08  8.70014514e-10 -8.86586743e-12\n",
      "  4.60157706e-14 -1.20803538e-16  1.27732473e-19]\n",
      "SSD: 8431.236307286306, RSE: 4.562660126000871, Y_mean: 23.51457286432162, error: 19.403542442923726%\n",
      "Regresión de grado 11\n",
      "R2:0.6511663023950045\n",
      "36.41004334298087\n",
      "[ 0.00000000e+00 -6.36130810e-12 -7.34513859e-15 -4.92520665e-15\n",
      " -3.14729648e-13 -1.49252137e-11 -4.09650002e-10  1.04700269e-11\n",
      " -1.08552700e-13  5.67263121e-16 -1.48811921e-18  1.56362003e-21]\n",
      "SSD: 8460.115580221123, RSE: 4.570467620731048, Y_mean: 23.51457286432162, error: 19.436745234976236%\n"
     ]
    }
   ],
   "source": [
    "for d in range(2,12):\n",
    "    poly = PolynomialFeatures(degree=d)\n",
    "    X_data = poly.fit_transform(X[:,np.newaxis])\n",
    "    lm = linear_model.LinearRegression()\n",
    "    lm.fit(X_data, Y)\n",
    "    print(\"Regresión de grado \"+str(d))\n",
    "    print(\"R2:\" +str(lm.score(X_data, Y)))\n",
    "    print(lm.intercept_)\n",
    "    print(lm.coef_)\n",
    "    regresion_validation(X_data, Y, lm.predict(X_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regresion_validation(X_data, Y, Y_pred):\n",
    "    SSD = np.sum((Y - Y_pred)**2)\n",
    "    RSE = np.sqrt(SSD/(len(X_data)-1))\n",
    "    y_mean = np.mean(Y)\n",
    "    error = RSE/y_mean\n",
    "    print(\"SSD: \"+str(SSD)+\", RSE: \" +str(RSE) + \", Y_mean: \" +str(y_mean) +\", error: \" + str(error*100)+ \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "source": [
    "print(regresion_validation(lm, X_data, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# El problema de los outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1f7e97b8>]"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1f05e5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data_auto[\"displacement\"], data_auto[\"mpg\"], \"ro\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data_auto[\"displacement\"].fillna(data_auto[\"displacement\"].mean())\n",
    "X = X[:,np.newaxis]\n",
    "Y = data_auto[\"mpg\"].fillna(data_auto[\"mpg\"].mean())\n",
    "\n",
    "lm = LinearRegression()\n",
    "lm.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6261049762826918"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1e713080>]"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2090bdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.plot(X,Y, \"ro\")\n",
    "plt.plot(X, lm.predict(X), color=\"blue\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model year</th>\n",
       "      <th>origin</th>\n",
       "      <th>car name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>395</th>\n",
       "      <td>38.0</td>\n",
       "      <td>6</td>\n",
       "      <td>262.0</td>\n",
       "      <td>85.0</td>\n",
       "      <td>3015</td>\n",
       "      <td>17.0</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>oldsmobile cutlass ciera (diesel)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mpg  cylinders  displacement  horsepower  weight  acceleration  \\\n",
       "395  38.0          6         262.0        85.0    3015          17.0   \n",
       "\n",
       "     model year  origin                           car name  \n",
       "395          82       1  oldsmobile cutlass ciera (diesel)  "
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto[(data_auto[\"displacement\"]>250)&(data_auto[\"mpg\"]>35)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model year</th>\n",
       "      <th>origin</th>\n",
       "      <th>car name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>258</th>\n",
       "      <td>20.2</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>139.0</td>\n",
       "      <td>3570</td>\n",
       "      <td>12.8</td>\n",
       "      <td>78</td>\n",
       "      <td>1</td>\n",
       "      <td>mercury monarch ghia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>305</th>\n",
       "      <td>23.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>125.0</td>\n",
       "      <td>3900</td>\n",
       "      <td>17.4</td>\n",
       "      <td>79</td>\n",
       "      <td>1</td>\n",
       "      <td>cadillac eldorado</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>372</th>\n",
       "      <td>26.6</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>105.0</td>\n",
       "      <td>3725</td>\n",
       "      <td>19.0</td>\n",
       "      <td>81</td>\n",
       "      <td>1</td>\n",
       "      <td>oldsmobile cutlass ls</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mpg  cylinders  displacement  horsepower  weight  acceleration  \\\n",
       "258  20.2          8         302.0       139.0    3570          12.8   \n",
       "305  23.0          8         350.0       125.0    3900          17.4   \n",
       "372  26.6          8         350.0       105.0    3725          19.0   \n",
       "\n",
       "     model year  origin               car name  \n",
       "258          78       1   mercury monarch ghia  \n",
       "305          79       1      cadillac eldorado  \n",
       "372          81       1  oldsmobile cutlass ls  "
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto[(data_auto[\"displacement\"]>300)&(data_auto[\"mpg\"]>20)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_auto_clean = data_auto.drop([395, 258, 305, 372])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data_auto_clean[\"displacement\"].fillna(data_auto_clean[\"displacement\"].mean())\n",
    "X = X[:,np.newaxis]\n",
    "Y = data_auto_clean[\"mpg\"].fillna(data_auto_clean[\"mpg\"].mean())\n",
    "\n",
    "lm = LinearRegression()\n",
    "lm.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6466514317531822"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a20a61e48>]"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2081b128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.plot(X,Y, \"ro\")\n",
    "plt.plot(X, lm.predict(X), color=\"blue\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}