Machine Learning Regression Predicting Energy Efficiency of Buildings.ipynb

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  {
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   "metadata": {},
   "source": [
    "# Machine Learning: Regression - Predicting Energy Efficiency of Buildings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59fd5b0e",
   "metadata": {},
   "source": [
    "### We will develop a multivariate multiple regression model to study the effect of eight input variables on two output variables, which are the heating load and the cooling load, of residential buildings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "23a98311",
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       "       X1     X2     X3      X4   X5  X6   X7  X8     Y1     Y2  Unnamed: 10  \\\n",
       "0    0.98  514.5  294.0  110.25  7.0   2  0.0   0  15.55  21.33          NaN   \n",
       "1    0.98  514.5  294.0  110.25  7.0   3  0.0   0  15.55  21.33          NaN   \n",
       "2    0.98  514.5  294.0  110.25  7.0   4  0.0   0  15.55  21.33          NaN   \n",
       "3    0.98  514.5  294.0  110.25  7.0   5  0.0   0  15.55  21.33          NaN   \n",
       "4    0.90  563.5  318.5  122.50  7.0   2  0.0   0  20.84  28.28          NaN   \n",
       "..    ...    ...    ...     ...  ...  ..  ...  ..    ...    ...          ...   \n",
       "763  0.64  784.0  343.0  220.50  3.5   5  0.4   5  17.88  21.40          NaN   \n",
       "764  0.62  808.5  367.5  220.50  3.5   2  0.4   5  16.54  16.88          NaN   \n",
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       "766  0.62  808.5  367.5  220.50  3.5   4  0.4   5  16.48  16.61          NaN   \n",
       "767  0.62  808.5  367.5  220.50  3.5   5  0.4   5  16.64  16.03          NaN   \n",
       "\n",
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       "0            NaN  \n",
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       "3            NaN  \n",
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       "..           ...  \n",
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   ],
   "source": [
    "# importing the necessary libraries\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "df=pd.read_excel('https://archive.ics.uci.edu/ml/machine-learning-databases/00242/ENB2012_data.xlsx', engine='openpyxl')\n",
    "\n",
    "df"
   ]
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       "      <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",
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       "      <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",
       "      <td>NaN</td>\n",
       "      <td>NaN</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",
       "      <td>NaN</td>\n",
       "      <td>NaN</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",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "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",
       "\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",
       "\n",
       "   Cooling_Load  Unnamed: 10  Unnamed: 11  \n",
       "0         21.33          NaN          NaN  \n",
       "1         21.33          NaN          NaN  \n",
       "2         21.33          NaN          NaN  \n",
       "3         21.33          NaN          NaN  \n",
       "4         28.28          NaN          NaN  "
      ]
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     "execution_count": 78,
     "metadata": {},
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   ],
   "source": [
    "# rename columns\n",
    "column_names = {'X1': 'Relative_Compactness', 'X2': 'Surface_Area', \n",
    "               'X3': 'Wall_Area', 'X4': 'Roof_Area', 'X5': 'Overall_Height', \n",
    "               'X6': 'Orientation', 'X7': 'Glazing-Area', \n",
    "                'X8': 'Glazing_Area_Distribution', \n",
    "                'Y1': 'Heating_Load', 'Y2': 'Cooling_Load'}\n",
    "\n",
    "df = df.rename(columns = column_names)\n",
    "\n",
    "df.head()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0315428a",
   "metadata": {},
   "source": [
    "## Data Exploration\n",
    "\n",
    "\n",
    "#### check for duplicate entries\n",
    "#### check for null values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "e08dbf6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.duplicated().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "482206fe",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Relative_Compactness           0\n",
       "Surface_Area                   0\n",
       "Wall_Area                      0\n",
       "Roof_Area                      0\n",
       "Overall_Height                 0\n",
       "Orientation                    0\n",
       "Glazing-Area                   0\n",
       "Glazing_Area_Distribution      0\n",
       "Heating_Load                   0\n",
       "Cooling_Load                   0\n",
       "Unnamed: 10                  768\n",
       "Unnamed: 11                  768\n",
       "dtype: int64"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "ce534505",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.drop(['Unnamed: 10', 'Unnamed: 11'], inplace = True, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "791f33b7",
   "metadata": {
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       "      <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",
       "  </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",
       "\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",
       "\n",
       "   Cooling_Load  \n",
       "0         21.33  \n",
       "1         21.33  \n",
       "2         21.33  \n",
       "3         21.33  \n",
       "4         28.28  "
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "be7c045f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Relative_Compactness', ylabel='Cooling_Load'>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#select a sample of dataset\n",
    "# We select a sample of the dataset and use the relative compactness column as the predictor(independent variable) and the heating load column the response variable(dependent variable).\n",
    "simple_liner_reg_df = df[['Relative_Compactness', 'Cooling_Load']].sample(15, random_state=2)\n",
    "\n",
    "# regression plot\n",
    "sns.regplot(x = \"Relative_Compactness\", y = \"Cooling_Load\",\n",
    "           data = simple_liner_reg_df)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35a06947",
   "metadata": {},
   "source": [
    "### Normalisation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "4977cb45",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Firstly we have to normalise our dataset to a common scale using the MinMaxScaler\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaler = MinMaxScaler()\n",
    "normalised_df = pd.DataFrame(scaler.fit_transform(df), columns = df.columns)\n",
    "features_df = normalised_df.drop(columns = ['Heating_Load', 'Cooling_Load'])\n",
    "heating_target = normalised_df['Heating_Load']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "2f9a4d5d",
   "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>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",
       "  </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",
       "\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",
       "\n",
       "   Cooling_Load  \n",
       "0         21.33  \n",
       "1         21.33  \n",
       "2         21.33  \n",
       "3         21.33  \n",
       "4         28.28  "
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "d3f41680",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now, we split our dataset into the training and testing dataset. Recall that we\n",
    "# had earlier segmented the features and target variables.\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "x_train, x_test, y_train, y_test = train_test_split(features_df, heating_target,\n",
    "test_size=0.3, random_state=1)\n",
    "linear_model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "ddb80476",
   "metadata": {},
   "outputs": [],
   "source": [
    "#fit the model to the training dataset\n",
    "reg =linear_model.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "095557ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8938550769308062"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.score(x_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "8f673d42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9252691483376907"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.score(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "a052dae7",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.19171335, 0.57861912, 0.73990043, 0.71445968, 0.75810474,\n",
       "       0.24871954, 0.16921186, 0.60311106, 0.24501095, 0.54737107,\n",
       "       0.31823959, 0.65925977, 0.69331771, 0.30343424, 0.19027072,\n",
       "       0.71785863, 0.57207665, 0.3159481 , 0.26210611, 0.74693205,\n",
       "       0.69900815, 0.06941108, 0.60925257, 0.3270687 , 0.21248809,\n",
       "       0.74445789, 0.33479036, 0.18715589, 0.80079078, 0.27003867,\n",
       "       0.67806128, 0.73420999, 0.14215292, 0.28571674, 0.5633094 ,\n",
       "       0.8076142 , 0.33505064, 0.1353295 , 0.72354907, 0.24727691,\n",
       "       0.82414823, 0.15809126, 0.11176667, 0.16578739, 0.117612  ,\n",
       "       0.15327352, 0.48452124, 0.68989323, 0.75354728, 0.72015012,\n",
       "       0.10167366, 0.66495022, 0.09850946, 0.25072523, 0.76371047,\n",
       "       0.76826793, 0.73647596, 0.62801172, 0.15118472, 0.29887678,\n",
       "       0.19284633, 0.59447275, 0.60356213, 0.76484345, 0.5686777 ,\n",
       "       0.92641767, 0.68193683, 0.31937257, 0.66950767, 0.23759893,\n",
       "       0.54397212, 0.25185821, 0.23182538, 0.72232476, 0.28684972,\n",
       "       0.68405669, 0.63825962, 0.74124161, 0.25641567, 0.53042681,\n",
       "       0.13419651, 0.64395006, 0.26182199, 0.75688705, 0.23751582,\n",
       "       0.90252292, 0.91959424, 0.82870569, 0.25984014, 0.18118134,\n",
       "       0.63599366, 0.5122225 , 0.14671038, 0.74785684, 0.27091138,\n",
       "       0.67064066, 0.1432859 , 0.68306981, 0.05576424, 0.77964881,\n",
       "       0.76513635, 0.28229226, 0.61494301, 0.15687516, 0.27461997,\n",
       "       0.18484056, 0.59560573, 0.58317657, 0.62063345, 0.8378206 ,\n",
       "       0.91503678, 0.45390461, 0.56217642, 0.14549428, 0.84577701,\n",
       "       0.10649139, 0.62926157, 0.69626558, 0.7075194 , 0.2879827 ,\n",
       "       0.54966256, 0.59968659, 0.26321525, 0.5451051 , 0.71216819,\n",
       "       0.2800263 , 0.07396854, 0.76940091, 0.1041999 , 0.25554296,\n",
       "       0.79167586, 0.12443542, 0.70865238, 0.80192376, 0.04448875,\n",
       "       0.67350382, 0.52929383, 0.09268966, 0.72584056, 0.21135511,\n",
       "       0.30799169, 0.60016319, 0.35299466, 0.23960462, 0.45050566,\n",
       "       0.62687874, 0.05233976, 0.82301525, 0.63039455, 0.26522094,\n",
       "       0.16663625, 0.55761896, 0.77282538, 0.80418973, 0.31025766,\n",
       "       0.3293602 , 0.64064245, 0.18826503, 0.70990222, 0.24529506,\n",
       "       0.53615485, 0.61335896, 0.72459072, 0.25410034, 0.72003326,\n",
       "       0.1678186 , 0.7257237 , 0.63608499, 0.34274677, 0.34161378,\n",
       "       0.16352142, 0.83213016, 0.71672565, 0.23504716, 0.13988695,\n",
       "       0.69057514, 0.14209533, 0.72697354, 0.731531  , 0.2327812 ,\n",
       "       0.75575406, 0.09155668, 0.61675791, 0.59569044, 0.74010862,\n",
       "       0.08372963, 0.14557739, 0.5979564 , 0.18033247, 0.16009695,\n",
       "       0.2398649 , 0.74559087, 0.74806503, 0.61267705, 0.15574218,\n",
       "       0.71434282, 0.04335576, 0.65202333, 0.06714512, 0.90934634,\n",
       "       0.33618362, 0.63950946, 0.33162616, 0.22052761, 0.53728783,\n",
       "       0.30116827, 0.74919801, 0.10280664, 0.22166059, 0.22392656,\n",
       "       0.71559266, 0.55306151, 0.56981069, 0.18458028, 0.09511051,\n",
       "       0.72241609, 0.17232669, 0.58088508, 0.22848402, 0.67624639,\n",
       "       0.68649428, 0.22955941, 0.60766852, 0.10950071, 0.53498427,\n",
       "       0.77395837, 0.53385128, 0.91047933, 0.22500196, 0.48792019,\n",
       "       0.75944591])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#obtain predictions\n",
    "predicted_values = linear_model.predict(x_test)\n",
    "predicted_values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eef9ed27",
   "metadata": {},
   "source": [
    "### Error metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "af208246",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.063"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#MAE\n",
    "# it calculates the sum of the average of the absolute error between the predicted values and the true values.\n",
    "# does not consider direction.\n",
    "# The smaller the MAE is, the better the model. \n",
    "from sklearn.metrics import mean_absolute_error\n",
    "mae = mean_absolute_error(y_test, predicted_values)\n",
    "round(mae, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "73d4239f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.894"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# R-Squared\n",
    "# r-squared is a metric used in regression to determine the goodness of fit of the model. With values ranging from 0 to 1\n",
    "# the higher the value, the better the model \n",
    "from sklearn.metrics import r2_score\n",
    "r2_score = r2_score(y_test, predicted_values)\n",
    "round(r2_score, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "f0da42ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.817"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Residual Sum of Squares(RSS)\n",
    "#this metric explains the variance in the representation of the dataset by the model; it measures how well the model approximates the data. A residual is the estimated error made by a model.\n",
    "# The lower the RSS, the better the model’s estimations and vice versa.\n",
    "import numpy as np\n",
    "rss = np.sum(np.square(y_test - predicted_values))\n",
    "round(rss, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "32d889c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.089"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Root Mean Square Error(RMSE)\n",
    "# This is the same as the mean square error (MSE) but, it is the square root of the MSE that estimates the standard deviation of the residuals. \n",
    "# the RMSE is low, it means that the error made by the model has a small deviation from the true values.\n",
    "from sklearn.metrics import  mean_squared_error\n",
    "rmse = np.sqrt(mean_squared_error(y_test, predicted_values))\n",
    "round(rmse, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ca5c90",
   "metadata": {},
   "source": [
    "### we can conclude that the model is not overfitting or underfitting from the evaludation metrics on test and train dataset"
   ]
  }
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