Multiple linear regression (Scikit-Learn on Real Estate).ipynb

{
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  {
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   "execution_count": 1,
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   "outputs": [
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     "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": 1,
     "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",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "#Load the data\n",
    "data = pd.read_csv(\"real_estate_price_size_year.csv\")\n",
    "data.head()"
   ]
  },
  {
   "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>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",
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      ],
      "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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#5 number summary\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Creating the multi-linear regression model\n",
    "x = data[[\"size\", \"year\"]]\n",
    "y = data[\"price\"]\n",
    "reg = LinearRegression()\n",
    "reg.fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 227.70085401, 2916.78532684])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Coefficients\n",
    "reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5772267.017463277"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Intercept\n",
    "reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7764803683276794"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Finding the R-Squared\n",
    "reg.score(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7718717161282501"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculating Adjusted R-Squared\n",
    "r2 = reg.score(x,y)\n",
    "n = x.shape[0] #Number of observations from x.shape\n",
    "p = x.shape[1] #Number of predictors from x.shape\n",
    "adjusted_r2 = 1 - (1 - r2) * (n - 1)/(n - p -1)\n",
    "adjusted_r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([285.92105192,   0.85525799]), array([8.12763222e-31, 3.57340758e-01]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Feature selection through p-values (F-regression)\n",
    "from sklearn.feature_selection import f_regression\n",
    "f_regression(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.12763222e-31, 3.57340758e-01])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#p-values\n",
    "p_values = f_regression(x, y)[1]\n",
    "p_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.   , 0.357])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Rounding p-values by 3 decimal points\n",
    "p_values.round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>Features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>size</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>year</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Features\n",
       "0     size\n",
       "1     year"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Creating a summary table\n",
    "reg_summary = pd.DataFrame(data = x.columns.values, columns = [\"Features\"])\n",
    "reg_summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>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>227.700854</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>year</td>\n",
       "      <td>2916.785327</td>\n",
       "      <td>0.357</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Features  Coefficients  p-values\n",
       "0     size    227.700854     0.000\n",
       "1     year   2916.785327     0.357"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Coefficents\n",
    "reg_summary[\"Coefficients\"] = reg.coef_\n",
    "reg_summary[\"p-values\"] = p_values.round(3)\n",
    "reg_summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StandardScaler(copy=True, with_mean=True, with_std=True)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Standardization\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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       "       [ 2.21224194,  1.14763808],\n",
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       "       [ 1.45329055,  0.51006137],\n",
       "       [-0.08495304, -1.40266877],\n",
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       "       [-0.70708471, -1.40266877],\n",
       "       [-0.66387316,  0.51006137],\n",
       "       [-1.02285625,  0.51006137],\n",
       "       [-0.56517136,  1.14763808],\n",
       "       [-0.56517136,  1.14763808],\n",
       "       [ 1.11464825,  1.14763808],\n",
       "       [ 1.62279723, -1.40266877],\n",
       "       [-0.57603328, -0.76509206],\n",
       "       [ 1.13205431, -1.40266877],\n",
       "       [-0.58004747, -1.40266877],\n",
       "       [ 0.90847416,  0.51006137],\n",
       "       [-0.58004747, -1.40266877],\n",
       "       [-0.70816415,  1.14763808],\n",
       "       [-0.56517136,  1.14763808],\n",
       "       [ 0.52699137,  1.14763808],\n",
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       "       [ 0.59162317, -0.76509206],\n",
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       "       [ 1.29501685,  1.14763808],\n",
       "       [-0.53467702,  1.14763808],\n",
       "       [ 0.73714592,  0.51006137],\n",
       "       [-0.53467702,  0.51006137],\n",
       "       [-0.5219598 ,  1.14763808],\n",
       "       [-0.5219598 , -1.40266877],\n",
       "       [-1.02285625, -0.76509206],\n",
       "       [ 0.62208377, -0.76509206],\n",
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       "       [-0.69062317,  0.51006137],\n",
       "       [-0.49834693, -1.40266877]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Transforming x \n",
    "x_scaled = scaler.transform(x)\n",
    "x_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Regression with scaled features\n",
    "reg = LinearRegression()\n",
    "reg.fit(x_scaled,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([67501.57614152, 13724.39708231])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Coefficents\n",
    "reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "292289.4701599997"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Intercept\n",
    "reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>Features</th>\n",
       "      <th>Weights</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Bias</td>\n",
       "      <td>292289.470160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>size</td>\n",
       "      <td>67501.576142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>year</td>\n",
       "      <td>13724.397082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Features        Weights\n",
       "0     Bias  292289.470160\n",
       "1     size   67501.576142\n",
       "2     year   13724.397082"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Creating summary table for Regression with scaled features\n",
    "reg_summary = pd.DataFrame([[\"Bias\"],[\"size\"],[\"year\"]], columns = [\"Features\"])\n",
    "reg_summary[\"Weights\"] = reg.intercept_, reg.coef_[0], reg.coef_[1]\n",
    "reg_summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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>size</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>650</td>\n",
       "      <td>2009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>700</td>\n",
       "      <td>2011</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   size  year\n",
       "0   650  2009\n",
       "1   700  2011"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Making predictions with the standardized coefficients (i.e. weights)\n",
    "new_data = pd.DataFrame(data = [[650,2009], [700,2011]], columns = [\"size\", \"year\"])\n",
    "new_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([71740627.70050645, 75143155.30174717])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.predict(new_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.68485488, -0.76509206],\n",
       "       [-0.51619152, -0.34004091]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Transforming standardized data\n",
    "new_data_scaled = scaler.transform(new_data)\n",
    "new_data_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([235560.2592592 , 252778.87261325])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.predict(new_data_scaled)"
   ]
  }
 ],
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