Regression_Model_Evaluation_techniques.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The models that we built , needs proper evaluation to understand how they will perform on real world data in production. That's why we have some set evaluation techniques in place for specific kinds of machine learning problems. We will discuss all of them one by one here."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Regression Problems\n",
    "\n",
    "Regression problems are those kind of problems where our target variable or ourput is a continuous variable. Like predicting weather temparature , salary etc etc. And there are some set model evaluation techniques present for such problems. Let's look into it.\n",
    "\n",
    "    -   Mean Squared Error (MSE)\n",
    "        \n",
    "    In regression problems let's understand the error part first. We get an actual value(target variable) present in our test data and our regression model will also predict a value for the target variable. Now this predicted value and the actual value will continue to have some differences. This differences are called errors. In certain cases this differences can be positive , in some cases it can be negative as well. So to bring all the values in the positive section , we square up the errors. And at the end we go ahead find out the mean of all the errors. That's called mean Squared Error or MSE. Below is given the formual of MSE\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Alt text](Mean%20Squared%20Error%20Formual.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's understand mean squared error with code example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#importing the neccesary libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split as tts\n",
    "from sklearn.linear_model import LinearRegression as lr\n",
    "from sklearn.metrics import mean_squared_error as mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>crim</th>\n",
       "      <th>zn</th>\n",
       "      <th>indus</th>\n",
       "      <th>chas</th>\n",
       "      <th>nox</th>\n",
       "      <th>rm</th>\n",
       "      <th>age</th>\n",
       "      <th>dis</th>\n",
       "      <th>rad</th>\n",
       "      <th>tax</th>\n",
       "      <th>ptratio</th>\n",
       "      <th>b</th>\n",
       "      <th>lstat</th>\n",
       "      <th>medv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      crim    zn  indus  chas    nox     rm   age     dis  rad  tax  ptratio  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        b  lstat  medv  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lets import our dataset , we will work with boston data itself\n",
    "df = pd.read_csv('BostonHousing.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the missing value level present in the data is as below crim       0\n",
      "zn         0\n",
      "indus      0\n",
      "chas       0\n",
      "nox        0\n",
      "rm         0\n",
      "age        0\n",
      "dis        0\n",
      "rad        0\n",
      "tax        0\n",
      "ptratio    0\n",
      "b          0\n",
      "lstat      0\n",
      "medv       0\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# let's check few details of the data\n",
    "print(f'the missing value level present in the data is as below {df.isnull().sum()}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's divide our data in x and y for feature and target variable identification\n",
    "x = df.iloc[:, 0:-1]\n",
    "y = df.iloc[:, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "      <th>crim</th>\n",
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       "      <th>indus</th>\n",
       "      <th>chas</th>\n",
       "      <th>nox</th>\n",
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       "      <th>tax</th>\n",
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       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
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       "      <td>7.07</td>\n",
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       "      <td>0.469</td>\n",
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       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
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       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
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       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
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       "      <td>2.94</td>\n",
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       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>391.99</td>\n",
       "      <td>9.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>393.45</td>\n",
       "      <td>6.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1</td>\n",
       "      <td>273</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>7.88</td>\n",
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       "<p>506 rows × 13 columns</p>\n",
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      "text/plain": [
       "        crim    zn  indus  chas    nox     rm   age     dis  rad  tax  \\\n",
       "0    0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296   \n",
       "1    0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242   \n",
       "2    0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242   \n",
       "3    0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222   \n",
       "4    0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222   \n",
       "..       ...   ...    ...   ...    ...    ...   ...     ...  ...  ...   \n",
       "501  0.06263   0.0  11.93     0  0.573  6.593  69.1  2.4786    1  273   \n",
       "502  0.04527   0.0  11.93     0  0.573  6.120  76.7  2.2875    1  273   \n",
       "503  0.06076   0.0  11.93     0  0.573  6.976  91.0  2.1675    1  273   \n",
       "504  0.10959   0.0  11.93     0  0.573  6.794  89.3  2.3889    1  273   \n",
       "505  0.04741   0.0  11.93     0  0.573  6.030  80.8  2.5050    1  273   \n",
       "\n",
       "     ptratio       b  lstat  \n",
       "0       15.3  396.90   4.98  \n",
       "1       17.8  396.90   9.14  \n",
       "2       17.8  392.83   4.03  \n",
       "3       18.7  394.63   2.94  \n",
       "4       18.7  396.90   5.33  \n",
       "..       ...     ...    ...  \n",
       "501     21.0  391.99   9.67  \n",
       "502     21.0  396.90   9.08  \n",
       "503     21.0  396.90   5.64  \n",
       "504     21.0  393.45   6.48  \n",
       "505     21.0  396.90   7.88  \n",
       "\n",
       "[506 rows x 13 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      24.0\n",
       "1      21.6\n",
       "2      34.7\n",
       "3      33.4\n",
       "4      36.2\n",
       "       ... \n",
       "501    22.4\n",
       "502    20.6\n",
       "503    23.9\n",
       "504    22.0\n",
       "505    11.9\n",
       "Name: medv, Length: 506, dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we need to scale our features so that it remains in the same scale with standaradscaler\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "x = scaler.fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.41978194,  0.28482986, -1.2879095 , ..., -1.45900038,\n",
       "         0.44105193, -1.0755623 ],\n",
       "       [-0.41733926, -0.48772236, -0.59338101, ..., -0.30309415,\n",
       "         0.44105193, -0.49243937],\n",
       "       [-0.41734159, -0.48772236, -0.59338101, ..., -0.30309415,\n",
       "         0.39642699, -1.2087274 ],\n",
       "       ...,\n",
       "       [-0.41344658, -0.48772236,  0.11573841, ...,  1.17646583,\n",
       "         0.44105193, -0.98304761],\n",
       "       [-0.40776407, -0.48772236,  0.11573841, ...,  1.17646583,\n",
       "         0.4032249 , -0.86530163],\n",
       "       [-0.41500016, -0.48772236,  0.11573841, ...,  1.17646583,\n",
       "         0.44105193, -0.66905833]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now let's go ahead and do our train test split\n",
    "xtrain,xtest,ytrain,ytest = tts(x,y,test_size=0.2,random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now let's train our model\n",
    "lr = lr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(xtrain,ytrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.668759493535632"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.score(xtest,ytest)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that our linear regression model is built , let's build a prediction variable as ypred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "ypred = lr.predict(xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([28.99672362, 36.02556534, 14.81694405, 25.03197915, 18.76987992,\n",
       "       23.25442929, 17.66253818, 14.34119   , 23.01320703, 20.63245597,\n",
       "       24.90850512, 18.63883645, -6.08842184, 21.75834668, 19.23922576,\n",
       "       26.19319733, 20.64773313,  5.79472718, 40.50033966, 17.61289074,\n",
       "       27.24909479, 30.06625441, 11.34179277, 24.16077616, 17.86058499,\n",
       "       15.83609765, 22.78148106, 14.57704449, 22.43626052, 19.19631835,\n",
       "       22.43383455, 25.21979081, 25.93909562, 17.70162434, 16.76911711,\n",
       "       16.95125411, 31.23340153, 20.13246729, 23.76579011, 24.6322925 ,\n",
       "       13.94204955, 32.25576301, 42.67251161, 17.32745046, 27.27618614,\n",
       "       16.99310991, 14.07009109, 25.90341861, 20.29485982, 29.95339638,\n",
       "       21.28860173, 34.34451856, 16.04739105, 26.22562412, 39.53939798,\n",
       "       22.57950697, 18.84531367, 32.72531661, 25.0673037 , 12.88628956,\n",
       "       22.68221908, 30.48287757, 31.52626806, 15.90148607, 20.22094826,\n",
       "       16.71089812, 20.52384893, 25.96356264, 30.61607978, 11.59783023,\n",
       "       20.51232627, 27.48111878, 11.01962332, 15.68096344, 23.79316251,\n",
       "        6.19929359, 21.6039073 , 41.41377225, 18.76548695,  8.87931901,\n",
       "       20.83076916, 13.25620627, 20.73963699,  9.36482222, 23.22444271,\n",
       "       31.9155003 , 19.10228271, 25.51579303, 29.04256769, 20.14358566,\n",
       "       25.5859787 ,  5.70159447, 20.09474756, 14.95069156, 12.50395648,\n",
       "       20.72635294, 24.73957161, -0.164237  , 13.68486682, 16.18359697,\n",
       "       22.27621999, 24.47902364])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "173    23.6\n",
       "274    32.4\n",
       "491    13.6\n",
       "72     22.8\n",
       "452    16.1\n",
       "       ... \n",
       "412    17.9\n",
       "436     9.6\n",
       "411    17.2\n",
       "86     22.5\n",
       "75     21.4\n",
       "Name: medv, Length: 102, dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ytest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102\n"
     ]
    }
   ],
   "source": [
    "print(len(xtest))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102\n"
     ]
    }
   ],
   "source": [
    "print(len(ytest))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102\n"
     ]
    }
   ],
   "source": [
    "print(len(ypred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='medv'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets visualiza our model prediction and actual values\n",
    "import seaborn as sns\n",
    "sns.regplot(x = ytest , y = ypred )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's create a list of errors , which is simply substracting the actual values from the predicted values\n",
    "changes = list(ypred-ytest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5.396723619824883,\n",
       " 3.625565335672313,\n",
       " 1.216944045388285,\n",
       " 2.2319791503995674,\n",
       " 2.669879915248149,\n",
       " 3.2544292914679716,\n",
       " -0.13746181779418976,\n",
       " 0.3411899997547092,\n",
       " 3.413207026913337,\n",
       " 3.8324559727508465,\n",
       " 3.408505116349641,\n",
       " -0.2611635466075555,\n",
       " -13.088421842193625,\n",
       " 0.5583466809972926,\n",
       " 0.7392257593035794,\n",
       " -3.6068026717863546,\n",
       " 1.8477331297073185,\n",
       " -4.405272821115485,\n",
       " -9.499660339492422,\n",
       " 3.5128907427671674,\n",
       " 2.0490947868518354,\n",
       " 0.9662544095122598,\n",
       " -1.3582072271767238,\n",
       " 1.7607761605923677,\n",
       " 3.660584986887809,\n",
       " 2.036097647919295,\n",
       " 2.4814810552120647,\n",
       " -0.3229555113683009,\n",
       " 0.7362605243684825,\n",
       " 0.8963183464667104,\n",
       " -0.6661654488658755,\n",
       " 1.4197908067564846,\n",
       " 10.939095624449543,\n",
       " -3.0983756592133993,\n",
       " -2.3308828901820533,\n",
       " -2.448745890731942,\n",
       " -3.4665984706249944,\n",
       " 0.6324672853666868,\n",
       " -0.6342098892753363,\n",
       " 1.2322924971596656,\n",
       " -5.757950450869547,\n",
       " 4.055763011339312,\n",
       " -7.327488388980569,\n",
       " -0.07254953572099865,\n",
       " 4.676186138004901,\n",
       " 1.893109908316207,\n",
       " 0.9700910916451431,\n",
       " 1.7034186116046754,\n",
       " 0.39485982256238117,\n",
       " 5.953396377335693,\n",
       " 2.388601728145286,\n",
       " -1.055481435365131,\n",
       " 0.8473910498621962,\n",
       " -0.27437588371694943,\n",
       " -3.9606020216584454,\n",
       " 1.3795069680653747,\n",
       " 0.44531366626455693,\n",
       " 4.22531661496572,\n",
       " 1.1673036969031934,\n",
       " -5.613710435657753,\n",
       " -2.3177809226427364,\n",
       " -4.917122425865042,\n",
       " 0.02626806478218313,\n",
       " -4.298513929639672,\n",
       " -3.8790517385940504,\n",
       " -3.2891018813931687,\n",
       " 7.423848928753118,\n",
       " 1.1635626380438566,\n",
       " -0.18392022376720618,\n",
       " -1.1021697741712622,\n",
       " 0.5123262743265968,\n",
       " 3.7811187778861104,\n",
       " 0.21962332247759342,\n",
       " -4.919036556871728,\n",
       " 2.9931625127084764,\n",
       " 1.1992935939490827,\n",
       " 1.503907303225084,\n",
       " -7.0862277486752845,\n",
       " 7.86548694981486,\n",
       " 1.8793190117150314,\n",
       " -0.06923083841214961,\n",
       " -3.943793731695459,\n",
       " -0.16036301161222966,\n",
       " -0.3351777834577092,\n",
       " 3.824442713498069,\n",
       " 2.915500297944522,\n",
       " 2.702282710679661,\n",
       " 0.5157930325947824,\n",
       " 4.042567694388353,\n",
       " 3.0435856607765217,\n",
       " 2.385978704279765,\n",
       " -4.698405529660532,\n",
       " 0.4947475582042209,\n",
       " -2.2493084376549604,\n",
       " -14.996043515817975,\n",
       " -2.273647060854195,\n",
       " -25.260428393480627,\n",
       " -18.06423699568657,\n",
       " 4.084866815285885,\n",
       " -1.016403028286554,\n",
       " -0.22378000646660112,\n",
       " 3.0790236390206616]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "changes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>actual_value</th>\n",
       "      <th>predicted_value</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>23.6</td>\n",
       "      <td>28.996724</td>\n",
       "      <td>5.396724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>274</th>\n",
       "      <td>32.4</td>\n",
       "      <td>36.025565</td>\n",
       "      <td>3.625565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>13.6</td>\n",
       "      <td>14.816944</td>\n",
       "      <td>1.216944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>22.8</td>\n",
       "      <td>25.031979</td>\n",
       "      <td>2.231979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>452</th>\n",
       "      <td>16.1</td>\n",
       "      <td>18.769880</td>\n",
       "      <td>2.669880</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     actual_value  predicted_value     error\n",
       "173          23.6        28.996724  5.396724\n",
       "274          32.4        36.025565  3.625565\n",
       "491          13.6        14.816944  1.216944\n",
       "72           22.8        25.031979  2.231979\n",
       "452          16.1        18.769880  2.669880"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# creating a dataframe storing actual , predicted and changed values \n",
    "ch_df = pd.DataFrame(data = {\"actual_value\":ytest,\n",
    "                                 \"predicted_value\":ypred,\n",
    "                                 \"error\":changes})\n",
    "ch_df.head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see through visualization that there are errors present in the data and also we have checked through the list called 'changes' that how scattered our errors are , lets with the help of numpy first find out our mean squared error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# squaring all the errors\n",
    "sq_error_list = []\n",
    "for i in changes:\n",
    "    sq_error_list.append(np.square(i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[29.124625828775784,\n",
       " 13.144724003228692,\n",
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       " 11.61790712818168,\n",
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       " 171.30678631921117,\n",
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       " 13.009025513205186,\n",
       " 3.4141177186180025,\n",
       " 19.406428628458784,\n",
       " 90.24354656572528,\n",
       " 12.340401370619261,\n",
       " 4.198789445503369,\n",
       " 0.933647583901886,\n",
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       " 3.1003326877103996,\n",
       " 13.39988244622842,\n",
       " 4.1456936318624855,\n",
       " 6.157748227376382,\n",
       " 0.10430026232316074,\n",
       " 0.5420795597433529,\n",
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       " 119.66381308085113,\n",
       " 9.599931725606067,\n",
       " 5.433015047743442,\n",
       " 5.996356437376573,\n",
       " 12.01730495653955,\n",
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       " 1.5185447985560045,\n",
       " 33.153993394668824,\n",
       " 16.449213604148127,\n",
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       " 55.11353291694883,\n",
       " 1.3538780126515788,\n",
       " 0.033826648710579194,\n",
       " 1.2147782110967311,\n",
       " 0.26247821136537136,\n",
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       " 24.19692064784046,\n",
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       " 3.531839947793562,\n",
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       " 15.553508998160396,\n",
       " 0.025716295493344102,\n",
       " 0.11234414652362301,\n",
       " 14.626362068828472,\n",
       " 8.500141987314597,\n",
       " 7.302331848438217,\n",
       " 0.26604245247332226,\n",
       " 16.342353563712365,\n",
       " 9.263413674484456,\n",
       " 5.692894377276546,\n",
       " 22.07501452114466,\n",
       " 0.24477514634903894,\n",
       " 5.059388447705799,\n",
       " 224.88132112830635,\n",
       " 5.16947095733092,\n",
       " 638.0892426221623,\n",
       " 326.31665823633136,\n",
       " 16.686136898623847,\n",
       " 1.0330751159100773,\n",
       " 0.05007749129419204,\n",
       " 9.480386569648036]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sq_error_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the mean squared error through numpy method is 24.29111947497352\n"
     ]
    }
   ],
   "source": [
    "# now let's find the mean of this squared list\n",
    "mse_numpy = np.mean(sq_error_list)\n",
    "print(f'the mean squared error through numpy method is {mse_numpy}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the mean squared error through sklearn method is 24.29111947497352\n"
     ]
    }
   ],
   "source": [
    "# now let's find out the MSE through our sklearn method.\n",
    "from sklearn.metrics import mean_squared_error\n",
    "mse_sklearn = mean_squared_error(ytest,ypred)\n",
    "print(f'the mean squared error through sklearn method is {mse_sklearn}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus our theory is proved to be right as in both occasions we have got the same result of mean squared error. Near to 0 MSE indicates more accurate model."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    -   Mean Absolute Error (MAE)\n",
    "        This simply means the mean of total sum of all errors that has been produced from our model, We will look into it with both with and without sklearn metrics below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the mean absolute error with numpy method is 3.1890919658878505\n",
      "the mean absolute error with numpy method is 3.1890919658878505\n"
     ]
    }
   ],
   "source": [
    "# finding the mean of all errors with numpy method\n",
    "abs_error_lst = []\n",
    "for i in changes:\n",
    "    abs_error_lst.append(abs(i))\n",
    "mae_numpy = np.mean(abs_error_lst) \n",
    "print(f'the mean absolute error with numpy method is {mae_numpy}')\n",
    "#finding the mean of all errors with sklearn\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "mae_sklearn = mean_absolute_error(ytest,ypred)\n",
    "print(f'the mean absolute error with numpy method is {mae_sklearn}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    -   Root Mean Squared Error(RMSE)\n",
    "        This method potrays the root of our previously calculated mean squared error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the root mean squared error with numpy method is 4.928602182665337\n",
      "the root mean squared error with sklearn method is 4.928602182665337\n"
     ]
    }
   ],
   "source": [
    "# RMSE with numpy\n",
    "rmse_numpy = np.sqrt(mse_numpy)\n",
    "print(f'the root mean squared error with numpy method is {rmse_numpy}')\n",
    "# RMSE with sklearn , sklearn do not have a direct library for this , we will use the mse formula with a parameter called squared set to false\n",
    "rmse_sklearn = mean_squared_error(ytest,ypred,squared=False)\n",
    "print(f'the root mean squared error with sklearn method is {rmse_sklearn}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    -   R2 Score (Co efficient of determination)\n",
    "        This score can simply be found with 1 being substracted with the division of sum of squares or residuals and total sum of squares. Residuals are nothing but the errors present in our data. Like all methods before here also , we will look into the numpy method then sklearn method as well."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the r2 score with numpy method here is 0.9546026603697298\n"
     ]
    }
   ],
   "source": [
    "# R2 score with numpy\n",
    "sum_sq_residuals = sum(np.square(changes))\n",
    "sum_sq_total = sum(np.square(ytest,ypred))\n",
    "r2score_numpy = 1 - (sum_sq_residuals/sum_sq_total)\n",
    "print(f\"the r2 score with numpy method here is {r2score_numpy}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the r2 score with sklearn method here is -6696.531804262288\n"
     ]
    }
   ],
   "source": [
    "# R2 score with sklearn\n",
    "from sklearn.metrics import r2_score\n",
    "r2score_sklearn = r2_score(ytest,ypred)\n",
    "print(f\"the r2 score with sklearn method here is {r2score_sklearn}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "github1",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}