Linnear Regression.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Linear Regression\n",
    "Linear regression is one of the best-known methods of prediction and analysis of continuous variables. In the model there is a X number of predictor variables and a variable to predict, his formula is\n",
    "# $$ Y_i = \\beta_0 + \\beta_1X_1 + \\beta_2X_2 + \\beta_3X_3 + ... + \\beta_nX_n$$\n",
    "* $Y_i$: is the variable that we want to predict \n",
    "* $\\beta$: the constant or intercept, is a constant number in the prediction, you can create a linera regression function without this parameter\n",
    "* $X$: each feature\n",
    "* $\\beta_n$: the weigths that multiply the features\n",
    "\n",
    "This method consists of fitting a straight line to the data that can predict those data with the least possible error. This means that the distance from the points to the line is the minimum possible.\n",
    "\n",
    "Linear Regression belongs to the supervised machine learning methods, so it is for continuos data.\n",
    "![linear regression image](https://miro.medium.com/max/1200/1*LEmBCYAttxS6uI6rEyPLMQ.png)\n",
    "This read line is the line that best fit to all the points and have the minimun error for all the points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scikit Learn Linear Regression\n",
    "Now we are going to use the linear regression of sklearn no predict data and see all the posibilities that this package offer to us"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Import librarys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The version_information extension is already loaded. To reload it, use:\n",
      "  %reload_ext version_information\n"
     ]
    },
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         "version": "Linux 5.0.0 29 generic x86_64 with debian buster sid"
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         "module": "pandas",
         "version": "0.25.1"
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         "module": "matplotlib",
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         "version": "0.21.2"
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       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.7.4 64bit [GCC 7.3.0]</td></tr><tr><td>IPython</td><td>7.8.0</td></tr><tr><td>OS</td><td>Linux 5.0.0 29 generic x86_64 with debian buster sid</td></tr><tr><td>pandas</td><td>0.25.1</td></tr><tr><td>matplotlib</td><td>3.1.1</td></tr><tr><td>sklearn</td><td>0.21.2</td></tr><tr><td colspan='2'>Sat Sep 28 13:54:02 2019 CEST</td></tr></table>"
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       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.7.4 64bit [GCC 7.3.0] \\\\ \\hline\n",
       "IPython & 7.8.0 \\\\ \\hline\n",
       "OS & Linux 5.0.0 29 generic x86\\_64 with debian buster sid \\\\ \\hline\n",
       "pandas & 0.25.1 \\\\ \\hline\n",
       "matplotlib & 3.1.1 \\\\ \\hline\n",
       "sklearn & 0.21.2 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Sat Sep 28 13:54:02 2019 CEST} \\\\ \\hline\n",
       "\\end{tabular}\n"
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       "Software versions\n",
       "Python 3.7.4 64bit [GCC 7.3.0]\n",
       "IPython 7.8.0\n",
       "OS Linux 5.0.0 29 generic x86_64 with debian buster sid\n",
       "pandas 0.25.1\n",
       "matplotlib 3.1.1\n",
       "sklearn 0.21.2\n",
       "Sat Sep 28 13:54:02 2019 CEST"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score\n",
    "\n",
    "%load_ext version_information\n",
    "%matplotlib inline\n",
    "%version_information pandas, matplotlib, sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Dataset\n",
    "This is a dataset about the investment in diferent communication media and the sales of each store that we have in different cities, The communication media investmen is a calculation of the money that each shop contribute to the communitacion media budget. \n",
    "\n",
    "* The rows: each row is a shop\n",
    "* TV: investment in TV in euros\n",
    "* Radio: investmen in radio in  euros\n",
    "* Newspaper: investment in newspapes in euros\n",
    "* Sales: the money earned in each store in one month\n",
    "* City size: if the city have a population bigger than 500.000 is big if not is small\n",
    "\n",
    "You can find this dataset [here](https://www.kaggle.com/fayomi/advertising) and download the original dataset, but I've made some modifications, so you have to download from my github account [here]()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "      <th>City_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>2210.0</td>\n",
       "      <td>big</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>1040.0</td>\n",
       "      <td>small</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>930.0</td>\n",
       "      <td>small</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>1850.0</td>\n",
       "      <td>big</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>1290.0</td>\n",
       "      <td>small</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <td>195</td>\n",
       "      <td>38.2</td>\n",
       "      <td>3.7</td>\n",
       "      <td>13.8</td>\n",
       "      <td>760.0</td>\n",
       "      <td>small</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>196</td>\n",
       "      <td>94.2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>8.1</td>\n",
       "      <td>970.0</td>\n",
       "      <td>small</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>197</td>\n",
       "      <td>177.0</td>\n",
       "      <td>9.3</td>\n",
       "      <td>6.4</td>\n",
       "      <td>1280.0</td>\n",
       "      <td>small</td>\n",
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       "    <tr>\n",
       "      <td>198</td>\n",
       "      <td>283.6</td>\n",
       "      <td>42.0</td>\n",
       "      <td>66.2</td>\n",
       "      <td>2550.0</td>\n",
       "      <td>big</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>199</td>\n",
       "      <td>232.1</td>\n",
       "      <td>8.6</td>\n",
       "      <td>8.7</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>small</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 5 columns</p>\n",
       "</div>"
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      "text/plain": [
       "        TV  Radio  Newspaper   Sales City_size\n",
       "0    230.1   37.8       69.2  2210.0       big\n",
       "1     44.5   39.3       45.1  1040.0     small\n",
       "2     17.2   45.9       69.3   930.0     small\n",
       "3    151.5   41.3       58.5  1850.0       big\n",
       "4    180.8   10.8       58.4  1290.0     small\n",
       "..     ...    ...        ...     ...       ...\n",
       "195   38.2    3.7       13.8   760.0     small\n",
       "196   94.2    4.9        8.1   970.0     small\n",
       "197  177.0    9.3        6.4  1280.0     small\n",
       "198  283.6   42.0       66.2  2550.0       big\n",
       "199  232.1    8.6        8.7  1340.0     small\n",
       "\n",
       "[200 rows x 5 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ad = pd.read_csv('data/Advertising.csv')\n",
    "df_ad.drop(columns='Unnamed: 0', inplace=True)\n",
    "df_ad['Sales'] = df_ad['Sales'] * 100\n",
    "df_ad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3 Prepare the data to the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "train, test = train_test_split(df_ad)\n",
    "X_train = train.drop(columns=['Sales', 'City_size'])\n",
    "y_train = train['Sales']\n",
    "X_test = test.drop(columns=['Sales', 'City_size'])\n",
    "y_test = test['Sales']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Train the model and test it\n",
    "First of all we are going to see the hyperparameters that Linear regressiona have\n",
    "\n",
    "* fit_intercept: True or False if you want a constant $\\beta$\n",
    "* normalize: if you want to normalize the data before train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error in train:  128.21029897094616\n",
      "Root of mean square error in train:  171.33757670207248\n",
      "Mean absolute error in test:  123.62715721572802\n",
      "Root of mean square error in test:  155.77727445907922\n",
      "R2 in train:  0.8801657130921301\n",
      "R2 in test:  0.900788975289897\n",
      "Min sales:  160.0\n",
      "Max sales:  2700.0\n"
     ]
    }
   ],
   "source": [
    "lm = LinearRegression(fit_intercept=True, normalize=True)\n",
    "lm.fit(X_train, y_train)\n",
    "predictions_train = lm.predict(X_train)\n",
    "predictions_test = lm.predict(X_test)\n",
    "print(\"Mean absolute error in train: \", mean_absolute_error(predictions_train, y_train))\n",
    "print(\"Root of mean square error in train: \", np.sqrt(mean_squared_error(predictions_train, y_train)))\n",
    "print(\"Mean absolute error in test: \", mean_absolute_error(predictions_test, y_test))\n",
    "print(\"Root of mean square error in test: \", np.sqrt(mean_squared_error(predictions_test, y_test)))\n",
    "print(\"R2 in train: \", r2_score(predictions_train, y_train))\n",
    "print(\"R2 in test: \", r2_score(predictions_test, y_test))\n",
    "print(\"Min sales: \", np.min(df_ad['Sales']))\n",
    "print(\"Max sales: \", np.max(df_ad['Sales']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We have a mean absolute error of 135 € per store in test, wich is not good but we can work with him.  \n",
    "* Our root mean squared error is higher which means that some data suffers a big error\n",
    "* Our R2 says that we can explain the 87% of the sells with this model and this variables, i don't like to much this metric, and is not very recommendable to use it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Interprete the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <td>TV</td>\n",
       "      <td>4.604620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Radio</td>\n",
       "      <td>18.615614</td>\n",
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       "      <td>Newspaper</td>\n",
       "      <td>0.087046</td>\n",
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      "text/plain": [
       "           Coefficient\n",
       "TV            4.604620\n",
       "Radio        18.615614\n",
       "Newspaper     0.087046"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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   ],
   "source": [
    "pd.DataFrame(lm.coef_, X_train.columns, columns=['Coefficient'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the below result we can make the following interpretation\n",
    "1. For each euro that i invest in TV, my earns will increase in 4,6 euros\n",
    "2. For each euro that i invest in Radio, my earns will increase in 18,61 euros\n",
    "3. For each euro that i invest in Newspaper, my earns will increse in 0.08 euros.\n",
    "\n",
    "Sometimes the coeffiecients of the variables could be negative, This is for the Intercept, if we set the intercept to false, the coefficients variables that were negative will be positive with a very low increase."
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intercept tell us which is the minimun that i will earn, for example if my invest are zero in all communications media, my earns will be 290"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
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       "      <td>52</td>\n",
       "      <td>2260.0</td>\n",
       "      <td>2054.946754</td>\n",
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       "    <tr>\n",
       "      <td>114</td>\n",
       "      <td>1460.0</td>\n",
       "      <td>1513.084006</td>\n",
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       "      <td>69</td>\n",
       "      <td>2230.0</td>\n",
       "      <td>2096.663577</td>\n",
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       "      <td>188</td>\n",
       "      <td>1590.0</td>\n",
       "      <td>1854.789245</td>\n",
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       "    <tr>\n",
       "      <td>74</td>\n",
       "      <td>1700.0</td>\n",
       "      <td>1720.499162</td>\n",
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       "    <tr>\n",
       "      <td>154</td>\n",
       "      <td>1560.0</td>\n",
       "      <td>1537.152881</td>\n",
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       "    <tr>\n",
       "      <td>117</td>\n",
       "      <td>940.0</td>\n",
       "      <td>646.762626</td>\n",
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       "    <tr>\n",
       "      <td>133</td>\n",
       "      <td>1960.0</td>\n",
       "      <td>1918.433181</td>\n",
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       "    <tr>\n",
       "      <td>84</td>\n",
       "      <td>2170.0</td>\n",
       "      <td>2065.288786</td>\n",
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       "      <td>142</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>1915.444996</td>\n",
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       "      <td>150</td>\n",
       "      <td>1610.0</td>\n",
       "      <td>1833.283408</td>\n",
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       "      <td>58</td>\n",
       "      <td>2380.0</td>\n",
       "      <td>2176.058847</td>\n",
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       "      <td>17</td>\n",
       "      <td>2440.0</td>\n",
       "      <td>2316.564398</td>\n",
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       "      <td>197</td>\n",
       "      <td>1280.0</td>\n",
       "      <td>1267.488898</td>\n",
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       "      <td>162</td>\n",
       "      <td>1490.0</td>\n",
       "      <td>1485.470259</td>\n",
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       "    <tr>\n",
       "      <td>123</td>\n",
       "      <td>1520.0</td>\n",
       "      <td>1490.797212</td>\n",
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       "    <tr>\n",
       "      <td>62</td>\n",
       "      <td>1570.0</td>\n",
       "      <td>1671.592784</td>\n",
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       "    <tr>\n",
       "      <td>116</td>\n",
       "      <td>1220.0</td>\n",
       "      <td>1188.183635</td>\n",
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       "    <tr>\n",
       "      <td>90</td>\n",
       "      <td>1120.0</td>\n",
       "      <td>989.215369</td>\n",
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       "    <tr>\n",
       "      <td>144</td>\n",
       "      <td>1140.0</td>\n",
       "      <td>1000.650513</td>\n",
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       "    <tr>\n",
       "      <td>91</td>\n",
       "      <td>730.0</td>\n",
       "      <td>441.276979</td>\n",
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       "    <tr>\n",
       "      <td>191</td>\n",
       "      <td>990.0</td>\n",
       "      <td>828.008600</td>\n",
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       "    <tr>\n",
       "      <td>138</td>\n",
       "      <td>960.0</td>\n",
       "      <td>960.716407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>161</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>1344.135186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>76</td>\n",
       "      <td>690.0</td>\n",
       "      <td>437.002787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>53</td>\n",
       "      <td>2120.0</td>\n",
       "      <td>1984.743459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>26</td>\n",
       "      <td>1500.0</td>\n",
       "      <td>1483.323336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>970.0</td>\n",
       "      <td>801.806397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>1550.0</td>\n",
       "      <td>1523.026003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>560.0</td>\n",
       "      <td>639.875650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>172</td>\n",
       "      <td>760.0</td>\n",
       "      <td>744.693081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>72</td>\n",
       "      <td>880.0</td>\n",
       "      <td>1018.187972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>55</td>\n",
       "      <td>2370.0</td>\n",
       "      <td>2119.481886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>145</td>\n",
       "      <td>1030.0</td>\n",
       "      <td>960.970131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>187</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>1694.584098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>40</td>\n",
       "      <td>1660.0</td>\n",
       "      <td>1629.103255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>110</td>\n",
       "      <td>1340.0</td>\n",
       "      <td>1476.078191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>92</td>\n",
       "      <td>1940.0</td>\n",
       "      <td>1909.973425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>164</td>\n",
       "      <td>1190.0</td>\n",
       "      <td>1092.569909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>79</td>\n",
       "      <td>1100.0</td>\n",
       "      <td>958.275789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>1740.0</td>\n",
       "      <td>1714.523677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>43</td>\n",
       "      <td>1290.0</td>\n",
       "      <td>1390.153903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>48</td>\n",
       "      <td>1480.0</td>\n",
       "      <td>1623.428820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>47</td>\n",
       "      <td>2320.0</td>\n",
       "      <td>2157.595514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>158</td>\n",
       "      <td>730.0</td>\n",
       "      <td>1023.513613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>194</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>1631.338612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>176</td>\n",
       "      <td>2020.0</td>\n",
       "      <td>1986.535026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>68</td>\n",
       "      <td>1890.0</td>\n",
       "      <td>1884.812519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>160</td>\n",
       "      <td>1440.0</td>\n",
       "      <td>1412.700742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>104</td>\n",
       "      <td>2070.0</td>\n",
       "      <td>2014.586226</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     real_values  predictions\n",
       "52        2260.0  2054.946754\n",
       "114       1460.0  1513.084006\n",
       "69        2230.0  2096.663577\n",
       "188       1590.0  1854.789245\n",
       "74        1700.0  1720.499162\n",
       "154       1560.0  1537.152881\n",
       "117        940.0   646.762626\n",
       "133       1960.0  1918.433181\n",
       "84        2170.0  2065.288786\n",
       "142       2010.0  1915.444996\n",
       "150       1610.0  1833.283408\n",
       "58        2380.0  2176.058847\n",
       "17        2440.0  2316.564398\n",
       "197       1280.0  1267.488898\n",
       "162       1490.0  1485.470259\n",
       "123       1520.0  1490.797212\n",
       "62        1570.0  1671.592784\n",
       "116       1220.0  1188.183635\n",
       "90        1120.0   989.215369\n",
       "144       1140.0  1000.650513\n",
       "91         730.0   441.276979\n",
       "191        990.0   828.008600\n",
       "138        960.0   960.716407\n",
       "161       1330.0  1344.135186\n",
       "76         690.0   437.002787\n",
       "53        2120.0  1984.743459\n",
       "26        1500.0  1483.323336\n",
       "24         970.0   801.806397\n",
       "97        1550.0  1523.026003\n",
       "22         560.0   639.875650\n",
       "172        760.0   744.693081\n",
       "72         880.0  1018.187972\n",
       "55        2370.0  2119.481886\n",
       "145       1030.0   960.970131\n",
       "187       1730.0  1694.584098\n",
       "40        1660.0  1629.103255\n",
       "110       1340.0  1476.078191\n",
       "92        1940.0  1909.973425\n",
       "164       1190.0  1092.569909\n",
       "79        1100.0   958.275789\n",
       "11        1740.0  1714.523677\n",
       "43        1290.0  1390.153903\n",
       "48        1480.0  1623.428820\n",
       "47        2320.0  2157.595514\n",
       "158        730.0  1023.513613\n",
       "194       1730.0  1631.338612\n",
       "176       2020.0  1986.535026\n",
       "68        1890.0  1884.812519\n",
       "160       1440.0  1412.700742\n",
       "104       2070.0  2014.586226"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = pd.DataFrame({'real_values':y_test, 'predictions':predictions_test})\n",
    "preds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "preds.plot(kind='bar',figsize=(18,8))\n",
    "plt.grid(linewidth='2')\n",
    "plt.grid(linewidth='2')\n",
    "plt.grid(None)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}