sklearn - Feature Scaling .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature scaling with sklearn - Exercise Solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>size</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>234314.144</td>\n",
       "      <td>643.09</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>228581.528</td>\n",
       "      <td>656.22</td>\n",
       "      <td>2009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>281626.336</td>\n",
       "      <td>487.29</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>401255.608</td>\n",
       "      <td>1504.75</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>458674.256</td>\n",
       "      <td>1275.46</td>\n",
       "      <td>2009</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        price     size  year\n",
       "0  234314.144   643.09  2015\n",
       "1  228581.528   656.22  2009\n",
       "2  281626.336   487.29  2018\n",
       "3  401255.608  1504.75  2015\n",
       "4  458674.256  1275.46  2009"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(r'D:\\Stu\\Data Science\\Exercises Regression\\real_estate_price_size_year.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>size</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>292289.470160</td>\n",
       "      <td>853.024200</td>\n",
       "      <td>2012.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>77051.727525</td>\n",
       "      <td>297.941951</td>\n",
       "      <td>4.729021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>154282.128000</td>\n",
       "      <td>479.750000</td>\n",
       "      <td>2006.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>234280.148000</td>\n",
       "      <td>643.330000</td>\n",
       "      <td>2009.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>280590.716000</td>\n",
       "      <td>696.405000</td>\n",
       "      <td>2015.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>335723.696000</td>\n",
       "      <td>1029.322500</td>\n",
       "      <td>2018.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>500681.128000</td>\n",
       "      <td>1842.510000</td>\n",
       "      <td>2018.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               price         size         year\n",
       "count     100.000000   100.000000   100.000000\n",
       "mean   292289.470160   853.024200  2012.600000\n",
       "std     77051.727525   297.941951     4.729021\n",
       "min    154282.128000   479.750000  2006.000000\n",
       "25%    234280.148000   643.330000  2009.000000\n",
       "50%    280590.716000   696.405000  2015.000000\n",
       "75%    335723.696000  1029.322500  2018.000000\n",
       "max    500681.128000  1842.510000  2018.000000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Declare the dependent and the independent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data[['size','year']]\n",
    "y = data['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scale the inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(x)\n",
    "x_scaled = scaler.transform(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg = LinearRegression()\n",
    "reg.fit(x_scaled,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "292289.4701599997"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([67501.57614152, 13724.39708231])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the R-squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7764803683276793"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.score(x_scaled,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the Adjusted R-squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's use the handy function we created\n",
    "def adj_r2(x,y):\n",
    "    r2 = reg.score(x,y)\n",
    "    n = x.shape[0]\n",
    "    p = x.shape[1]\n",
    "    adjusted_r2 = 1-(1-r2)*(n-1)/(n-p-1)\n",
    "    return adjusted_r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.77187171612825"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adj_r2(x_scaled,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare the R-squared and the Adjusted R-squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems the the R-squared is only slightly larger than the Adjusted R-squared, implying that we were not penalized a lot for the inclusion of 2 independent variables. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare the Adjusted R-squared with the R-squared of the simple linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing the Adjusted R-squared with the R-squared of the simple linear regression (when only 'size' was used), we realize that 'Year' is not bringing too much value to the result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making predictions\n",
    "\n",
    "Find the predicted price of an apartment that has a size of 750 sq.ft. from 2009."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_data = [[750,2009]]\n",
    "new_data_scaled = scaler.transform(new_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([258330.34465995])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.predict(new_data_scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the univariate p-values of the variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import f_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([285.92105192,   0.85525799]), array([8.12763222e-31, 3.57340758e-01]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_regression(x_scaled,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.12763222e-31, 3.57340758e-01])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_values = f_regression(x,y)[1]\n",
    "p_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.   , 0.357])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_values.round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a summary table with your findings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Coefficients</th>\n",
       "      <th>p-values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>size</td>\n",
       "      <td>67501.576142</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>year</td>\n",
       "      <td>13724.397082</td>\n",
       "      <td>0.357</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Features  Coefficients  p-values\n",
       "0     size  67501.576142     0.000\n",
       "1     year  13724.397082     0.357"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_summary = pd.DataFrame(data = x.columns.values, columns=['Features'])\n",
    "reg_summary ['Coefficients'] = reg.coef_\n",
    "reg_summary ['p-values'] = p_values.round(3)\n",
    "reg_summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that 'Year' is not event significant, therefore we should remove it from the model.\n",
    "\n",
    "Note that this dataset is extremely clean and probably artificially created, therefore standardization does not really bring any value to it."
   ]
  }
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