Linear Regression-Energy Efficiency.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "# Make plots bigger.\n",
    "plt.rcParams['figure.figsize'] = (14,6)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>relative_compactness</th>\n",
       "      <th>surface_area</th>\n",
       "      <th>wall_area</th>\n",
       "      <th>roof_area</th>\n",
       "      <th>overall_height</th>\n",
       "      <th>orientation</th>\n",
       "      <th>glazing_area</th>\n",
       "      <th>glazing_area_distribution</th>\n",
       "      <th>heating_load</th>\n",
       "      <th>cooling_load</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.98</td>\n",
       "      <td>514.5</td>\n",
       "      <td>294.0</td>\n",
       "      <td>110.25</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>15.55</td>\n",
       "      <td>21.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.98</td>\n",
       "      <td>514.5</td>\n",
       "      <td>294.0</td>\n",
       "      <td>110.25</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>15.55</td>\n",
       "      <td>21.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.98</td>\n",
       "      <td>514.5</td>\n",
       "      <td>294.0</td>\n",
       "      <td>110.25</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>15.55</td>\n",
       "      <td>21.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.98</td>\n",
       "      <td>514.5</td>\n",
       "      <td>294.0</td>\n",
       "      <td>110.25</td>\n",
       "      <td>7.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>15.55</td>\n",
       "      <td>21.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.90</td>\n",
       "      <td>563.5</td>\n",
       "      <td>318.5</td>\n",
       "      <td>122.50</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>20.84</td>\n",
       "      <td>28.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.90</td>\n",
       "      <td>563.5</td>\n",
       "      <td>318.5</td>\n",
       "      <td>122.50</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>21.46</td>\n",
       "      <td>25.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.90</td>\n",
       "      <td>563.5</td>\n",
       "      <td>318.5</td>\n",
       "      <td>122.50</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>20.71</td>\n",
       "      <td>25.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.90</td>\n",
       "      <td>563.5</td>\n",
       "      <td>318.5</td>\n",
       "      <td>122.50</td>\n",
       "      <td>7.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>19.68</td>\n",
       "      <td>29.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.86</td>\n",
       "      <td>588.0</td>\n",
       "      <td>294.0</td>\n",
       "      <td>147.00</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>19.50</td>\n",
       "      <td>27.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.86</td>\n",
       "      <td>588.0</td>\n",
       "      <td>294.0</td>\n",
       "      <td>147.00</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>19.95</td>\n",
       "      <td>21.97</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   relative_compactness  surface_area  wall_area  roof_area  overall_height  \\\n",
       "0                  0.98         514.5      294.0     110.25             7.0   \n",
       "1                  0.98         514.5      294.0     110.25             7.0   \n",
       "2                  0.98         514.5      294.0     110.25             7.0   \n",
       "3                  0.98         514.5      294.0     110.25             7.0   \n",
       "4                  0.90         563.5      318.5     122.50             7.0   \n",
       "5                  0.90         563.5      318.5     122.50             7.0   \n",
       "6                  0.90         563.5      318.5     122.50             7.0   \n",
       "7                  0.90         563.5      318.5     122.50             7.0   \n",
       "8                  0.86         588.0      294.0     147.00             7.0   \n",
       "9                  0.86         588.0      294.0     147.00             7.0   \n",
       "\n",
       "   orientation  glazing_area  glazing_area_distribution  heating_load  \\\n",
       "0            2           0.0                          0         15.55   \n",
       "1            3           0.0                          0         15.55   \n",
       "2            4           0.0                          0         15.55   \n",
       "3            5           0.0                          0         15.55   \n",
       "4            2           0.0                          0         20.84   \n",
       "5            3           0.0                          0         21.46   \n",
       "6            4           0.0                          0         20.71   \n",
       "7            5           0.0                          0         19.68   \n",
       "8            2           0.0                          0         19.50   \n",
       "9            3           0.0                          0         19.95   \n",
       "\n",
       "   cooling_load  \n",
       "0         21.33  \n",
       "1         21.33  \n",
       "2         21.33  \n",
       "3         21.33  \n",
       "4         28.28  \n",
       "5         25.38  \n",
       "6         25.16  \n",
       "7         29.60  \n",
       "8         27.30  \n",
       "9         21.97  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "\n",
    "PROBLEM STATEMENT:\n",
    "\n",
    "How should we design buildings (with respect to heating load) in the future?\n",
    "\n",
    "Additional questions:\n",
    "\n",
    "    1. Is there a relationship between building features and heating load?\n",
    "    2. How strong is that relationship?\n",
    "    3. Which are the strongest contributing features to heating load?\n",
    "    4. Can heating load be predicted given a particular building design?\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "##################################################################################################\n",
    "##################################################################################################\n",
    "\n",
    "\"\"\"\n",
    "The dataset contains eight features (relative _compactness\tglazing_area_distribution) \n",
    "and two outcomes (heating_load & cooling_load).\n",
    "The aim is to use the eight features to predict, in this case, one of the two responses (Heating Load).\n",
    "\"\"\" \n",
    "\n",
    "df_energy_efficiency = pd.read_excel(\"../../../data/RCC/ENB2012_data.xlsx\", index_col=None)\n",
    "df_energy_efficiency.columns = [\"relative_compactness\", \"surface_area\", \"wall_area\", \"roof_area\", \"overall_height\", \"orientation\", \"glazing_area\", \"glazing_area_distribution\", \"heating_load\", \"cooling_load\"]\n",
    "df_energy_efficiency.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(768, 10)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_energy_efficiency.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1b160e97cf8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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uluRwCj/81eEi7Ye/Omz0HQbPqOsDSp9O2Kj/TNTTNtHZFvoOEaSC0kvZ2nMEn3nkZXz5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\nQCymgiAIgiAIgiAIGuA/iJ5OOw/8ZxUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b160b5d128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"Visualize the relationship between the features and the responses.\"\"\"\n",
    "\n",
    "fig, axs = plt.subplots(1, 8, sharey=True)\n",
    "df_energy_efficiency.plot(kind='scatter', x='relative_compactness', y='heating_load', ax=axs[0], figsize=(14, 6))\n",
    "df_energy_efficiency.plot(kind='scatter', x='surface_area', y='heating_load', ax=axs[1])\n",
    "df_energy_efficiency.plot(kind='scatter', x='wall_area', y='heating_load', ax=axs[2])\n",
    "df_energy_efficiency.plot(kind='scatter', x='roof_area', y='heating_load', ax=axs[3])\n",
    "df_energy_efficiency.plot(kind='scatter', x='overall_height', y='heating_load', ax=axs[4])\n",
    "df_energy_efficiency.plot(kind='scatter', x='orientation', y='heating_load', ax=axs[5])\n",
    "df_energy_efficiency.plot(kind='scatter', x='glazing_area', y='heating_load', ax=axs[6])\n",
    "df_energy_efficiency.plot(kind='scatter', x='glazing_area_distribution', y='heating_load', ax=axs[7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept              -23.053014\n",
       "relative_compactness    59.359053\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Estimate Model Coefficients for Relative Compactness\"\"\"\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# Create fitted model.\n",
    "lm = smf.ols(formula='heating_load ~ relative_compactness', data=df_energy_efficiency).fit()\n",
    "\n",
    "# Get coefficients.\n",
    "lm.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "570.5375160000001"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "FINDINGS:\n",
    "\n",
    "    1. An increase in relative compactness leads to a decrease in heating load.\n",
    "    2. A decrease in Relative Compactness is associated with a 59.359053 \"unit\" increase in Heating Load.\n",
    "\n",
    "######################################################\n",
    "\n",
    "Use model to make predictions (manually).\n",
    "A 10% increase in overall relative compactness \n",
    "translates to a decrease in heating load.\n",
    "\"\"\"\n",
    "\n",
    "-23.053014+59.359053*10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>relative_compactness</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   relative_compactness\n",
       "0                    10"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create A DataFrame\n",
    "X_new = pd.DataFrame({'relative_compactness': [10]})\n",
    "X_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    570.537512\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Use model to make predictions on a new value.\n",
    "The model works; compare to manual prediction above.\n",
    "\"\"\"\n",
    "\n",
    "lm.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>relative_compactness</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   relative_compactness\n",
       "0                  0.62\n",
       "1                  0.98"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Plotting Least Squares\n",
    "\n",
    "Create a DataFrame with the minimum and maximum relative compactness values.\n",
    "\"\"\"\n",
    "\n",
    "X_new = pd.DataFrame({'relative_compactness': [df_energy_efficiency.relative_compactness.min(), df_energy_efficiency.relative_compactness.max()]})\n",
    "X_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    13.749599\n",
       "1    35.118858\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Make and store predictions of min. & max. values.\"\"\"\n",
    "\n",
    "presage = lm.predict(X_new)\n",
    "presage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b1626586a0>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hcr/e5hpXieWZG04lb20pH67azqjjOgdeWlWMCW8ET0TuA5KB14Dymrgx5svo\nNK2unJwck5eXF4tTqSbE15YYxsAXX9iuohdeqFsW8/LLbUIYOTKsspiRsLpkD+c8/OFh8XdvGRWf\n23uoJklEFhtjcvwc4+eK4RTne+0TGOBsPydUKpL6Z7Y9+ptoaWmoLOaSJaH4qafaZHD55dBW34iV\nquFnVpLXlFSl4k91NeTm2mTw+ut1y2JOm2b3Kxo8ONAmzlvmvrJ13rJivWJQgTpqYhCRqcaYZ0Xk\nF24/r71wTanAffONLYn5j3/A+vU2JgLnnWevDiZOjEhZzEjYd7DSV1ypWAnniiHN+e72EUaL86jg\nlZfDG2/Yq4P580NlMfv0CZXFjMNNGE/Icp+n7hVXKlaOmhiMMX93br5rjPmk9s+ctQ1KBWPZMpsM\nnnkGtjvzwFNT4eKL7dXB2WdHrSxmJIzsl4FQ99OVOHGlguRn8Pkv2G23jxZTKnr27IHZs21C+Oyz\nUHzoULt53VVXQUbTeGPNSG/Jo1dkc9vL+QhJGKp56NJsMtJbBt00leDCGWMYCZwGdKk3ztAOO31V\nqegyBhYtCpXF3OvsJdSund24bvp0u5FdjKaZRtLE7B6c3r8zG3fsp2fH1gmbFErLyhP+NYgn4Vwx\npALpzmNrjzPsBqZEo1FKAbB1a6gs5tdfh+JnnmmvDqZMgTaxq10QLRnpLRP6zXBu/ibufLWQlKQk\nKqqreeCSYUzM1kKPQQpnjOED4AMRecoYsz4GbVKJrKoqVBbzjTdCZTEzM0NlMQcMCLSJKnJKy8q5\n89VCDlRUcwC7N9UdrxZyev/OCZ0sg+ZnjGGfiDwIDAYObStpjNEFbqrx1q4NlcXc6NRBTkqCCy8M\nlcVMiW0BGxV9G3fsJyUp6VBSALvd9MYd+zUxBMhPYngOmA1MAH4IXAMcvtGLUuE6cMAuPnviCXjv\nvVC8Xz+bDK65Brp3D659Kup6dmzNgcq6e3IeqKyip24kGCg/iSHDGDNTRG6q1b30RbQappqxggKb\nDJ57DnbssLFWrUJlMUeNapIDyaphKqvMEe+r2POTGGqqh2wRkQuAzUCnyDdJNUs7d9qN62bOhMWL\nQ/ERI2wyuPJK6BCjes0qbizbvPuwVbLGiY8a0CWIJin8JYZ7RKQ9cCt2/UI7bH0GTyLSC5gFZGL/\nvWcYYx4VkU7Ybqm+2NKelxljdvhuvYpvxsCHH9pk8PLLobKYHTqEymJmZwfbRhUwr6sDvWoIkp9N\n9N50bu4HAuFSAAAcZ0lEQVTCu8ZzfZXArcaYL0WkLbBYRBZg60fnGmPuE5FfAr8E7gy/2Squbdli\ni97MnAmrV4fiZ58dKovZWvuQ40WQawgGd29PSrJQUav7KCVZGBxgWUvlr7TnAOBvQKYxZoiIDAMm\nGmPu8TrGGLMF2OLc3iMiy4EewCRgtPOwp4GFaGJo2iorbTnMJ56w36ucAcUePULTTCNYFlNFRtBr\nCDLSW/KnS4dz28sFiAjGGB66dLjOSAqYn41kHgd+hTPWYIwpBK4I92AR6QucCHyOTS5bnB8VY7ua\n3I65UUTyRCRv27b4mgC1umQPr+RtYHXJnqCbEqxVq+CXv4RevWDSJPjnP+3A8UUX2frJ69fDPfdo\nUohDtdcQ7Cmv5EBFNXe8WkhpWfnRD44gA4gIyUmC6KSDuOBnjKGNMebf9f7hwtofWETSgVeBm40x\nu2s/hzHGiIhrh6IxZgYwA2wFNx9tjarfzFnCrM/qlpT8/aShAbYoxvbts2UxZ860Ywg1Bg60A8lX\nX20XpKm4tnHHfs94rD6x1ySn8srQOgZd4BY8P4lhu4j0wxkVEpEpON1ERyIiKdik8Jwx5jUnXCIi\nWcaYLSKSBWz12e7ArC7ZUycpAMxa9A3TTu3bvIurGGNnE82cCc8/D7t323ibNqGymKedptNMm5C0\n1GQOVFTXiR2oqCYtNXZboOkCt/jkJzH8BPvp/XgR2QSsBa460gFiLw1mAsvrFfR5A7tA7j7n+1w/\njQ5SwlXd+vZbu97giSegsDAUP+WUUFnMdu2Ca59qsM27DnjGY/W33LNjayqq6yaniupqXeAWMD+J\nYRPwD+B97PqF3dg39d8f4ZjTgauBJSKS78TuwiaEl0RkOrAeuMxnuwOzeqv7mIJXvEmqrrYrkWvK\nYpY7fc4ZGbabaPp0GDIk2DaqCAh+qmhGekseuGQYd9QbANerhWD5SQxzgZ3Al9jFbUdljPkYW3vE\nzVgf544bm3d6fMryiDcpGzbYvYqefBLWrbMxETj33FBZzJb6H7a5iJeporr1ePzxkxh6GmPOi1pL\nmojWKe4Tubzice/gQTuTaOZMu6tpzWV9nz5w3XV2qmmfPoE2UUVHPE0VTfStx+ONn8TwqYgMNcYs\niVprmoBBPdqzcFWpa7xJWb7cJoNZs6BmKnBqKkyebGcWjR0b12UxVWTUnipaVX3Uh6sEEU4FtyXY\nv58WwHUisgYox3YRGWPMsOg2Mb4M6JruKx5XyspCZTEXLQrFhwyxyWDq1CZTFlM1nk4VVV7CuWKY\nEPVWNCFfrN/pGZ88oleMWxMGY2xt5JkzbVIoK7Pxtm1DZTFPOkmnmSYgnSqqvIRTwU2rttXSobX7\nS+YVD8y2bfDMMzYhFBWF4mecYZPBpZdCWlpw7VOB06miyot2Ivs0ZmBXX/GYqqqCd96xdQ169IBb\nb7VJoWtXuP12O67w0Ud2QFmTQtwoLSunYMPOmG9FUTNVtFVKEm1btqBVSpJOFVWAv8HnZmV1yR7y\nN+wku1cHX4t59lVU+YrHxLp1obKYGzbYWFISTJhgrw4uuEDLYsapoDex06miyk1CJobG7HW0sth9\nIdvK4j2MGhDDq4YDB2DOHNtVlJtrxxLAlsW8/npbFrNH7N5glH+1N7Gr6ecPYvBXp4qq+hIuMTR2\nr6N1pft8xSOusNAmg2eftdtVgC2Leckl9urgrLN0mmkTEQ+b2CnlJuESw/Ofu4+lP//5en4z8ejb\nPHjN3YnqnJ5du+DFF+1+RXl5ofiJJ9pk8L3vQceO0WyBioJ42MROKTcJlxhWlpT5iteXv8G9AqlX\nvMGMgY8/tsng5Zdhv/Ppsn37UFnME0+M7DlVTMXDJnZKuUm4xNDKY+sKr3h9Jbvd/zN7xX0rLrZl\nMZ98ElauDMXHjLHJ4OKLtSxmsxH8JnZKuUm4xLDJo1/XK15f21YpbC2rcI03WGUlvP22HTt4881Q\nWczu3UNlMfv1a/jzq7gUL5vYKVVfwo1S1l7+H068vguHd/cVP6JVq+BXv4Leve3OpXPn2hXIkyfb\nBLF+PfzhD5oUmqmaTexSk4WWLZJITRb+pPWOVRxIuMRwziD3kpNe8fquHtnXV/ww+/bZFcmjR8OA\nAXDffbBli739wAOwcaOtgXDBBdAi4S7oEo7WO1bxKOESww/Ocv/07RWvLyO9JY9dkU0LgSSBFgKP\nXZF95E95NWUxf/xj2z00bRp88IEti3nttXY18tdf29XJWis5YdTexG7fwSrKK6u549XCmK+AVvEh\nt6iYO18pILfIvUpkLCXcR9KaN/abX8y3n9aAR472xl7PxOwefLiihAXLtzLuhK7eK1V37AiVxSwo\nCMVPPpnl353CC8eexlk5/Rg7qFujfifVNOkmdqrG+IcXsrJkLwCz8zYyMDONebeMDqw9CZcYwL6x\nd2/fig9XbWfUcZ3JOcbfVtN9f/nWoduvfLWFV756i3X3XWAD1dWwcKFNBq+9FiqL2anTobKY498t\ntX8ERTuZVbQ48D8CFQzdxE6BvVKoSQo1VpTsJbeoOLAPjVHtShKRJ0Vkq4gsrRW7W0Q2iUi+83V+\nNNvg5jdzljDl75/x2HurmfL3z/jN3PBrD/3XawWu8Qcenw/33AP9+9siNy+8YKujjR9vt7vevBke\neYTc5C6efwQqsegmdgpgflGJr3gsRPuK4Sngr8CsevGHjTEPRfncrhq7JcZLeRsP3U6pquDs1V9w\neeF8zlr7JRjn01/v3rYs5nXXHVYW8753lrs+733vLI/4p4PSsnLdHC3O6SZ2avygTGbXel+pHQ9K\nVBODMeZDEekbzXP49fpXh/8D1MRvP++EsJ6jX+kGLitcwCVLc+m8bxcAB5NakDzlklBZzGT3bQ02\n7nDfU8kr3lBz8zdxS71xFL+7dj48bzlzC4uZNKwbt5wb3mvjR0N3uG1udBO7xDZ2UDcGZqaxolZP\nwsDMtEDHHoMaY/iZiEwD8oBbjTGu+0mIyI3AjQC9e/eOyIl37a/0FT+krAxefpkFrz1KnxWh7qQV\nnXsze9i5tLj6e9x17eijnr9Tm5Zs2nX4rJNObSL3xlBaVs5NL+Yfum+An7+Y72vXzuN+9RYVzrqr\nR99fw/8uXMOqP14QsTY2ZodbpZqbebeMJreomPlFJYwflBn4hJQgpqv+DTgWyAa2AH/yeqAxZoYx\nJscYk9OlS5eInLx1C/e54q7xmrKY3/8+ZGXB9dfTZ0UBZamteX74uUy++k+ce/3/8ORJk8JKCgAX\nDHNfCOcVb4i/f/AfX/H6Hp63/FBSqFFhbDwSvLrzVpe4b2muVCIYO6gb908ZHnhSgAASgzGmxBhT\nZYypBh4HTo7l+fM37T56fPt2ePhhGDoURo60M4zKyuD00+HJJ0kv3UrRb+5nw3FDmHpKr9CMpDCc\ncZx7gvOKN8RbhZt9xet74Qv37javuF+/nlPoK66Uiq2YdyWJSJYxZotz9yJg6ZEeH2nZPdrxxbrD\ne65O7JYG8+bZ/YrmzIEKZz+krl3tgrTp0+H44w89/p6Lh3PPxf7PP7h7O1okQe0dOFok2Xik7Peo\nJucVry8jLZWtZQdd45FQsGGnr7hSKraimhhE5AVgNNBZRDYCvwVGi0g2tut7HfCDaLahvh31xhJ6\n7NrKpUsWcM0T70OpM2U0KQnOP98OJE+YENGymBnpLfnzZdnc/koByZJElanmwSmR3R+nXasWfLvv\n8DGTdq3C++e+6pTe/NcbRa7xSGjfOoUDew7fiLB9ay0/qlQ8iPaspCtdwjOjec6j2b6nnNTKCsav\nWsRlhQs4Y10+STXbHB97bKgsZs+eUWtDtKcojuzXmXXfHt7tM7Jf57CO33XAY4DeI+7X5Oye/P2j\nta5xpVTwEm7lc9tWLfjdgr9xZeF8AMqTU3h74GlsmHQFP7vnxpiVxYzmFMXpZxzrOh4w/Yxjwzp+\n30H3BOAV92tozw6+4kqp2Eq4xHBa/868MegshhWvZvawccwZPIbdrdL546QhMa2VPOfLDby5pJgJ\nQ7sxeUSviD53/8y2TBvZm1mL6k4HDXetwAlZ7vUAvOJ+tWvt/mfnFVdKxVbC/U8cP7gbd/UexgXX\nPXYoJk48Vk69dwHFu+3g7rvLt3L/O1+z6K5xET3H7ycNpWOrFg1aoDayXwZC3Tpi4sQjQQvUKBXf\nEm7b7Yz0lph6+94bJx4Lc77ccCgp1Niy+yBzvtwQ0fMMv/sdHn1/DetK9/Ho+2sYfvc7YR+bkd6S\nR6/IJiUJUpKElCR41OcOtEd7/j9dOpyWLZJok5pMyxZJWqBGqTiScInhttlf+opH2v3vrPAVb4hn\nP13LrgN1p6buOlDFs58ePuDrxQAGobLaYIh8AZmJ2T1462dn8PuJg3nrZ2f43q5DKRU9CZcY/lmw\nxVc80r7d616ExSveEDM+WuMrXl/Nlho2KUBlteHnL+ZHtIDM3PxNnPPwh9z2SiHnPPwhb+Rvithz\nK6UaJ+ESQ2qK+6/sFY+0jDT37hKveEN4fb4P93P/Y++u9BX3q/5eTkDEE49SquESLjF8p09HX/FI\nu+O8gb7iDXFSX/ffxSte39tL3a+evOJ+/W6u+2J3r7hSKrYSLjH8dMxxvuKRNnlEL7La1d1aIqtd\nakSnrK4r3e8rXt/+gx5banjE/fpo9XZfcaVUbCVcYsg5JoMz+9eddnlm/wzf5T0bY9Fd47hwSFfS\nUpO4cEjXiE9V7eSxp5FXvL4qY3zF/eqc7t4Or7hSKrYSbh0DwDM3nEre2tIG13xurBP+61/sr7Rv\nsv9cupV3/+tfLL8nchVObxx1LPOXb3WNh+PM/l2Y53L8mf0jswPs8d3asWrb4YWJju8WuY0ElVIN\nl3BXDDVyjsngF+MHxjwp/P39VYeSQo39lYa/v78qYufIOSaD9q3qVpBr3yo57N/13kuG+Yr7ldXB\nvdi9V1wpFVsJmxiCMuMj92I5XvGGyFtb6rqOIW9taVjHZ6S35LErsuvEHovgAjeDe5eUV1wpFVsJ\n2ZUUCaVl5Q3aHXWfxwCuV7wh/vreas/4U9PDu2qYmN2DQVntolKT+dxB3Xj8o3WucaVU8DQxNMDc\n/E3cUa+eQrgrdzPbt3adHZTZPnLdKIu/+dZX3M3c/E111ho8dkV2xFYn10wA+Gh16Aom1hMAlFLe\ntCvJp9Kycm59KZ/ySsO+iirKKw2/eCn8xVk3j3WfFusVb4iKSvcuGa94fbFYgPbMDady05hj6ZvR\nhpvGHMszN5wasedWSjWOJgaflm3eXacsJ9gyncs2u9eSri8W6xgmDHPvkvGK13fVjEW+4g1x6r0L\n6mzyN/LeBRF7bqVU42hi8GnTjsOnWR4p7mbRXeN45LJhnHNCVx65bFjE1zE8dPkIX/H6Vm7d6yvu\nV6x2mFVKNUxUE4OIPCkiW0Vkaa1YJxFZICKrnO+x2YsiQsrrXy4cJe5l8ohePHHNSREv0lNj3X0X\nMOXELNq3SmbKiVmsu++CsI/t3dF9vMMr7tcf/7XcV1wpFVvRvmJ4CjivXuyXQK4x5jgg17nfZJzR\n371uslc8SA9dPoKCu88L+0qhxhPXnuQr7te3+yp8xZVSsRXVxGCM+RCoPxVmEvC0c/tpYHI02xBp\nNWUza/NTNrMpiPbvmNWhla+4Uiq2xERo/xvPE4j0Bd40xgxx7u80xnRwbguwo+a+y7E3AjcC9O7d\n+zvr16+Palv9WF2yJypz/ONJtH7H3KJips9afFh85rTvMFbXMigVUSKy2BiT4+eYQNcxGGOMiHhm\nJmPMDGAGQE5OTlwti+2f2bbZJoQa0fodxw7qxsDMNFaUhAazB2amaVJQKk4EkRhKRCTLGLNFRLKA\nw3drU83evFtGk1tUzPyiEsYPytSkoFQcCSIxvAFcA9znfJ8bQBtUHBg7qJsmBKXiULSnq74ALAIG\nishGEZmOTQjjRGQVcI5zP+ZKy8op2LBTy0kqpVQ9Ub1iMMZc6fGjsdE879HMzd/EbS/lY6sgG/50\nWeT2AVJKqaYu4VY+1+wDVFENFdWGimotRK+UUrUlXGKYv6zYV1wppRJNwiWGNdvLfMWVUirRJFxi\n8CoGo0VilFLKSrjEUFMkpjYtEqOUUiEJWcHtmRtOJW9tKR+u2s6o4zprUlBKqVoSMjGAvXIIMiHo\nql+lVLxK2MQQpPEPL2Sls0/Q7LyNDMxMY94toyN+ntKycjbu2E/Pjq3JSG8Z8edXSjVPmhhiLLeo\n+FBSqLGiZC+5RcURvXLQRXxKqYZKuMHnoM0vKvEVbwhdxKeUagxNDDE2flCmr3hDRGoRX25RMXe+\nUkBukS7+UyqRaFdSjMWiFkEkFvHFahxEKRV/NDEEINq1CM4d1I3HP1rnGg9HrMZBdGaWUvFJE0NA\nolmLoGYR30erSw/F/CziO9I4SKTarFckSsUvTQzNVGMW8Y0flMnsvI2u8UiI1RWJUqphNDE0Yw1d\nxBftcZBYXJEopRpOE4NyFc1xkGhfkSilGiewxCAi64A9QBVQaYzJCaotyl20xkFiMTNLKdVwQV8x\njDHGbA+4DSoA0Z6ZpZRquKATg0pg0ZyZpZRquCBXPhvgXRFZLCI3uj1ARG4UkTwRydu2bVuMm6eU\nUokpyMRwhjEmG/gu8BMRGVX/AcaYGcaYHGNMTpcuXWLfQqWUSkCBJQZjzCbn+1bgdeDkoNqilFIq\nJJDEICJpItK25jYwHlgaRFuUUkrVFdTgcybwuojUtOF5Y8w7AbVFKaVULWKMCboNYRGRbcD6WqHO\nQLxPddU2Nl68tw+0jZGibWw8t/b1Mcb4GqRtMomhPhHJi/dFcdrGxov39oG2MVK0jY0XqfZpoR6l\nlFJ1aGJQSilVR1NODDOCbkAYtI2NF+/tA21jpGgbGy8i7WuyYwxKKaWioylfMSillIoCTQxKKaXq\niMvEICLnicgKEVktIr/0eMxoEckXkWUi8oGfYwNu3zoRWeL8LC8a7QunjSJyu9OGfBFZKiJVItIp\n3N8vDtoYL69jexH5p4gUOP/W14V7bBy0L15ew44i8rqIFIrIv0VkSLjHxkkbo/46isiTIrJVRFx3\niBDrMaf9hSIyItzfzZUxJq6+gGTgP8CxQCpQAAyq95gOQBHQ27nfNdxjg2yfc3sd0Dno17De4y8E\n3ovVa9jYNsbT6wjcBdzv3O4CfOs8Nl7+Fl3bF2ev4YPAb53bxwO58fa36NXGGL6Oo4ARwFKPn58P\nvA0IcCrweWNew3i8YjgZWG2MWWOMOQi8CEyq95jvAa8ZY76BQxvxhXtskO2LFb+vw5XACw08Nog2\nxko4bTRAWxERIB37xlsZ5rFBti9WwmnjIOA9AGPM10BfEckM89ig2xgTxpgPsf92XiYBs4z1GdBB\nRLJo4GsYj4mhB7Ch1v2NTqy2AUBHEVkotp7DNB/HBtk+CKMORYzaCICItAHOA171e2yAbYT4eR3/\nCpwAbAaWADcZY6rDPDbI9kH8vIYFwMUAInIy0AfoGeaxQbcRYvM6Ho3X79Cg17CpVnBrAXwHGAu0\nBhaJyGfBNqkO1/YZY1Zi61BsEpGuwAIR+dr5NBCUC4FPjDFH+jQSNLc2xsvreC6QD5wN9HPa8lEA\n7fDi2j5jzG7i5zW8D3hURPKxyesrbC34eHKkNsbL6xgx8XjFsAnoVet+TydW20ZgnjFmr7E1oz8E\nhod5bJDtw8SmDoWf1+EK6nbRxOI19Hue+m2Mp9fxOmy3oTHGrAbWYvug4+Vv0at9cfMaGmN2G2Ou\nM7Zw1zTsWMiacI6NgzbG6nU8Gq/foWGvYTQHTBryhf20vQY4htBgyeB6jzkByHUe2wZby2FIOMcG\n3L40oK3zmDTgU+C8IF5D53Htsf2WaX6PDbiNcfM6An8D7nZuZzr/6TrH0d+iV/vi6TXsQGhA/PvY\nvvK4+ls8Qhtj8jo6z98X78HnC6g7+PzvxryGEW98hF6A84GV2NH0XzuxHwI/rPWY27Ezf5YCNx/p\n2HhpH3ZmQIHztSxa7fPRxmuBF8M5Np7aGE+vI9AdmI/tXlgKTI2nv0Wv9sXZazjS+fkK4DWgY7z9\nLXq1MVavI/aKeQtQge2RmF6vfQL8j9P+JUBOY15D3RJDKaVUHfE4xqCUUipAmhiUUkrVoYlBKaVU\nHZoYlFJK1aGJQSmlVB2aGJRSStWhiUHFJWefqZyjPOZmZx+lmvv/EpEO0W9dsESkg4j8OOh2qOZL\nE4MKjLOHfGP+Bm/GriwHwBhzvjFmZ+NbFvc6AJoYVNRoYlAxJSJ9naIhs7Arca8WkUUi8qWIvCwi\n6S7H/E1E8pxCM79zYj/Hrup9X0Ted2LrRKSziNwnIj+pdfzdInKbc/t2EfnCKWbyu6O0dZrzuAIR\neaZW+99z4rki0tuJP+W08zMRWSO2UNOTIrJcRJ6q9ZxlIvKw87vkikgXJ/59p10FIvJqzZWQiGQ6\nBWIKnK/TsBu69XMKwzzonGuhiLwiIl+LyHPONtuIyHdE5ANn5895zlbMiMjPRaTI+T1edGJnSagw\n0lci0rYB/8SqOYjWEnP90i+3L+x+L9XY/Vw6YzcYTHN+difwG+f2Qpxl/UAn53uyEx/m3F9HrQIp\nNfeBE4EPasWLsBuJjQdmYLcPSALeBEZ5tHMwdhuBzvXa8E/gGuf29cAc5/ZT2L3uBbvf/W5gqHOe\nxUC28zgDXOXc/g3wV+d2Rq1z3wP8zLk9m9CWKsnYvaP6UmvPHGA0sAu7QVoSsAg4A0jB7t3TxXnc\n5cCTzu3NQEvndodav9vpzu10oEXQfy/6FcxXU912WzVt640xn4nIBGwBlE+cD7ip2De1+i5z9rlv\nAWQ5xxR6Pbkx5isR6Soi3bG7YO4wxmwQkZuwyeEr56HpwHHY5FTf2cDLxu6Oiwlt+T0SZ19+4Bng\ngVrH/NMYY0RkCVBijFkCICLLsG/m+dikONt5/LPYfXcAhojIPdhuonRgXq12THPaUAXsEpGOLu39\ntzFmo3O+fOd8O7GbNy5wXt9k7H47YF+/50RkDjDHiX0C/FlEnsPuyLrR5TwqAWhiUEHY63wXYIEx\n5kqvB4rIMcBtwEnGmB1Ot0yrMM7xMjAF6EbojViAPxpj/t7Qhh9FufO9utbtmvte/9dqNit7Cphs\njCkQkWuxVwENOTfYOgEtsL/vMmPMSJfHX4AtF3kh8GsRGWqMuU9E3sJuuvaJiJxrbLUylWB0jEEF\n6TPgdBHpDyAiaSIyoN5j2mETyS6xpRS/W+tnewCvfvDZ2DoOU7BJAuyn8OtrxjFEpIdTXMXNe8Cl\nIpLhPLaTE//UeV6AqwC/RXmSnDaBLQH7sXO7LbBFRFKc562RC/zIaUOyiLTnyL93bSuALiIy0jk+\nRUQGOwP+vYwx72O779oD6SLSzxizxBhzP/AFTt0GlXg0MajAGGO2YbfVfkFECrHdSMfXe0wBtuvn\na+B5bHdHjRnAOzWDz/WOW4Z989xkjNnixOY7z7HI6e55BY83WOf4PwAfiEgB8GfnRz8DrnPaezVw\nk89fey9wsogsxXYT/d6J/z/gc+f3q/0p/SZgjNPexdhC7qXYT/RLReRBrxMZW+N3CnC/8zvkA6dh\nu5SedZ7zK+AxY2dz3ew8ZyF2e+e3ff5uqpnQbbeViiERKTPGHDbzSql4olcMSiml6tArBpXQnDGE\nXJcfjXW6bJRKOJoYlFJK1aFdSUopperQxKCUUqoOTQxKKaXq0MSglFKqjv8PBeUOHGTi7a8AAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b1626589b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"Plot the observed data then plot the least squares line.\"\"\"\n",
    "\n",
    "df_energy_efficiency.plot(kind='scatter', x='relative_compactness', y='heating_load')\n",
    "plt.plot(X_new, presage, c='red', linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>-27.138867</td>\n",
       "      <td>-18.967161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>relative_compactness</th>\n",
       "      <td>54.062678</td>\n",
       "      <td>64.655427</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              0          1\n",
       "Intercept            -27.138867 -18.967161\n",
       "relative_compactness  54.062678  64.655427"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Confidence Intervals for the Model Coefficients\"\"\"\n",
    "\n",
    "\"\"\"\n",
    "Statsmodels calculates 95% confidence intervals for our model coefficients, interpreted thus: \n",
    "for every 100 times the population is sampled, approximately 95 (confidence intervals) would \n",
    "contain the \"true\" coefficient.\n",
    "\"\"\"\n",
    "\n",
    "lm.conf_int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept               1.503456e-26\n",
       "relative_compactness    1.591576e-83\n",
       "dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Null Hypothesis Testing & Model Coefficients p-values\"\"\"\n",
    "\n",
    "\"\"\"\n",
    "If the 95% confidence interval includes zero, the p-value for that coefficient \n",
    "will be greater than 0.05. If the 95% confidence interval does not include zero, \n",
    "the p-value will be less than 0.05. Thus, a p-value less than 0.05 is one way to \n",
    "decide whether there is likely a relationship between the feature and the response.\n",
    "\n",
    "FINDINGS:\n",
    "    \n",
    "    1. The p-value for Relative Compactness is less than 0.05; ergo, there is a \n",
    "    correlation between Relative Compactness and Heating Load.\"\"\"\n",
    "\n",
    "lm.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38722236193215909"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Get the R-squared value for the model.\"\"\"\n",
    "\n",
    "lm.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                    84.013418\n",
       "relative_compactness        -64.773432\n",
       "surface_area                 -0.062606\n",
       "wall_area                     0.036129\n",
       "roof_area                    -0.049368\n",
       "overall_height                4.169954\n",
       "orientation                  -0.023330\n",
       "glazing_area                 19.932736\n",
       "glazing_area_distribution     0.203777\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Use multiple linear regression to make predictions.\"\"\"\n",
    "\n",
    "# create a fitted model with all three features\n",
    "lm = smf.ols(formula='heating_load ~ relative_compactness + surface_area + wall_area + roof_area + overall_height + orientation + glazing_area + glazing_area_distribution', data=df_energy_efficiency).fit()\n",
    "\n",
    "# print the coefficients\n",
    "lm.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>heating_load</td>   <th>  R-squared:         </th> <td>   0.916</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.915</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1187.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 23 Jul 2017</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:24:40</td>     <th>  Log-Likelihood:    </th> <td> -1912.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   768</td>      <th>  AIC:               </th> <td>   3841.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   760</td>      <th>  BIC:               </th> <td>   3878.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     7</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "              <td></td>                 <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                 <td>   84.0134</td> <td>   19.034</td> <td>    4.414</td> <td> 0.000</td> <td>   46.649</td> <td>  121.378</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>relative_compactness</th>      <td>  -64.7734</td> <td>   10.289</td> <td>   -6.295</td> <td> 0.000</td> <td>  -84.973</td> <td>  -44.574</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>surface_area</th>              <td>   -0.0626</td> <td>    0.013</td> <td>   -4.670</td> <td> 0.000</td> <td>   -0.089</td> <td>   -0.036</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>wall_area</th>                 <td>    0.0361</td> <td>    0.004</td> <td>    9.386</td> <td> 0.000</td> <td>    0.029</td> <td>    0.044</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>roof_area</th>                 <td>   -0.0494</td> <td>    0.008</td> <td>   -6.569</td> <td> 0.000</td> <td>   -0.064</td> <td>   -0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>overall_height</th>            <td>    4.1700</td> <td>    0.338</td> <td>   12.338</td> <td> 0.000</td> <td>    3.506</td> <td>    4.833</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>orientation</th>               <td>   -0.0233</td> <td>    0.095</td> <td>   -0.246</td> <td> 0.805</td> <td>   -0.209</td> <td>    0.163</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glazing_area</th>              <td>   19.9327</td> <td>    0.814</td> <td>   24.488</td> <td> 0.000</td> <td>   18.335</td> <td>   21.531</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glazing_area_distribution</th> <td>    0.2038</td> <td>    0.070</td> <td>    2.915</td> <td> 0.004</td> <td>    0.067</td> <td>    0.341</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>18.647</td> <th>  Durbin-Watson:     </th> <td>   0.654</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  37.707</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.044</td> <th>  Prob(JB):          </th> <td>6.49e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.082</td> <th>  Cond. No.          </th> <td>5.54e+15</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           heating_load   R-squared:                       0.916\n",
       "Model:                            OLS   Adj. R-squared:                  0.915\n",
       "Method:                 Least Squares   F-statistic:                     1187.\n",
       "Date:                Sun, 23 Jul 2017   Prob (F-statistic):               0.00\n",
       "Time:                        12:24:40   Log-Likelihood:                -1912.5\n",
       "No. Observations:                 768   AIC:                             3841.\n",
       "Df Residuals:                     760   BIC:                             3878.\n",
       "Df Model:                           7                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=============================================================================================\n",
       "                                coef    std err          t      P>|t|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------------------\n",
       "Intercept                    84.0134     19.034      4.414      0.000      46.649     121.378\n",
       "relative_compactness        -64.7734     10.289     -6.295      0.000     -84.973     -44.574\n",
       "surface_area                 -0.0626      0.013     -4.670      0.000      -0.089      -0.036\n",
       "wall_area                     0.0361      0.004      9.386      0.000       0.029       0.044\n",
       "roof_area                    -0.0494      0.008     -6.569      0.000      -0.064      -0.035\n",
       "overall_height                4.1700      0.338     12.338      0.000       3.506       4.833\n",
       "orientation                  -0.0233      0.095     -0.246      0.805      -0.209       0.163\n",
       "glazing_area                 19.9327      0.814     24.488      0.000      18.335      21.531\n",
       "glazing_area_distribution     0.2038      0.070      2.915      0.004       0.067       0.341\n",
       "==============================================================================\n",
       "Omnibus:                       18.647   Durbin-Watson:                   0.654\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               37.707\n",
       "Skew:                           0.044   Prob(JB):                     6.49e-09\n",
       "Kurtosis:                       4.082   Cond. No.                     5.54e+15\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 1.48e-23. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "FINDINGS: \n",
    "\n",
    "    A given amount of the additional features (surface are\tglazing area dist.), \n",
    "    results in a decrease in heating load (-64.7734320000000)0.0\n",
    "\"\"\"\n",
    "###############################################################################\n",
    "\"\"\"Summarize Fitted Model\"\"\"\n",
    "\n",
    "lm.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "CONCLUSIONS:\n",
    "\n",
    "    \n",
    "    1. Orientation has no significant p-value, in contrast to the other features \n",
    "    (reject the null hypothesis for those features with significant p-values), and fail to \n",
    "    reject the null hypothesis for Orientation.\n",
    "    2. Those features with significant p-values show a direct correlation with Heating Load; \n",
    "    Orientation has negative association. (However, this is irrelevant since we have failed \n",
    "    to reject the null hypothesis for Newspaper.)\n",
    "    3. This model has a higher R-squared (0.916) than the previous model, indicating that \n",
    "    this model provides a better fit to the data than a model that only includes Relative Compactness.\n",
    "\n",
    "#######################################################################################################\n",
    "\n",
    "SOURCE:\n",
    "\n",
    "http://archive.ics.uci.edu/ml/datasets/Energy+efficiency\n",
    "\n",
    "The dataset was created by Angeliki Xifara (angxifara '@' gmail.com, Civil/Structural Engineer) \n",
    "and was processed by Athanasios Tsanas (tsanasthanasis '@' gmail.com, Oxford Centre for Industrial \n",
    "and Applied Mathematics, University of Oxford, UK).\n",
    "\n",
    "#######################################################################################################\n",
    "\n",
    "FEATURES INFORMATION:\n",
    "\n",
    "The dataset contains eight attributes (or features, denoted by X1...X8) and two responses \n",
    "(or outcomes, denoted by y1 and y2). The aim is to use the eight features to predict each \n",
    "of the two responses.\n",
    "\n",
    "Specifically:\n",
    "\n",
    "    X1 Relative Compactness\n",
    "    X2 Surface Area\n",
    "    X3 Wall Area\n",
    "    X4 Roof Area\n",
    "    X5 Overall Height\n",
    "    X6 Orientation\n",
    "    X7 Glazing Area\n",
    "    X8 Glazing Area Distribution\n",
    "    y1 Heating Load\n",
    "    y2 Cooling Load\n",
    "\n",
    "NOTE: \n",
    "\n",
    "    Feature names were changed to facilitate human readability.\n",
    "\n",
    "#######################################################################################################\n",
    "\n",
    "RELEVANT PAPERS:\n",
    "\n",
    "    A. Tsanas, A. Xifara: 'Accurate quantitative estimation of energy performance \n",
    "    of residential buildings using statistical machine learning tools', Energy and\n",
    "    Buildings, Vol. 49, pp. 560-567, 2012\n",
    "\n",
    "#######################################################################################################\n",
    "\n",
    "CITATIONS:\n",
    "\n",
    "    1. Tsanas, A. Xifara: 'Accurate quantitative estimation of energy performance of \n",
    "    residential buildings using statistical machine learning tools', Energy and Buildings, \n",
    "    Vol. 49, pp. 560-567, 2012.\n",
    "\n",
    "    For further details on the data analysis methodology:\n",
    "    \n",
    "    2. Tsanas, 'Accurate telemonitoring of Parkinson's disease symptom severity using nonlinear \n",
    "    speech signal processing and statistical machine learning', D.Phil. thesis, University of Oxford, 2012.\n",
    "    \n",
    "#######################################################################################################\n",
    "\n",
    "ADDITIONAL SOURCES:\n",
    "\n",
    "    1. Based upon this tutorial by Kevin Markham: https://github.com/justmarkham/DAT4/blob/master/notebooks/08_linear_regression.ipynb\n",
    "\"\"\""
   ]
  }
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