Machine Learning Regression - Predicting Energy Efficiency of Buildings.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stage B Quiz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing libraries\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>Appliances</th>\n",
       "      <th>lights</th>\n",
       "      <th>T1</th>\n",
       "      <th>RH_1</th>\n",
       "      <th>T2</th>\n",
       "      <th>RH_2</th>\n",
       "      <th>T3</th>\n",
       "      <th>RH_3</th>\n",
       "      <th>T4</th>\n",
       "      <th>...</th>\n",
       "      <th>T9</th>\n",
       "      <th>RH_9</th>\n",
       "      <th>T_out</th>\n",
       "      <th>Press_mm_hg</th>\n",
       "      <th>RH_out</th>\n",
       "      <th>Windspeed</th>\n",
       "      <th>Visibility</th>\n",
       "      <th>Tdewpoint</th>\n",
       "      <th>rv1</th>\n",
       "      <th>rv2</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2016-01-11 17:00:00</td>\n",
       "      <td>60</td>\n",
       "      <td>30</td>\n",
       "      <td>19.89</td>\n",
       "      <td>47.596667</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.790000</td>\n",
       "      <td>19.79</td>\n",
       "      <td>44.730000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>17.033333</td>\n",
       "      <td>45.53</td>\n",
       "      <td>6.600000</td>\n",
       "      <td>733.5</td>\n",
       "      <td>92.0</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>63.000000</td>\n",
       "      <td>5.3</td>\n",
       "      <td>13.275433</td>\n",
       "      <td>13.275433</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2016-01-11 17:10:00</td>\n",
       "      <td>60</td>\n",
       "      <td>30</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.693333</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.722500</td>\n",
       "      <td>19.79</td>\n",
       "      <td>44.790000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>17.066667</td>\n",
       "      <td>45.56</td>\n",
       "      <td>6.483333</td>\n",
       "      <td>733.6</td>\n",
       "      <td>92.0</td>\n",
       "      <td>6.666667</td>\n",
       "      <td>59.166667</td>\n",
       "      <td>5.2</td>\n",
       "      <td>18.606195</td>\n",
       "      <td>18.606195</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2016-01-11 17:20:00</td>\n",
       "      <td>50</td>\n",
       "      <td>30</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.300000</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.626667</td>\n",
       "      <td>19.79</td>\n",
       "      <td>44.933333</td>\n",
       "      <td>18.926667</td>\n",
       "      <td>...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>45.50</td>\n",
       "      <td>6.366667</td>\n",
       "      <td>733.7</td>\n",
       "      <td>92.0</td>\n",
       "      <td>6.333333</td>\n",
       "      <td>55.333333</td>\n",
       "      <td>5.1</td>\n",
       "      <td>28.642668</td>\n",
       "      <td>28.642668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2016-01-11 17:30:00</td>\n",
       "      <td>50</td>\n",
       "      <td>40</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.066667</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.590000</td>\n",
       "      <td>19.79</td>\n",
       "      <td>45.000000</td>\n",
       "      <td>18.890000</td>\n",
       "      <td>...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>45.40</td>\n",
       "      <td>6.250000</td>\n",
       "      <td>733.8</td>\n",
       "      <td>92.0</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>51.500000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>45.410389</td>\n",
       "      <td>45.410389</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2016-01-11 17:40:00</td>\n",
       "      <td>60</td>\n",
       "      <td>40</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.333333</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.530000</td>\n",
       "      <td>19.79</td>\n",
       "      <td>45.000000</td>\n",
       "      <td>18.890000</td>\n",
       "      <td>...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>45.40</td>\n",
       "      <td>6.133333</td>\n",
       "      <td>733.9</td>\n",
       "      <td>92.0</td>\n",
       "      <td>5.666667</td>\n",
       "      <td>47.666667</td>\n",
       "      <td>4.9</td>\n",
       "      <td>10.084097</td>\n",
       "      <td>10.084097</td>\n",
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       "                  date  Appliances  lights     T1       RH_1    T2       RH_2  \\\n",
       "0  2016-01-11 17:00:00          60      30  19.89  47.596667  19.2  44.790000   \n",
       "1  2016-01-11 17:10:00          60      30  19.89  46.693333  19.2  44.722500   \n",
       "2  2016-01-11 17:20:00          50      30  19.89  46.300000  19.2  44.626667   \n",
       "3  2016-01-11 17:30:00          50      40  19.89  46.066667  19.2  44.590000   \n",
       "4  2016-01-11 17:40:00          60      40  19.89  46.333333  19.2  44.530000   \n",
       "\n",
       "      T3       RH_3         T4  ...         T9   RH_9     T_out  Press_mm_hg  \\\n",
       "0  19.79  44.730000  19.000000  ...  17.033333  45.53  6.600000        733.5   \n",
       "1  19.79  44.790000  19.000000  ...  17.066667  45.56  6.483333        733.6   \n",
       "2  19.79  44.933333  18.926667  ...  17.000000  45.50  6.366667        733.7   \n",
       "3  19.79  45.000000  18.890000  ...  17.000000  45.40  6.250000        733.8   \n",
       "4  19.79  45.000000  18.890000  ...  17.000000  45.40  6.133333        733.9   \n",
       "\n",
       "   RH_out  Windspeed  Visibility  Tdewpoint        rv1        rv2  \n",
       "0    92.0   7.000000   63.000000        5.3  13.275433  13.275433  \n",
       "1    92.0   6.666667   59.166667        5.2  18.606195  18.606195  \n",
       "2    92.0   6.333333   55.333333        5.1  28.642668  28.642668  \n",
       "3    92.0   6.000000   51.500000        5.0  45.410389  45.410389  \n",
       "4    92.0   5.666667   47.666667        4.9  10.084097  10.084097  \n",
       "\n",
       "[5 rows x 29 columns]"
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     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df = pd.read_csv(r\"C:\\Users\\User\\OneDrive\\Desktop\\Lizzy's Folder\\Hamoye Internship Files\\Sprint 2\\energydata_complete.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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   "outputs": [
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       "      <th>Press_mm_hg</th>\n",
       "      <th>RH_out</th>\n",
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       "      <th>Tdewpoint</th>\n",
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       "      <th>0</th>\n",
       "      <td>60</td>\n",
       "      <td>19.89</td>\n",
       "      <td>47.596667</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.790000</td>\n",
       "      <td>19.79</td>\n",
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       "      <td>19.000000</td>\n",
       "      <td>45.566667</td>\n",
       "      <td>17.166667</td>\n",
       "      <td>...</td>\n",
       "      <td>17.033333</td>\n",
       "      <td>45.53</td>\n",
       "      <td>6.600000</td>\n",
       "      <td>733.5</td>\n",
       "      <td>92.0</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>63.000000</td>\n",
       "      <td>5.3</td>\n",
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       "      <td>13.275433</td>\n",
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       "      <th>1</th>\n",
       "      <td>60</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.693333</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.722500</td>\n",
       "      <td>19.79</td>\n",
       "      <td>44.790000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>45.992500</td>\n",
       "      <td>17.166667</td>\n",
       "      <td>...</td>\n",
       "      <td>17.066667</td>\n",
       "      <td>45.56</td>\n",
       "      <td>6.483333</td>\n",
       "      <td>733.6</td>\n",
       "      <td>92.0</td>\n",
       "      <td>6.666667</td>\n",
       "      <td>59.166667</td>\n",
       "      <td>5.2</td>\n",
       "      <td>18.606195</td>\n",
       "      <td>18.606195</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>50</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.300000</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.626667</td>\n",
       "      <td>19.79</td>\n",
       "      <td>44.933333</td>\n",
       "      <td>18.926667</td>\n",
       "      <td>45.890000</td>\n",
       "      <td>17.166667</td>\n",
       "      <td>...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>45.50</td>\n",
       "      <td>6.366667</td>\n",
       "      <td>733.7</td>\n",
       "      <td>92.0</td>\n",
       "      <td>6.333333</td>\n",
       "      <td>55.333333</td>\n",
       "      <td>5.1</td>\n",
       "      <td>28.642668</td>\n",
       "      <td>28.642668</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>50</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.066667</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.590000</td>\n",
       "      <td>19.79</td>\n",
       "      <td>45.000000</td>\n",
       "      <td>18.890000</td>\n",
       "      <td>45.723333</td>\n",
       "      <td>17.166667</td>\n",
       "      <td>...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>45.40</td>\n",
       "      <td>6.250000</td>\n",
       "      <td>733.8</td>\n",
       "      <td>92.0</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>51.500000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>45.410389</td>\n",
       "      <td>45.410389</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60</td>\n",
       "      <td>19.89</td>\n",
       "      <td>46.333333</td>\n",
       "      <td>19.2</td>\n",
       "      <td>44.530000</td>\n",
       "      <td>19.79</td>\n",
       "      <td>45.000000</td>\n",
       "      <td>18.890000</td>\n",
       "      <td>45.530000</td>\n",
       "      <td>17.200000</td>\n",
       "      <td>...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>45.40</td>\n",
       "      <td>6.133333</td>\n",
       "      <td>733.9</td>\n",
       "      <td>92.0</td>\n",
       "      <td>5.666667</td>\n",
       "      <td>47.666667</td>\n",
       "      <td>4.9</td>\n",
       "      <td>10.084097</td>\n",
       "      <td>10.084097</td>\n",
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       "   Appliances     T1       RH_1    T2       RH_2     T3       RH_3         T4  \\\n",
       "0          60  19.89  47.596667  19.2  44.790000  19.79  44.730000  19.000000   \n",
       "1          60  19.89  46.693333  19.2  44.722500  19.79  44.790000  19.000000   \n",
       "2          50  19.89  46.300000  19.2  44.626667  19.79  44.933333  18.926667   \n",
       "3          50  19.89  46.066667  19.2  44.590000  19.79  45.000000  18.890000   \n",
       "4          60  19.89  46.333333  19.2  44.530000  19.79  45.000000  18.890000   \n",
       "\n",
       "        RH_4         T5  ...         T9   RH_9     T_out  Press_mm_hg  RH_out  \\\n",
       "0  45.566667  17.166667  ...  17.033333  45.53  6.600000        733.5    92.0   \n",
       "1  45.992500  17.166667  ...  17.066667  45.56  6.483333        733.6    92.0   \n",
       "2  45.890000  17.166667  ...  17.000000  45.50  6.366667        733.7    92.0   \n",
       "3  45.723333  17.166667  ...  17.000000  45.40  6.250000        733.8    92.0   \n",
       "4  45.530000  17.200000  ...  17.000000  45.40  6.133333        733.9    92.0   \n",
       "\n",
       "   Windspeed  Visibility  Tdewpoint        rv1        rv2  \n",
       "0   7.000000   63.000000        5.3  13.275433  13.275433  \n",
       "1   6.666667   59.166667        5.2  18.606195  18.606195  \n",
       "2   6.333333   55.333333        5.1  28.642668  28.642668  \n",
       "3   6.000000   51.500000        5.0  45.410389  45.410389  \n",
       "4   5.666667   47.666667        4.9  10.084097  10.084097  \n",
       "\n",
       "[5 rows x 27 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dropping lights and date column\n",
    "df.drop(columns=['date', 'lights'], inplace=True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalising to a common scale using MinMaxScaler\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "\n",
    "scaler = MinMaxScaler()\n",
    "norm_df = pd.DataFrame(scaler.fit_transform(df), columns=df.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# selecting the features and target variable\n",
    "\n",
    "feat_df = norm_df.drop(columns=['Appliances'])\n",
    "app_target = norm_df['Appliances']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# splitting into training and testing dataset\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(feat_df, app_target, test_size = 0.3, random_state = 42)\n",
    "model = LinearRegression()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fitting the model to the training dataset and obtaining predictions\n",
    "\n",
    "model.fit(x_train, y_train)\n",
    "pred_values = model.predict(x_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> * R-squared value gives information on the percentage of the response. Therefore, a best fit line relating X and Y having r-squared value of 0.75 means the model is performing at 75% accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=0.001)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Training lasso regression\n",
    "\n",
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.001)\n",
    "lasso_reg.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "    }\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>Lasso_Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>RH_out</td>\n",
       "      <td>-0.049557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>RH_8</td>\n",
       "      <td>-0.000110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>T1</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Tdewpoint</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Visibility</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Press_mm_hg</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>T_out</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>RH_9</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>T9</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>T8</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>RH_7</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rv1</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>T7</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>T6</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>RH_5</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>T5</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>RH_4</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>T4</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>RH_3</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>T3</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>RH_2</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>T2</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>RH_6</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>rv2</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Windspeed</td>\n",
       "      <td>0.002912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>RH_1</td>\n",
       "      <td>0.017880</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Features  Lasso_Weight\n",
       "0        RH_out     -0.049557\n",
       "1          RH_8     -0.000110\n",
       "2            T1      0.000000\n",
       "3     Tdewpoint      0.000000\n",
       "4    Visibility      0.000000\n",
       "5   Press_mm_hg     -0.000000\n",
       "6         T_out      0.000000\n",
       "7          RH_9     -0.000000\n",
       "8            T9     -0.000000\n",
       "9            T8      0.000000\n",
       "10         RH_7     -0.000000\n",
       "11          rv1     -0.000000\n",
       "12           T7     -0.000000\n",
       "13           T6      0.000000\n",
       "14         RH_5      0.000000\n",
       "15           T5     -0.000000\n",
       "16         RH_4      0.000000\n",
       "17           T4     -0.000000\n",
       "18         RH_3      0.000000\n",
       "19           T3      0.000000\n",
       "20         RH_2     -0.000000\n",
       "21           T2      0.000000\n",
       "22         RH_6     -0.000000\n",
       "23          rv2     -0.000000\n",
       "24    Windspeed      0.002912\n",
       "25         RH_1      0.017880"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# defining a function to return the weight of every feature in the dataset\n",
    "def get_weights_df(model, feat, col_name):\n",
    "    weights= pd.Series(model.coef_, feat.columns).sort_values()\n",
    "    weights_df= pd.DataFrame(weights).reset_index()\n",
    "    weights_df.columns = ['Features', col_name]\n",
    "    weights_df[col_name].round(3)\n",
    "    return weights_df\n",
    "\n",
    "# to get the weights for the lasso regression\n",
    "lasso_weights = get_weights_df(lasso_reg, x_train, 'Lasso_Weight')\n",
    "lasso_weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3\n",
    ">  Lasso regression uses L1 regularisation to include the absolute value of the magnitiude to the loss functiom thereby resulting in a simpler model that allows better interpretation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             Linear_Model_Weight\n",
      "Features                        \n",
      "RH_2                   -0.456698\n",
      "T_out                  -0.321860\n",
      "T2                     -0.236178\n",
      "T9                     -0.189941\n",
      "RH_8                   -0.157595\n",
      "RH_out                 -0.077671\n",
      "RH_7                   -0.044614\n",
      "RH_9                   -0.039800\n",
      "T5                     -0.015657\n",
      "T1                     -0.003281\n",
      "rv1                     0.000770\n",
      "rv2                     0.000770\n",
      "Press_mm_hg             0.006839\n",
      "T7                      0.010319\n",
      "Visibility              0.012307\n",
      "RH_5                    0.016006\n",
      "RH_4                    0.026386\n",
      "T4                      0.028981\n",
      "Windspeed               0.029183\n",
      "RH_6                    0.038049\n",
      "RH_3                    0.096048\n",
      "T8                      0.101995\n",
      "Tdewpoint               0.117758\n",
      "T6                      0.236425\n",
      "T3                      0.290627\n",
      "RH_1                    0.553547\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(Linear_Model_Weight   -0.456698\n",
       " dtype: float64,\n",
       " Linear_Model_Weight   -0.456698\n",
       " dtype: float64)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to get the weights for the linear model\n",
    "linear_model_weights = get_weights_df(model, x_train, 'Linear_Model_Weight')\n",
    "\n",
    "# setting the features column as index\n",
    "linear_model_weights.set_index('Features', inplace=True)\n",
    "\n",
    "# getting the minimum and maximum weights\n",
    "print(linear_model_weights)\n",
    "linear_model_weights.min(), linear_model_weights.min()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Variance tells how much the values estimated by a model varies acroos different training data. A high variance causes overfitting and an overfit data will perform well on the training data but porly on the test data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45.35"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the Residual sum of squares in 2dp\n",
    "\n",
    "rss = np.sum(np.square(y_test - pred_values))\n",
    "round(rss,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> A simple linea regression can be represented as:\n",
    "        > * $Y = O_0X + O_1$\n",
    "        > * where $O_0 and O_1$ are coefficients\n",
    "            > * Y is the dependent variable.\n",
    "            > * X is the independent variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculating the coefficient of determination(rscore)\n",
    "\n",
    "from sklearn.metrics import r2_score\n",
    "rscore = r2_score(y_test, pred_values)\n",
    "round(rscore,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> L2 regularization also known as Ridge regression is equivalent to imposing a Gaussian Prior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the mean absolute error to 2dp\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "\n",
    "mae = mean_absolute_error(y_test, pred_values)\n",
    "round(mae, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.088"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the RMSE with the lasso regression to 3dp\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "rmse = np.sqrt(mean_squared_error(y_test, pred_values))\n",
    "round(rmse, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The assumptions of Linear Regression are:\n",
    "> * Linearity\n",
    "> * Homoscedasticity\n",
    "> * Normality\n",
    "> * Independence of observations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=0.4)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Training a ridge regression\n",
    "\n",
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=0.4)\n",
    "ridge_reg.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.088"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the RMSE\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "rmse = np.sqrt(mean_squared_error(y_test, pred_values))\n",
    "round(rmse, 3)\n",
    "\n",
    "# There is no change in the root mean square error (RMSE) when evaluated on the test set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The least square error can be used to find the best fit line for data in linear regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Adding more basis function in a linear model decreases model bias."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 16"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Cross validation is guaranteed to prevent overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.088"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the RMSE\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "rmse = np.sqrt(mean_squared_error(y_test, pred_values))\n",
    "round(rmse, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fitting a linear model on the relationship between temperature in the living room in Celsius(x = T2)\n",
    "# and the temperature outside the building (y = T6)\n",
    "x = df[['T2']] #chosen predictor\n",
    "y = df[['T6']] # target variable\n",
    "\n",
    "# splitting into training and testing dataset\n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x, y, test_size=0.3, random_state=1)\n",
    "linear_model = LinearRegression()\n",
    "\n",
    "# fitting the model and and obtaining predicted variables\n",
    "linear_model.fit(x_train1, y_train1)\n",
    "npred_values = linear_model.predict(x_test1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.65"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculating the coefficient of determination(rscore)\n",
    "\n",
    "from sklearn.metrics import r2_score\n",
    "rscore = r2_score(y_test1, npred_values)\n",
    "round(rscore,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 19"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Ridge regression reduces variance at the expense of higher bias."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Linear regression is sensititve to outliers."
   ]
  }
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