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": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_csv('../GitHub/python-ml-course/datasets/ecom-expense/Ecom Expense.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Transaction ID</th>\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",
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       "...             ...   ...      ...             ...               ...     ...   \n",
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       "2360        TXN2361    45       12           19294        658.439838       7   \n",
       "2361        TXN2362    46        7            2855        560.514341       8   \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  \n",
       "...      ...       ...          ...  \n",
       "2357    Male    Tier 2  2909.619546  \n",
       "2358    Male    Tier 2  7968.633136  \n",
       "2359  Female    Tier 3  8816.406448  \n",
       "2360  Female    Tier 1  7915.595856  \n",
       "2361    Male    Tier 1  6832.401686  \n",
       "\n",
       "[2362 rows x 9 columns]"
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": 5,
   "metadata": {},
   "outputs": [
    {
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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\n",
       "...           ...          ...          ...\n",
       "2357            0            1            0\n",
       "2358            0            1            0\n",
       "2359            0            0            1\n",
       "2360            1            0            0\n",
       "2361            1            0            0\n",
       "\n",
       "[2362 rows x 3 columns]"
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     "execution_count": 5,
     "metadata": {},
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   "source": [
    "dummy_city_tier"
   ]
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  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols=df.columns.values.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_new=df[cols].join(dummy_gender)\n",
    "cols=df_new.columns.values.tolist()\n",
    "df_new=df_new[cols].join(dummy_city_tier)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "      <td>46</td>\n",
       "      <td>7</td>\n",
       "      <td>2855</td>\n",
       "      <td>560.514341</td>\n",
       "      <td>8</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>6832.401686</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2362 rows × 14 columns</p>\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",
       "2357        TXN2358    50        7            5705        460.157207       3   \n",
       "2358        TXN2359    35       11           11202        851.924751       8   \n",
       "2359        TXN2360    27        5           21335        435.145358       8   \n",
       "2360        TXN2361    45       12           19294        658.439838       7   \n",
       "2361        TXN2362    46        7            2855        560.514341       8   \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",
       "2357    Male    Tier 2  2909.619546              0            1            0   \n",
       "2358    Male    Tier 2  7968.633136              0            1            0   \n",
       "2359  Female    Tier 3  8816.406448              1            0            0   \n",
       "2360  Female    Tier 1  7915.595856              1            0            1   \n",
       "2361    Male    Tier 1  6832.401686              0            1            1   \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  \n",
       "...           ...          ...  \n",
       "2357            1            0  \n",
       "2358            1            0  \n",
       "2359            0            1  \n",
       "2360            0            0  \n",
       "2361            0            0  \n",
       "\n",
       "[2362 rows x 14 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_cols=cols[3:5]+df_new.columns.values.tolist()[-5:]+[\"Record\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Monthly Income',\n",
       " 'Transaction Time',\n",
       " 'Gender_Female',\n",
       " 'Gender_Male',\n",
       " 'City_Tier 1',\n",
       " 'City_Tier 2',\n",
       " 'City_Tier 3',\n",
       " 'Record']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=df_new[feature_cols]\n",
    "Y=df_new[\"Total Spend\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm=LinearRegression()\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-79.41713030137544,\n",
       " array([ 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",
       " 0.9179923586131016)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_,lm.coef_,lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Monthly Income', 0.14753898049205746),\n",
       " ('Transaction Time', 0.15494612549589704),\n",
       " ('Gender_Female', -131.02501325554584),\n",
       " ('Gender_Male', 131.02501325554567),\n",
       " ('City_Tier 1', 76.76432601049501),\n",
       " ('City_Tier 2', 55.13897430923278),\n",
       " ('City_Tier 3', -131.90330031972783),\n",
       " ('Record', 772.233445744565)]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(zip(feature_cols,lm.coef_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "predic=np.ones((len(df_new.Gender_Female)))\n",
    "for x in range (0,len(predic)):\n",
    "    b=0\n",
    "    for i,j in zip(feature_cols,lm.coef_):\n",
    "        b+=df_new[i].loc[x]*j\n",
    "    predic[x]=lm.intercept_+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
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       "<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>pred</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",
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       "    <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",
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       "    <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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2357</th>\n",
       "      <td>TXN2358</td>\n",
       "      <td>50</td>\n",
       "      <td>7</td>\n",
       "      <td>5705</td>\n",
       "      <td>460.157207</td>\n",
       "      <td>3</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>2909.619546</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3336.456655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2358</th>\n",
       "      <td>TXN2359</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>11202</td>\n",
       "      <td>851.924751</td>\n",
       "      <td>8</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>7968.633136</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>8069.348522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2359</th>\n",
       "      <td>TXN2360</td>\n",
       "      <td>27</td>\n",
       "      <td>5</td>\n",
       "      <td>21335</td>\n",
       "      <td>435.145358</td>\n",
       "      <td>8</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 3</td>\n",
       "      <td>8816.406448</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9050.690358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <td>TXN2361</td>\n",
       "      <td>45</td>\n",
       "      <td>12</td>\n",
       "      <td>19294</td>\n",
       "      <td>658.439838</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7915.595856</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8220.596094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2361</th>\n",
       "      <td>TXN2362</td>\n",
       "      <td>46</td>\n",
       "      <td>7</td>\n",
       "      <td>2855</td>\n",
       "      <td>560.514341</td>\n",
       "      <td>8</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>6832.401686</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6814.313090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2362 rows × 15 columns</p>\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",
       "2357        TXN2358    50        7            5705        460.157207       3   \n",
       "2358        TXN2359    35       11           11202        851.924751       8   \n",
       "2359        TXN2360    27        5           21335        435.145358       8   \n",
       "2360        TXN2361    45       12           19294        658.439838       7   \n",
       "2361        TXN2362    46        7            2855        560.514341       8   \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",
       "2357    Male    Tier 2  2909.619546              0            1            0   \n",
       "2358    Male    Tier 2  7968.633136              0            1            0   \n",
       "2359  Female    Tier 3  8816.406448              1            0            0   \n",
       "2360  Female    Tier 1  7915.595856              1            0            1   \n",
       "2361    Male    Tier 1  6832.401686              0            1            1   \n",
       "\n",
       "      City_Tier 2  City_Tier 3         pred  \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  \n",
       "...           ...          ...          ...  \n",
       "2357            1            0  3336.456655  \n",
       "2358            1            0  8069.348522  \n",
       "2359            0            1  9050.690358  \n",
       "2360            0            0  8220.596094  \n",
       "2361            0            0  6814.313090  \n",
       "\n",
       "[2362 rows x 15 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new['pred']=predic\n",
    "df_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "SSD=sum((df_new.pred-df_new[\"Total Spend\"])**2)\n",
    "RSE=np.sqrt(SSD/(len(df_new)-len(feature_cols)-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "803.1318809818156"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13031135680294145"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error=RSE/np.mean(df_new[\"Total Spend\"])\n",
    "error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_new[\"prediction\"] = lm.predict(pd.DataFrame(df_new[feature_cols]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
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       "      <th>Gender_Male</th>\n",
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       "      <th>City_Tier 2</th>\n",
       "      <th>City_Tier 3</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>TXN001</td>\n",
       "      <td>42</td>\n",
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       "      <td>627.668127</td>\n",
       "      <td>5</td>\n",
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       "      <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",
       "      <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",
       "      <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",
       "      <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",
       "      <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",
       "      <td>3581.980335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2357</th>\n",
       "      <td>TXN2358</td>\n",
       "      <td>50</td>\n",
       "      <td>7</td>\n",
       "      <td>5705</td>\n",
       "      <td>460.157207</td>\n",
       "      <td>3</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>2909.619546</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3336.456655</td>\n",
       "      <td>3336.456655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2358</th>\n",
       "      <td>TXN2359</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>11202</td>\n",
       "      <td>851.924751</td>\n",
       "      <td>8</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>7968.633136</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>8069.348522</td>\n",
       "      <td>8069.348522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2359</th>\n",
       "      <td>TXN2360</td>\n",
       "      <td>27</td>\n",
       "      <td>5</td>\n",
       "      <td>21335</td>\n",
       "      <td>435.145358</td>\n",
       "      <td>8</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 3</td>\n",
       "      <td>8816.406448</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9050.690358</td>\n",
       "      <td>9050.690358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <td>TXN2361</td>\n",
       "      <td>45</td>\n",
       "      <td>12</td>\n",
       "      <td>19294</td>\n",
       "      <td>658.439838</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7915.595856</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8220.596094</td>\n",
       "      <td>8220.596094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2361</th>\n",
       "      <td>TXN2362</td>\n",
       "      <td>46</td>\n",
       "      <td>7</td>\n",
       "      <td>2855</td>\n",
       "      <td>560.514341</td>\n",
       "      <td>8</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>6832.401686</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6814.313090</td>\n",
       "      <td>6814.313090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2362 rows × 16 columns</p>\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",
       "2357        TXN2358    50        7            5705        460.157207       3   \n",
       "2358        TXN2359    35       11           11202        851.924751       8   \n",
       "2359        TXN2360    27        5           21335        435.145358       8   \n",
       "2360        TXN2361    45       12           19294        658.439838       7   \n",
       "2361        TXN2362    46        7            2855        560.514341       8   \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",
       "2357    Male    Tier 2  2909.619546              0            1            0   \n",
       "2358    Male    Tier 2  7968.633136              0            1            0   \n",
       "2359  Female    Tier 3  8816.406448              1            0            0   \n",
       "2360  Female    Tier 1  7915.595856              1            0            1   \n",
       "2361    Male    Tier 1  6832.401686              0            1            1   \n",
       "\n",
       "      City_Tier 2  City_Tier 3         pred   prediction  \n",
       "0               0            0  4903.696720  4903.696720  \n",
       "1               1            0  4799.434826  4799.434826  \n",
       "2               1            0  5157.082504  5157.082504  \n",
       "3               0            0  8068.012996  8068.012996  \n",
       "4               1            0  3581.980335  3581.980335  \n",
       "...           ...          ...          ...          ...  \n",
       "2357            1            0  3336.456655  3336.456655  \n",
       "2358            1            0  8069.348522  8069.348522  \n",
       "2359            0            1  9050.690358  9050.690358  \n",
       "2360            0            0  8220.596094  8220.596094  \n",
       "2361            0            0  6814.313090  6814.313090  \n",
       "\n",
       "[2362 rows x 16 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "Puede notarse que solo hacen falta *n-1* variables para una variable categórica de *n* niveles. Solo se necesitaria una para la variable **Gender** y 2 para **City Tier**. Por lo tanto se hace un enmascarado de las variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eliminar variables dummy redundantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy_gender=pd.get_dummies(df.Gender,prefix=\"Gender\").iloc[:,1:]\n",
    "dummy_city_tier=pd.get_dummies(df[\"City Tier\"],prefix=\"City\").iloc[:,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols=df.columns.values.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_new=df[cols].join(dummy_gender)\n",
    "cols=df_new.columns.values.tolist()\n",
    "df_new=df_new[cols].join(dummy_city_tier)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2357</th>\n",
       "      <td>TXN2358</td>\n",
       "      <td>50</td>\n",
       "      <td>7</td>\n",
       "      <td>5705</td>\n",
       "      <td>460.157207</td>\n",
       "      <td>3</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>2909.619546</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2358</th>\n",
       "      <td>TXN2359</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>11202</td>\n",
       "      <td>851.924751</td>\n",
       "      <td>8</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 2</td>\n",
       "      <td>7968.633136</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2359</th>\n",
       "      <td>TXN2360</td>\n",
       "      <td>27</td>\n",
       "      <td>5</td>\n",
       "      <td>21335</td>\n",
       "      <td>435.145358</td>\n",
       "      <td>8</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 3</td>\n",
       "      <td>8816.406448</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2360</th>\n",
       "      <td>TXN2361</td>\n",
       "      <td>45</td>\n",
       "      <td>12</td>\n",
       "      <td>19294</td>\n",
       "      <td>658.439838</td>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>7915.595856</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2361</th>\n",
       "      <td>TXN2362</td>\n",
       "      <td>46</td>\n",
       "      <td>7</td>\n",
       "      <td>2855</td>\n",
       "      <td>560.514341</td>\n",
       "      <td>8</td>\n",
       "      <td>Male</td>\n",
       "      <td>Tier 1</td>\n",
       "      <td>6832.401686</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2362 rows × 12 columns</p>\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",
       "2357        TXN2358    50        7            5705        460.157207       3   \n",
       "2358        TXN2359    35       11           11202        851.924751       8   \n",
       "2359        TXN2360    27        5           21335        435.145358       8   \n",
       "2360        TXN2361    45       12           19294        658.439838       7   \n",
       "2361        TXN2362    46        7            2855        560.514341       8   \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  \n",
       "...      ...       ...          ...          ...          ...          ...  \n",
       "2357    Male    Tier 2  2909.619546            1            1            0  \n",
       "2358    Male    Tier 2  7968.633136            1            1            0  \n",
       "2359  Female    Tier 3  8816.406448            0            0            1  \n",
       "2360  Female    Tier 1  7915.595856            0            0            0  \n",
       "2361    Male    Tier 1  6832.401686            1            0            0  \n",
       "\n",
       "[2362 rows x 12 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Monthly Income',\n",
       " 'Transaction Time',\n",
       " 'Gender_Male',\n",
       " 'City_Tier 2',\n",
       " 'City_Tier 3',\n",
       " 'Record']"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_cols=cols[3:5]+df_new.columns.values.tolist()[-3:]+[\"Record\"]\n",
    "feature_cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=df_new[feature_cols]\n",
    "Y=df_new[\"Total Spend\"]\n",
    "lm=LinearRegression()\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-133.67781754642238,\n",
       " array([ 1.47538980e-01,  1.54946125e-01,  2.62050027e+02, -2.16253517e+01,\n",
       "        -2.08667626e+02,  7.72233446e+02]),\n",
       " 0.9179923586131016)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_,lm.coef_,lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "cell_style": "center"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Monthly Income', 0.1475389804920575),\n",
       " ('Transaction Time', 0.1549461254958966),\n",
       " ('Gender_Male', 262.0500265110957),\n",
       " ('City_Tier 2', -21.625351701263007),\n",
       " ('City_Tier 3', -208.6676263302229),\n",
       " ('Record', 772.2334457445636)]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(zip(feature_cols,lm.coef_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9179923586131016"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sabiendo que la linea base es que sea mujer y viva en city tier 1 (Esto también se puede inferir porque son las varriables enmascaradas **Variables que no hacen parte del modelo**):\n",
    "* Gender_Male sería el coeficiente de un hombre que viviera en city tier 1\n",
    "* El de city tier 2 sería el de una mujer que vive en city tier 2 \n",
    "* El de city tier 3 sería el de una mujer que vive en city tier 3 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Antes del enmascarado:**\n",
    "\n",
    "* ('Monthly Income', 0.1475389804920575),\n",
    "* ('Transaction Time', 0.1549461254958966),\n",
    "* ('Gender_Male', 262.0500265110957),\n",
    "* ('City_Tier 2', -21.625351701263007),\n",
    "* ('City_Tier 3', -208.6676263302229),\n",
    "* ('Record', 772.2334457445636)]\n",
    "\n",
    "\n",
    "**Después del enmascarado:**\n",
    "\n",
    "* ('Monthly Income', 0.14753898049205746),\n",
    "* ('Transaction Time', 0.15494612549589704),\n",
    "* ('Gender_Female', -131.02501325554584),\n",
    "* ('Gender_Male', 131.02501325554567),\n",
    "* ('City_Tier 1', 76.76432601049501),\n",
    "* ('City_Tier 2', 55.13897430923278),\n",
    "* ('City_Tier 3', -131.90330031972783),\n",
    "* ('Record', 772.233445744565)]\n",
    "\n",
    "Los cambios entre antes y después del enmascarado se ve en:\n",
    "\n",
    "* Gender Male:\n",
    "    * Antes: 131.0250\n",
    "    * Después: 131.025 -(-131.025) = 262.05\n",
    "* City_Tier 2:\n",
    "    * Antes: 55.13\n",
    "    * Después:-21.62= 55.13 - 76.76 = -21.62\n",
    "* City_Tier 3:\n",
    "    * Antes: -131.90\n",
    "    * Después: -208.66 --> -131.90 - 76.76 = -208.66\n",
    "    \n",
    "Estos cambios se los lleva la ordenada en el origen (notar que el intercepto cambió"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformación de variables para conseguir una relación no lineal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_auto=pd.read_csv(\"../GitHub/python-ml-course/datasets/auto/auto-mpg.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>401</th>\n",
       "      <td>27.0</td>\n",
       "      <td>4</td>\n",
       "      <td>140.0</td>\n",
       "      <td>86.0</td>\n",
       "      <td>2790</td>\n",
       "      <td>15.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>ford mustang gl</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>402</th>\n",
       "      <td>44.0</td>\n",
       "      <td>4</td>\n",
       "      <td>97.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>2130</td>\n",
       "      <td>24.6</td>\n",
       "      <td>82</td>\n",
       "      <td>2</td>\n",
       "      <td>vw pickup</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>403</th>\n",
       "      <td>32.0</td>\n",
       "      <td>4</td>\n",
       "      <td>135.0</td>\n",
       "      <td>84.0</td>\n",
       "      <td>2295</td>\n",
       "      <td>11.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>dodge rampage</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>404</th>\n",
       "      <td>28.0</td>\n",
       "      <td>4</td>\n",
       "      <td>120.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>2625</td>\n",
       "      <td>18.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>ford ranger</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>405</th>\n",
       "      <td>31.0</td>\n",
       "      <td>4</td>\n",
       "      <td>119.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>2720</td>\n",
       "      <td>19.4</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>chevy s-10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>406 rows × 9 columns</p>\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",
       "401  27.0          4         140.0        86.0    2790          15.6   \n",
       "402  44.0          4          97.0        52.0    2130          24.6   \n",
       "403  32.0          4         135.0        84.0    2295          11.6   \n",
       "404  28.0          4         120.0        79.0    2625          18.6   \n",
       "405  31.0          4         119.0        82.0    2720          19.4   \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  \n",
       "..          ...     ...                        ...  \n",
       "401          82       1            ford mustang gl  \n",
       "402          82       2                  vw pickup  \n",
       "403          82       1              dodge rampage  \n",
       "404          82       1                ford ranger  \n",
       "405          82       1                 chevy s-10  \n",
       "\n",
       "[406 rows x 9 columns]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_auto.mpg=data_auto.mpg.dropna()\n",
    "data_auto.horsepower.mpg=data_auto.horsepower.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'CV vs MPG')"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dC7t2Ze+zdm3+HN1m3ly/HsbGpveNjbnD13GGkLLK/6lmdlP8xsxuBp5uZrflDZK0KHIUE6WEfhHwfUkHRX0CXgHc2InwfSPN5FImn8/OnaHlbc+jisybrVFG7SahcxxnVlBW+d8k6VxJL4jaBuDmyFb/cM64g4ArJG0Bvkuw+V8KTEq6AbgBWMggVgVrjeI555xq8vonac3Dk+UXKGuzX7cOdu+e3rd7t6dtdpwhpKzyfx1wK/CmqN0W9T0MHJ81yMy2mNmzzOwZZnaEmf1V1H+Cmf1m1HeqmeXYQgaEstW9ypJm4sm6S0/a7POyjeY5m71yl+MMFW2HevaDxoV6FlEmD1Aa8+fD/ffnzyFNj81PhncWhX8WydWEugKO41RG16GeTpt04hAGeEwi4jXrLt0sO7yzyCdQJJdX7nKcocGVf8yaNVO580dHw/tO6dQEdM894e/kZDDbpBEvyEoL7yyK4y8jV7sx/1703XEGk6xcz3EDRoC/K9qvzlZ7Pv8VK9Lz509MdD93Wm59KbseQDf5/JcsKa4z0Mm+7Xy2sjUHmozXNXBmCeTk8y+lfAk1e2en8t+0KV0JQijGUtUxksokr6hKllIeGSlWQu0o4yoUdxUXkKYxWy9ozlCSp/zLmn2ulXSJpNMkvSpu9TyL9Jg8G3dW/vtuOfbYmesEVq0KsmQ5ZMvI0k7Kh07SQ7QyG9NFVLGWwnEGgFLRPpLOT+k2M3t99SLNpNZon7xqWyMjsGdPd/NnReCsWgVf+lJQlAsWhCif1hj8VubOhfPOa040zmxMFJf1e2it0uY4A0DX0T5mdnpK64nir528vDZxZaws8pyd8bZTT02/kzz33KkY/p07ixU/hH2KUkCUka1dhqnou+c/coaFLHtQshGSsl1MyMy5HbgIOLjM2Cpa7Tb/NAfrihXtj0sWYR8by/YldNs6+Uyd2q2L5pptzlG3+TuzCCpw+F4GnE6o+TtKWN17WZmxVbTao306UWB5zs7x8foUfxnlX6UjdjY6dYuYbRc0Z2jJU/5lbf7XWUjLnNtXF41c4ZtnGy5xTjtmfBzuvjt/nyrt1m4Dd5yBpYoVvjslnRoVZhmRdCpQkIJyltMP2/DISEggV0SVsrkN3HFmJWWV/+uBU4C7onYywQw0O+jEOZrn7CyT3rkTslb9wvTPsGvXzLz9Epx4YvvHnI1OXcdxytn8+9167vAt6+DLsg1PTNRn70+ztad9htHRmWO7cfq6DdxxBg4qsPkfCpwDHAMYoYzjn1tBMZeqqNXmX0eseqdZPWOK/Aat29o53iDH4DuO0xZV2Pw/CXyGUJzliYT6vZ+qRrw+U+Uq1dj00o3inzcP3vCG/H0WLpxuompH1kFefes4TmWUVf7zzOxCM9sTtU3APnUK1jOqcmgmi6+0w/j4zBQLGzbkj9m5M9z9xzV8Fywofzx31DqOQ3nl/2VJZ0taKmmJpLOAL0laIClT80jaR9J3JF0v6SZJ74r6D5F0taRbJf2LpLlVfJiOqMqhmZYTpoh580L0TlqK5rLpoONjtn6GuXNnOn3dUes4TkRZ5X8K8CfAFcCVwATwauAaIM8Y/yvgBDN7JnAk8GJJxwDvAT5oZocDPwfO6Ej6KqgiwRm0b06ZMycc77TT0iOM1q8vX1x9507Yd9/wFBF/hjPOgP33n9pnfNyrdDmO8yhlc/scktMOzRlnNlWfdyxqBpwAfC7qvwB4RRefoXtai7G3qyDziq9k8cgj8MAD0803yQvAypVwwgnl59u5Ex56CC68MFw4Lrgg9MU89FC63F6IxXGGktG6DyBphPCEcDjwD8CPgXvNLE6XeQfwpLrlqI3Y1t9t+ucHHwyZPmHq4nPrre3PEacezkpLHM/dmm00vgAlj+84zqylZwXcJR1ASA73/4CPRyYfJD0Z+LKZHdGy/2pgNcDixYuP3tpNBE2ddBvd00qyiHpeuuksYlNRUUqG2ZiO2XGcaTSigLuZ3UvwGTwXOEBS/NRxMHBnyv4bzWy5mS1ftGhRr8Rsn6pDJ5N371mROUuWZDuEFy8uF8E0GwuxOI5TmlLKX9KxkvaLXp8q6QOSCsNRJC2K7viRtC/wIuAWwkXg5Gi3VcAXOxG+I9Ls3N3YvrMUbVlnbRqxAj7xxJnzjI2F9A1bt87cNm9eGLNrFzMYG5se6eM5exxnuMla+ptswBZAwDOBa4E/Bb5eYtwzov23ADcCb4/6DwW+A9xKWDD2mLx5KkvvkJYGYWzMbO7cztMgZKWHmJiYSokwf377KRyy6gy0pm2Ii8Fn1QaO29y50z/TIOWt9/QSjtMRVJDP/3vR37cDZyT7etEqU/5Zuem7zVdfRjllKfOs/DudyFo0pvUzDYJSHaSLlOM0jDzlX9bmf7+ktwKnAv8maQ4hbHOwqCsNQplQ0eR6gjxiZ28nshaNGUR7vhdUd5xaKKv8/4CwYOsMM7uL4KR9X21S1UU79uw6bN/xRWJkJH37yMjUhaMTWYvGJLcn01FYxlqDJuCOacephbKLvO4ysw+Y2Tei9z81s0/UK1oNpKVyGBsLqRCS1J0GIaswfLJ//fqZFwlppqwQFPfoKBx++MzPlxy7dWtICrdwYXZh+VWrmrXoyx3TjlMLZaN9jpH0XUm7JO2WtFfSL+oWrnLSUjmcfz6cd1736R3aYcMGmJiYUu4jI+F9MqHbVVfNXDhmFhR8WiTR3r1w+eXw3OdOmZbi+ZMponfunL7yN22eKp8Eul1F7MVkHKcespwByUbI33M4IXJnhFDF691lxlbRai/g3kRGRso7fJNtZGT6PO04jrt1fLdSlbN2EBzTjtNAqKCYy2YzWy5pi5k9I+q71syeVdtVKUEjC7jXTTfrBJLfaSerhFtZsiTY2BcvDnfcZZ+KfBWx4/SVKlb4PhilXb5O0nsl/XkbY508sswiWU7hIuIEc/G83Sr+2FcQm4JOOy30lTHhuLPWcRpLWQV+GsHc80bgAeDJwO/XJdRAUEVGzLyImyyn8IoV2U5dCA7s2KHbbc6htHKS8fsyPgF31jpOc8myBzWpNc7mX5UtO8seH9vZJyambP8jI+F9fPxu7Ph5bb/9pmzr3foE3ObvOH2FTm3+km4AMnewyP5fN42z+Vdly86yxyezb7YrQ7eMjMCePeWPUSTrmjUhemrv3jD36tXFZSqTtKaehumZTx3HyaQbm/9JwEtz2nBSlS07y/wxZ06xGSktBLIKkuGlZY6RZ8KZnAxFZeI59+4N79sxkfkKX8ephVzlb2Zb81qvhGwcVdmys5Tr3r3F9vS0NQvj4+0dP42ko7k1JUVaFtG8ePsqFLc7jR2nFnKVv6T7Jd2X0u6XdF+vhGwcVS08ipVrWmRPGSXZmlPonHO6fxpodTTHxzALJSLbWQxXheJ2p7Hj1ELRnf9jzWz/lPZYM9s/b2wjWLMmpD2Qwt81a6qZt92i762RQWvWhIgcKUTlZJWAjNM2JOWfnJwaK4ULRxx6CdkXkzIsWwaf+czU3AsXzqwr3E6t404Vd/J87drV+/QbjjMMZHmCI0fw/tHfBWktb2yVraNon4mJ9OiUOGKmV5RN5VxFiyNpsqJsxsfbn3NsrPPomk6ifbJqLoyPe7SP47QJnebzBy6N/v4EuC36G7fb8sZW2TpS/lnpEVrTH9RNt+kV2m1x6GVaeGSnF6Lx8c5DLdsN0ywKf3UcpzR5yr9nBdy7oaNQz7z0CL38zO2mV5CCWaTTMM6i0MvJSVi7Nj+5WxF1hlrmna9O00w4zpBSSQF3Sc+Q9DJJr4pbdSLWQF7O/F7SjmNyyZIpe3qncpY53r33djZ3TJ2hlnk1kZtee8BxBoiyKZ3PA84jpHSIY/xPKhjzZElXSLpZ0k2S1kb975R0p6TronZil58hnTI583tBO/H4u3ZNKbRO5UzOkSR2FOc5mNuhylDLVgfvWEqRuNanAY/1d5zuyLIHJRtwc5n9WsYcBBwVvX4s8ENgGfBO4M3tzNVxeoes9Ai9ptXuPTGR7XxNOm3nzOnM7t/qVK3D6VyVDT5Ntrlzpxy8eU5qqRoZHGeWQgUF3P8ZWFZm35w5vgi8qKfKv06qyDeT59ysMg9/mbmk9uavKuKmyMGbJ7s7gR0nlzzlXzaf/wuAS4C7CLV8FR4ayuX2kbQU+E/gCOBM4HXAfYQiMX9hZj9PGbMaWA2wePHio7fWkcemU6rKN5OX2we6c0wnHb9V5PRvpar5ivIb5cm+aZM7fR0nhyocvv9MSOv8Yqbs/aVy+0iaD1wEvMnM7gPOBQ4DjgS2Ae9PG2dmG81suZktX7RoUUkxe0RV+WbyFkHlOW7LpHJIjq96NWyVTvOihWBZ28fHpxR/Fem1HWfYyHokSDbgW2X2Sxk3BnwFODNj+1LgxqJ5Gmf2yTKRtGuDzlsEtWnTzLUKIyNT5pY8O37rwqxObf55pqCqfCibNgUbf6vNP+9zJn0aVaWNdpxZCDlmn7J3/tdK+qSk15QN9ZQkwhPDLWb2gUT/QYndXgncWFKG5lBVvpm8NBFpBdz37g39ybFpTwCx2Si+Iz7tNNh33/ZLQ+btv3cvnHtuNSkzWs06yfdFqTQ866fjdERZm//5Kd1mZq/PGfM84BvADUC86ugvgdcQTD4G3A78iZltyzt+4/L59yLH/OhoekhmMt8+ZOfcHx+Hhx6aLuPcuUGxPvxwNTLGdLP4qtvaCN3URHCcWU6ezX/2rvCtm8nJcHdZ14rTsiuU23Xmjo/D/Pn1FIKB9i+C3SpvLxLvOJl07PCV9DZJC3K2nyApd7HXrKXdDJftUnaFcrumpnvuqVcptppcipyxCzJ+Xln9rVSVXttxhowim/8NwL9KulzS+ySdJentki6MSjy+FLi6fjF7SFMiR7JW+B533HT5TjxxpvLLe2qIUzWXYXS03H6txKt/8wrUV0WZ9NpN+U4dp0lkeYKTDXgKITb/rcCbgN8F9i0ztorWs2ifpkWOtK5QXrEiXb6JianFUO0u1mqN4EmmTl6xorN5ihZoJRdnVRU5lUXTvlPH6SEMZVbPTmi6/bhIvm6Kui9ZMtNvkeV0TiJNt9knbf5l7Pl1n/Omf6eOUyOVZPUcCppeL7ZIvqrlLJMAzizb5FImJHb9+pmJ3MbGqrPZN/07dZw+4co/SdPrxXa6GrYMafb4Mit54zvoNMd3WWdsq4+i3fUIeTT9O3WcPuHKP0nTI0eK5EvbPndueorkNFojdYrSShedmzLO2HXrYPfu6eN2765ukVbTv1PH6RNl8/kfLOliSTskbZd0kaSD6xau57RbmL1KsiJSkv3r1sGqVdnypcl/3nnwR39UPh9PMlLnS1/K3/fBB0NVsIULO4+kyTK/bN1aTWROP79Tx2kyWZ7gZAMuA04HRqP2OuCyMmOraI3L7VM1WREpExPdR6q0m9cnTk/daf7/dvPuFKWb9sgcx+kYKsjnf12ZvrrarFf+WQowqwh9O3ns26kLECvaqmoJlAn13LTJbHQ0f77585tRlMdxBow85V/W5r9T0qmSRqJ2KtBFBXBnGlmmj6xom3YiVYr2jZ2rSXNIt5EwRdFHyf6rrpqeqyiNXbumzkWVCeUcZ4gpq/xfD5xCKOayDTiZYAZyqiAr8iTLTt9OpEpRXYALLwz318lInW4jYYqij5L9Gzd2doxOxzmOA5RU/ma21cxeZmaLzOwJZvYKM/NA6arIinVfvbq7SJXJyXDXnMbERJhn3bqZztp2is63Uib6aNeuqWN2Wky+iiL0jjPElEreIukQ4M8IxVceHWNmL6tHrCEkLdb92GND6yR76OQknH56dvrmj34UPvaxqe1xnD9Mzb9qVbaSHRkJ2+J6AvfcM1O+ZM79n/40JGu77z7YuXPqmHnEqaItZZVwldXEHGcIKWv2+QIh9/5HCGUX4+ZUQV6se6fZQ9euzc/bv2fPzO3JOP+VK7NTKkthvBmcc05IEZ3FVVfBHXeEfXfuLF9LYL/9wud9wxvStxetQXAcJ5eyaRt/aWYfrlWSYaaOFAQ7O/THJ4+5YEH6PHG65daiNq1PD2vWBOdsJzzwQPi7YUP4u3FjeNIYGQnHiPsdx+mIsnf+50h6h6TnSjoqbrVKNkw0KQVBO1vIQOsAABbjSURBVMfMKqG4dm2w53eq+GG6WWfDhqknjT17mqf4PWW0M4CUVf6/Cfwx8LdMmXz+rmiQpCdLukLSzZJukrQ26l8g6TJJP4r+Pr7TDzArqCMFQZ4pJo+7755SXvfck75P3J/1ZLJzZ/eVwjp16PZaEfeiZoHj1EHWAoBkA24F5pbZt2XcQcBR0evHAj8ElgHvBc6O+s8G3pM3z6xf5GU2tbgqzqXf7arW8fHOF2nFi72y5hgfD8eYP7/zY8SfM2uO+BjtnsNe5+4vs5DNcfoE3ebzl/QFYLWZbe/mQiPpi8DfR+04M9sm6SDgSjN7Wta4RtbwbTrdZsZcsiSEZKbZ/MfHwxNCu/WDYyYmpkw38+dP2feT7LdfdphqFv3I3e8F5J0Gk5fPv6zD9wDg+5K+C/wq7rQ2Qj0lLQWeRSj7eKCZbYs23QUcmLL/amA1wGJPv9s+cShmp+Q5m2OzT7uKP81Zm6b48/rz6Efu/sWL0y84ZWsQO06fKGvzfwfwSuBv6CDUU9J84CLgTWZ2X3Jb9GgyQ4uY2UYzW25myxctWlT2UE5Mt4ugFi8udkSXjbWPn0IOPjisW6iLLHkXLKjPD7B+fVi41sp9900/jjuFnaaRZQ+qqgFjwFeAMxN9PwAOsim/wA/y5hgKm3/VdJOcLbaTb9pkNjaWbdPupMZvsuawZDZnTva+7fo+0mz+Y2Nmc+fW6wfI8o3Edn+vI+z0CSrI6nk/cF/UfgnsBe4rMU7AJ4APtfS/j+kO3/fmzePKvwMmJjpX/smUzK2Ks2xbsiRbKbZTZL6TFNZJx3mRYq6CoiL07hR2+kSe8m+7gLskAS8HjjGzswv2fR7wDeAGIPZ+/SXB7v8ZYDGwFTjFzDLiCt3h2xHdFHOPfxPdztGpQ7iVbhy2vXDIFjma3Sns9IlKC7hHF5QvAL9bYt9vmpnM7BlmdmTUvmRmO81shZk9xcxemKf4nQ6pwsnZ7RxVOeq7kaMXC+iK1mmUlcH9Ak4PKVvG8VWJdrKkvyWYf5ym0qlySzpxu1WQaUqxkxDUbuToRQ3folKRZWTwxWJOr8myByUbcH6ifRRYBzyhzNgqmtv8OyDNyZhVGSzZklWyOi3nuGzZ9DmSNvi00pTd2vyLFshVsYAub44y8xft434Bpwbo1uHb7+bKP0E7iixt32XLshXtihUz55iYKHfRiNu++04f3xoRtGLFdLny5ipTsrGqSJoi5Z51jKqOX+Q0dpwO6Fr5E9Ix7E8I27wc2AGcWmZsFc2Vf0S3iqYoAqh1rk7v/OOLSFYoaPIis99+7cnUShV3zEXnNe8YVd2xF6XSqIqq04g4jaYK5X9d9PeVwD8DjwOuLzO2iubKP6JdRdP6j14mxDI5VzdrBcyKt5uVy0GUp0i7vWPetCn7ySY+bt4x8s5p3nfRqnR7ofx9vcHQUYXyvzH6+zHgxdFrV/69ph1F1+lde3KuThV/O8q/XZla6ebOu+gclYnTz7tAxiarMkq3F2Yf9ysMHXnKv2yo56WSvg8cDVwuaREe7dN72glbTMu13+4xelEqscwx8qJ9uonmKTpH8XHzjpF3nLjIfFbdg7hqWvJYWTJUQT9yHznNJeuq0NqABcBI9Hoe8Gtlx3bb/M4/op3H9nZW0WbN1eldfzs2/3ZlyjovnUT75J2jsbHyET1FTzhl7urTUmm0I0MZ/M5/6KCKaB/gt4A/BF4bt7Jju22u/BOUVQBZ/+jz50/ZuKXwvt3wQwhzZCn35Dxp0T5J8moCVOGQzLtg5n2+uXPLHzsrP9GcOfnnMal001JpJGWowl7vNv+ho2vlD1wI/BewgVDE/SPAh8uMraK58u+AXiiLKu4kq7B1510Q82QssvkXfY6iC8h++03tV/RdFJ3Lqu7a64728WiiRlGF8r8FQh6gfjRX/h1S9+KmKhR3kcmkjHx5irVIxk2bso+f9znKONRbzTp530WRnIOwDsCfLBpHFcr/s0QpmPvRXPk3lCruRrPCLEdGqpGhjIxZ+4yPt/9E0el56NWdf50MgoxDRp7yLxvtsxC4WdJXJF0St+5czc7As359SEKWZM6c6REwa9bA6GjIeTM6Gt4nWb06fe6s/laKIljKRAOl7TN3bijIkpVrpyhCZmysfP6gycn0kpXS1By9yFEUy9JpcjmPJqqWuhP9ZV0Vkg14QVorM7aK5nf+DSVrxXAc31603SzcTbc6TOfMKW8qKOtMbTf3TlEdgKI7/7IO4yLzUdJB3gt7fTdmm16tUh4GKjKhUVG0z4HASVHrWVI3c+XfXIpMNmVMOt2aCuqyM5fxFRTZ/Mt8hjLmo17R7Xfhyr86KjKh5Sn/simdTwG+A/xv4BTgakknV/sM4gwcWXWC4/6i7dC9qWDlSli1amqx2MhIeB+nU+6UokVXyTTOWWzdOvW4nvUI3ySTSLffxT0ZZTmy+rPwuga9MaFlXRWSDbiexN0+sAhP7+DM5jv/duYtYwJqXcBVZq1Br+/8u71z70WSvWGhB3f+ZZX/DS3v57T2ZYw7D9hOlBso6nsncCdwXdROLJpnKJR/MnVymVTGTaAqm3/RytY86ox/L2tj7zSPUpm1Bmlptrsh7zN1q/yrUNydfp+zbX1BU2z+hILrXwFeF7UvU1B0PRr3fOCoFOX/5jLHjdusV/5llGQTScuIOTIy/QdadFErWtlaRFWLxKpYENdJFtR4bNZT0hOfWF6Gbj9nFU8f3SrhTmSYrU8LFVzQ8pR/6QLukl4FPC96+w0zu7jkuKXApWZ2RPT+ncAuM/u7UgdmCAq4j46m28dHRmDPnt7LU5aiwuW9mKMJMpSZK4v4/y+vvGXJ/9FCij5nE36HnchQ5fc3y+i4gLukwyUdC2BmnzezM83sTGCHpMO6kOmNkrZIOk/S4zOOvVrSZkmbd+zY0cWhBoAyjtEmUoVTqts5qoh/r9K5liZPt1Tl9Cz6nE34HXYig68v6IiiaJ8PAfel9P8i2tYJ5wKHAUcC24D3p+1kZhvNbLmZLV+0aFGHhxoQstIa9yKlcjdUkYa42zmKiqf3QoYiebLu6st+v1UVcy/6nFmRS3kRTVXTiQy9SIc9G8myB0XmoO/mbCt0+Eb7LSVh8y+7Ldnc5t9QZkumybplKPP9PvGJxf6BbtMkFH3OQf0umiB3Q6FThy/wo5xtt+aNTew3TcGTyBEE/Dnw6aI5Zr3yNxvMaB+z+pPH9Yp2ZOgkMijt+20dU8ZBnPe7KPMZyjjg2/0cVdPJ76HXv6Gi41XxXVRAN8r/U8Afp/T/EfAveWMT47cBDwN3AGcQ0kPfAGwBLqFEwrihUP7OYJB2lzk2NjNiqZO71bItTUmUufvt9g55UJ9Qq6aKJ6gencs85Z8b7SPpQOBiYDdwTdS9HJgLvNLM7urE1NQusz7axxkc2onmyYs2aTcqKEla5EuZiJduo2KaEA3UBIrOY5nz3KNzmRftUyrUU9LxwBHR25vM7GuVSVcCV/5OY5gzp3zopQSPPNL9PGm0js2aLylDmX3y6EU46iBQdB7LnOcencuOQz2nZLErzOwjUeup4necRlFFJFO787SSFiVUJuKl26iYQY1Kq5qi81jmPDfgXJbN5+84s5M4iZg01dLqDsSkxfGPjYUxSebOza9rcPjhna8H2Lt3ZsK4rVtn3k2m1S0YG5spe9n6C93WXihL0xO7FZ3HMmtPenUu88hyBjSpucPXqYUip2uW8601kmNiIj8/UZZzb8WKqXmy0jsccED2tjRHc5zuIisCJS+VRpETcsWK7M9R53fStLDNMilJBiDap3R6h37iNn+nFoqcrmWdb1WkTSiyAVfhaO5WziakoGgCgyBjRNcO337jyt+phTJO1zL/H0UOvjJKs2ifKhzN3crZC+XfrVO6FwyCjBFdO3wdZ1ZS5Ogs63wrcvBV4dyrM2VGlXJ2yyCkahgEGUvgyt8ZXoqSsJV1vhU5+Mo495YtS98n7s9yNM+dO71Pml5BrEjO5P7HHZcv54oV6duT/XkO4zJ0mqivl07iKpIJQv8d21nOgCY1d/g6tZGWh78T51sVaRGWLZsux7JlxcdIyt9a2yDNUVq0/4oV+XK2On2Tzt6qVq22m6qhH07ibtNJ9Ehm3OHrOLOcdp2QdTgt+7UCeIAcsI/SI5nd4es4s512nZB1OC37tQJ4gBywj9Ijmd3h6ziznU6dvGX7y9Avh/EgOmAbILMrf8dpCt04ANt1QlbltEzSr1WrdThgFy4MrS5nbB3nv12ynAFNau7wdWY9VRaRb8dRWmUO/E2bzEZHp3+G0dHerM6twwFbtwO5BzUIcIev4zScQXRatjLIn6HMCupB+BwtuM3fcZrObChCPsifoYyMg/A52sCVv+M0gQY4ALtmkD9DGRkH4XO0Qa3KX9J5krZLujHRt0DSZZJ+FP19fJ0yOM5A0AQHYLcM8mcoWu09KJ+jDeq+8/848OKWvrOBy83sKcDl0XvHGW5WroSNG4NdWQp/N24M/YNCUz5DJ1FTrbKPj4eW9Tn6nZqhAmp3+EpaClxqZkdE738AHGdm2yQdBFxpZk/Lm8Mdvo7jlGJyMoSWPvjgVN+8edVehHpxjIpomsP3QDPbFr2+CziwDzI4jjMbWbduulKG8H7dusE6Rg/oq8M3ikNNffSQtFrSZkmbd+zY0WPJHMcZSHoRcTTIUU0J+qH8fxaZe4j+bk/bycw2mtlyM1u+aNGingroOM6A0ouIo0GOakrQD+V/CbAqer0K+GIfZHAcZ5Ao62DtRcTRIEc1Jag71PNTwLeAp0m6Q9IZwN8CL5L0I+CF0XvHcZx0Ygfr1q0h2cLWreF92gWgFxFHTYlq6hJP7+A4TrMZ5LQRfaZp0T6O4zjlmSUO1qbhyt9xnGYzSxysTcOVv+M4zWaWOFibhit/x3GazSxxsDaN0X4L4DiOU8jKla7sK8bv/B3HcYYQV/6O4zhDiCt/x3GcIcSVv+M4zhDiyt9xHGcIGYj0DpJ2ACnru7tmIXB3DfNWzSDI6TJWxyDI6TJWR51yLjGz1LTIA6H860LS5qy8F01iEOR0GatjEOR0GaujX3K62cdxHGcIceXvOI4zhAy78t/YbwFKMghyuozVMQhyuozV0Rc5h9rm7ziOM6wM+52/4zjOUOLK33EcZwgZKuUv6XZJN0i6TtLmqG+BpMsk/Sj6+/g+yve0SLa43SfpTZLeKenORP+JfZDtPEnbJd2Y6Es9dwp8WNKtkrZIOqqPMr5P0vcjOS6WdEDUv1TSQ4lz+o99lDHz+5X01ug8/kDS7/ZCxhw5/yUh4+2Srov6+3UunyzpCkk3S7pJ0tqovzG/yxwZ+/+7NLOhacDtwMKWvvcCZ0evzwbe0285I1lGgLuAJcA7gTf3WZ7nA0cBNxadO+BE4MuAgGOAq/so4+8Ao9Hr9yRkXJrcr8/nMfX7BZYB1wOPAQ4BfgyM9EvOlu3vB97e53N5EHBU9PqxwA+jc9aY32WOjH3/XQ7VnX8GLwcuiF5fALyij7IkWQH82MzqWNncNmb2n8A9Ld1Z5+7lwCcs8G3gAEkH9UNGM/uqme2J3n4bOLhuOfLIOI9ZvBz4tJn9ysx+AtwKPKc24RLkySlJwCnAp3ohSxZmts3Mvhe9vh+4BXgSDfpdZsnYhN/lsCl/A74q6RpJq6O+A81sW/T6LuDA/og2g1cz/Z/rjdEj4nn9NE21kHXungT8d2K/O6K+fvN6wp1fzCGSrpX0dUm/3S+hItK+36aex98GfmZmP0r09fVcSloKPAu4mob+LltkTNKX3+WwKf/nmdlRwEuAP5X0/ORGC89dfY99lTQXeBnw2ajrXOAw4EhgG+GRu1E05dxlIWkdsAeYjLq2AYvN7FnAmcAnJe3fJ/Ea//228Bqm35j09VxKmg9cBLzJzO5LbmvK7zJLxn7+LodK+ZvZndHf7cDFhEfon8WPftHf7f2T8FFeAnzPzH4GYGY/M7O9ZvYI8FF69Ohfgqxzdyfw5MR+B0d9fUHS64CTgJWRMiAypeyMXl9DsKc/tR/y5Xy/jTqPAJJGgVcB/xL39fNcShojKNVJM/t81N2o32WGjH3/XQ6N8pe0n6THxq8JDpcbgUuAVdFuq4Av9kfCaUy7s2qxS76SIHcTyDp3lwCvjaIrjgF+kXgM7ymSXgycBbzMzB5M9C+SNBK9PhR4CnBbn2TM+n4vAV4t6TGSDiHI+J1ey9fCC4Hvm9kdcUe/zmXke/hn4BYz+0BiU2N+l1kyNuJ32QuvchMacCghcuJ64CZgXdQ/DlwO/Aj4D2BBn+XcD9gJPC7RdyFwA7CF8AM+qA9yfYrwSPowwVZ6Rta5I0RT/APhruUGYHkfZbyVYOe9Lmr/GO37+9Hv4Drge8BL+yhj5vcLrIvO4w+Al/Tz+476Pw68oWXffp3L5xFMOlsS3++JTfpd5sjY99+lp3dwHMcZQobG7OM4juNM4crfcRxnCHHl7ziOM4S48nccxxlCXPk7juMMIa78nb4g6dckfVrSj6N0G1+SlLmYJcp22Nb6Bkkfl3Ry9PpKSZUWyZa0q83946yyWyR9VdKvFez/l91JmDnvf9UxrzNYuPJ3ek608OVi4EozO8zMjgbeSnPyKtXJ8Wb2DGAzUKTca1H+ZvZbdczrDBau/J1+cDzwsJk9mqvczK43s29Imi/pcknfi+6SX54YNyppUtItkj4naR6ApLdL+q6kGyVtjC4umUh6TTT3jZLeE/WNRE8KN0bb/jxl3CGSvhVt/+uWbW+JZNgi6V0lzsF/AofnyPO3wL4KOd0no75TJX0n6vunxErQXZLWS7pe0rclHRj1H6iQK/76qP1WvH/0N+9cO7McV/5OPzgCuCZj2y+BV1pIwHc88P6EMn8asMHMfh24D1gT9f+9mT3bzI4A9iXkS0lF0hMJ+dNPICRSe7akV0Svn2RmR5jZbwLnpww/Bzg32r4tMefvEJbhPyea52i1JA1M4STghix5zOxs4CEzO9LMVkr6deAPgGPN7EhgL7Aymms/4Ntm9kzCReWPo/4PA1+P+o8irBxNkneunVmOK3+naQj4G0lbCEvzn8SUOei/zeyq6PUmwtJ5gOMlXS3pBoIS/Y2c+Z9NMDftsJBPfZJQuOQ24FBJH4nyrtyXMvZYpnIuXZjo/52oXUtYkv90wsUgjSsUKmDtD7w7R55WVgBHA9+Nxq8gpCwB2A1cGr2+hlAQBMK5OBfAQuK4X7TMmXeunVnOaL8FcIaSm4CTM7atBBYBR5vZw5JuB/aJtrXmIjFJ+wAbCHla/lvSOxP7l8bMfi7pmcDvAm8gFCt5fdquKX0C3m1m/1TiUMeb2d2PDix/oy3gAjN7a8q2h20qT8teyv9f551rZ5bjd/5OP/ga8BhNFdRB0jMUClc8DtgeKaPjCWUsYxZLem70+g+BbzKlrO5WyJmedVGJ+Q7wAkkLI5v5a4CvS1oIzDGzi4C3EcwkrVxFKLIDUyYXgK8Ar4+Oj6QnSXpCgRy58kTbHlZIBwwhUdnJ8bwKdWqXzJxuGpcDE9H+I5Ie17I971w7sxxX/k7Pie5SXwm8UCHU8yaCCeQugtljeWTCeS3w/cTQHxCK8NwCPJ5gf7+XkAP/RoIS/m7BsbcR6rpeQcjweo2ZfZFg8rgyMqlsIkQftbI2Ov4NJCpAmdlXgU8C34q2fY5Qr7XMuciSB2AjsEXSpJndTLgofTUy01xGqA+bx1qCSewGgjloWcv2vHPtzHI8q6fjOM4Q4nf+juM4Q4grf8dxnCHElb/jOM4Q4srfcRxnCHHl7ziOM4S48nccxxlCXPk7juMMIf8fdT0KPdMIB8EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
    "\n",
    "\\begin{equation}\n",
    "Y=\\alpha+\\beta*X\n",
    "\\end{equation}\n",
    "\n",
    "Y:mpg\\\n",
    "X:horsepower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=data_auto.horsepower.fillna(np.mean(data_auto.horsepower))\n",
    "Y=data_auto.mpg.fillna(np.mean(data_auto.mpg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=X[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm=LinearRegression()\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'CV vs MPG')"
      ]
     },
     "execution_count": 66,
     "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": [
    "plt.plot(data_auto.horsepower,data_auto.mpg,'ro')\n",
    "plt.plot(data_auto.horsepower,lm.predict(X),'b')\n",
    "plt.xlabel(\"Caballos de Potencia\")\n",
    "plt.ylabel(\"Consumo (millas por galeón)\")\n",
    "plt.title(\"CV vs MPG\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "cell_style": "center"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5746533406450252"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def error_standar(X,Y):\n",
    "    SSD=np.sum((Y-lm.predict(X))**2)\n",
    "    y_mean=np.mean(Y)\n",
    "    RSE=np.sqrt(SSD/(len(X)-1))\n",
    "    error=RSE/np.mean(Y)\n",
    "    print(\"SSD:\"+ str(SSD),\"y_mean: \"+str(y_mean),\"RSE: \"+str(RSE),\"error: \"+str(error*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SSD:10315.751960060918 y_mean: 23.514572864321607 RSE: 5.046879480825511 error: 21.462773361633474\n"
     ]
    }
   ],
   "source": [
    "error_standar(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modelo de regresión cuadrático"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "Y=\\alpha+\\beta*X^{2}\n",
    "\\end{equation}\n",
    "\n",
    "Y:mpg\\\n",
    "X:horsepower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_data=X**2\n",
    "Y=data_auto.mpg.fillna(np.mean(data_auto.mpg))\n",
    "# X=X[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm=LinearRegression()\n",
    "lm.fit(X_data,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'CV vs MPG')"
      ]
     },
     "execution_count": 72,
     "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": [
    "plt.plot(data_auto.horsepower,data_auto.mpg,'ro')\n",
    "plt.plot(data_auto.horsepower,lm.predict(X_data),'bo')\n",
    "plt.xlabel(\"Caballos de Potencia\")\n",
    "plt.ylabel(\"Consumo (millas por galeón)\")\n",
    "plt.title(\"CV vs MPG\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4849887034823205"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X_data,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SSD:12490.350340501926 y_mean: 23.514572864321607 RSE: 5.553410772769817 error: 23.616889852998113\n"
     ]
    }
   ],
   "source": [
    "error_standar(X_data,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Modelo de regresión polinómica"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A partir de una relación lineal en conjunto con una cuadrática\n",
    "\n",
    "\\begin{equation}\n",
    "Y=\\alpha+\\beta_{0}*X+\\beta_{1}*X^{2}\n",
    "\\end{equation}\n",
    "\n",
    "Y:mpg\\\n",
    "X:horsepower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly=PolynomialFeatures(degree=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_data=poly.fit_transform(X)\n",
    "lm=linear_model.LinearRegression()\n",
    "lm.fit(X_data,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6439066584257469"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X_data,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polinomio de grado 2\n",
      "[ 0.         -0.43404318  0.00112615]\n",
      "R2: 0.6439066584257469\n",
      "SSD:8636.180643524502 y_mean: 23.514572864321607 RSE: 4.61778115803654 error: 19.6379546619069\n",
      "\n",
      "\n",
      "Polinomio de grado 3\n",
      "[ 0.00000000e+00 -5.27113167e-01  1.89736722e-03 -1.95723195e-06]\n",
      "R2: 0.6444678885560744\n",
      "SSD:8622.56936742855 y_mean: 23.514572864321607 RSE: 4.614140736300908 error: 19.622473106036686\n",
      "\n",
      "\n",
      "Polinomio de grado 4\n",
      "[ 0.00000000e+00  1.62563541e-01 -7.10892744e-03  4.65580255e-05\n",
      " -9.15840092e-08]\n",
      "R2: 0.6467674189704502\n",
      "SSD:8566.799832491351 y_mean: 23.514572864321607 RSE: 4.599194731579757 error: 19.558912501268786\n",
      "\n",
      "\n",
      "Polinomio de grado 5\n",
      "[ 0.00000000e+00  4.00021894e+00 -7.54802468e-02  6.19621641e-04\n",
      " -2.36220984e-06  3.41983153e-09]\n",
      "R2: 0.6547512491371934\n",
      "SSD:8373.171388773775 y_mean: 23.514572864321607 RSE: 4.546921734122058 error: 19.33661206757895\n",
      "\n",
      "\n",
      "Polinomio de grado 6\n",
      "[ 0.00000000e+00  1.07622445e+01 -2.30165514e-01  2.40584068e-03\n",
      " -1.33797044e-05  3.79780867e-08 -4.32542890e-11]\n",
      "R2: 0.6572852671633754\n",
      "SSD:8311.714925332735 y_mean: 23.514572864321607 RSE: 4.530204509959361 error: 19.265519029831026\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for d in range(2,7):\n",
    "    print(\"Polinomio de grado \"+str(d))\n",
    "    poly=PolynomialFeatures(degree=d)\n",
    "    X_data=poly.fit_transform(X)\n",
    "    lm=linear_model.LinearRegression()\n",
    "    lm.fit(X_data,Y)\n",
    "    print(lm.coef_)\n",
    "    print(\"R2: \"+str(lm.score(X_data,Y)))\n",
    "    error_standar(X_data,Y)\n",
    "    print(\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# El problema de los outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'CV vs MPG')"
      ]
     },
     "execution_count": 80,
     "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": [
    "plt.plot(data_auto.displacement,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": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 81,
     "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(np.mean(data_auto.mpg))\n",
    "\n",
    "\n",
    "lm=LinearRegression()\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6261049762826918"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc5d0bf5d30>]"
      ]
     },
     "execution_count": 84,
     "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": [
    "plt.plot(X,Y,'ro')\n",
    "plt.plot(X,lm.predict(X),'blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "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": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto[(data_auto[\"displacement\"]>250) & (data_auto[\"mpg\"]>35)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "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": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto[(data_auto[\"displacement\"]>300) & (data_auto[\"mpg\"]>20)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Aquí se eliminan algunos outliers**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_auto_clean=data_auto.drop(index=[395,258,305,372])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>401</th>\n",
       "      <td>27.0</td>\n",
       "      <td>4</td>\n",
       "      <td>140.0</td>\n",
       "      <td>86.0</td>\n",
       "      <td>2790</td>\n",
       "      <td>15.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>ford mustang gl</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>402</th>\n",
       "      <td>44.0</td>\n",
       "      <td>4</td>\n",
       "      <td>97.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>2130</td>\n",
       "      <td>24.6</td>\n",
       "      <td>82</td>\n",
       "      <td>2</td>\n",
       "      <td>vw pickup</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>403</th>\n",
       "      <td>32.0</td>\n",
       "      <td>4</td>\n",
       "      <td>135.0</td>\n",
       "      <td>84.0</td>\n",
       "      <td>2295</td>\n",
       "      <td>11.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>dodge rampage</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>404</th>\n",
       "      <td>28.0</td>\n",
       "      <td>4</td>\n",
       "      <td>120.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>2625</td>\n",
       "      <td>18.6</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>ford ranger</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>405</th>\n",
       "      <td>31.0</td>\n",
       "      <td>4</td>\n",
       "      <td>119.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>2720</td>\n",
       "      <td>19.4</td>\n",
       "      <td>82</td>\n",
       "      <td>1</td>\n",
       "      <td>chevy s-10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>402 rows × 9 columns</p>\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",
       "401  27.0          4         140.0        86.0    2790          15.6   \n",
       "402  44.0          4          97.0        52.0    2130          24.6   \n",
       "403  32.0          4         135.0        84.0    2295          11.6   \n",
       "404  28.0          4         120.0        79.0    2625          18.6   \n",
       "405  31.0          4         119.0        82.0    2720          19.4   \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  \n",
       "..          ...     ...                        ...  \n",
       "401          82       1            ford mustang gl  \n",
       "402          82       2                  vw pickup  \n",
       "403          82       1              dodge rampage  \n",
       "404          82       1                ford ranger  \n",
       "405          82       1                 chevy s-10  \n",
       "\n",
       "[402 rows x 9 columns]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_auto_clean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 92,
     "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(np.mean(data_auto_clean.mpg))\n",
    "\n",
    "\n",
    "lm=LinearRegression()\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6466514317531822"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc5d0b842b0>]"
      ]
     },
     "execution_count": 94,
     "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": [
    "plt.plot(X,Y,'ro')\n",
    "plt.plot(X,lm.predict(X),'blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/franklin/my_projects_dir/entorno_jup/lib/python3.6/site-packages/matplotlib/cbook/__init__.py:1316: RuntimeWarning: invalid value encountered in less_equal\n",
      "  wiskhi = x[x <= hival]\n",
      "/home/franklin/my_projects_dir/entorno_jup/lib/python3.6/site-packages/matplotlib/cbook/__init__.py:1323: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  wisklo = x[x >= loval]\n",
      "/home/franklin/my_projects_dir/entorno_jup/lib/python3.6/site-packages/matplotlib/cbook/__init__.py:1331: RuntimeWarning: invalid value encountered in less\n",
      "  x[x < stats['whislo']],\n",
      "/home/franklin/my_projects_dir/entorno_jup/lib/python3.6/site-packages/matplotlib/cbook/__init__.py:1332: RuntimeWarning: invalid value encountered in greater\n",
      "  x[x > stats['whishi']],\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'whiskers': [<matplotlib.lines.Line2D at 0x7fc5cf8717b8>,\n",
       "  <matplotlib.lines.Line2D at 0x7fc5cf871b00>],\n",
       " 'caps': [<matplotlib.lines.Line2D at 0x7fc5cf871e48>,\n",
       "  <matplotlib.lines.Line2D at 0x7fc5cf7fe1d0>],\n",
       " 'boxes': [<matplotlib.lines.Line2D at 0x7fc5cf8714a8>],\n",
       " 'medians': [<matplotlib.lines.Line2D at 0x7fc5cf7fe518>],\n",
       " 'fliers': [<matplotlib.lines.Line2D at 0x7fc5cf7fe860>],\n",
       " 'means': []}"
      ]
     },
     "execution_count": 98,
     "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": [
    "plt.boxplot(data_auto[\"mpg\"])"
   ]
  },
  {
   "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": "3.6.8"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}