Day-1/Regressions/Lab_on_Linear_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align: center;\" markdown=\"1\">AI Winter School 2019</h1> \n",
    "<h2 style=\"text-align: center;\" markdown=\"2\">Dec 10 - Dec 20, 2019</h2>\n",
    "<h3 style=\"text-align: center;\" markdown=\"3\">Lab on Linear Regression</h3>\n",
    "\n",
    "\n",
    "> *This notebook is part of the AI Winter School 2019 organized by NAAMII. The objectives of this notebook is to use Linear Regression to predict district wise poverty rates in Nepal using predictor variables such as literacy rate, household size, share of kids etc. The data used in this exercise is part of Census 2011 conducted by the Central Bureau of Statistics (CBS), Nepal.*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table of Contents\n",
    "\n",
    "[Introduction](#introduction)  \n",
    "&nbsp;&nbsp;&nbsp;[Explanation and Theory](#introduction-theory)  \n",
    "[Data Setup](#setup)  \n",
    "[Two Dimensional Linear Regression](#1dlinreg)   \n",
    "[Scikit-Learn Linear Regression](#sklearn-linreg)    \n",
    "[Summary](#summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression Introduction <a class=\"anchor\" id=\"introduction\"></a>\n",
    "\n",
    "Linear regression is one of the most simple and well-known machine learning algorithms for regression. It approximates the relationship between two or more variables using a straight line. \n",
    "\n",
    "It assumes that there is a linear relationship between the independent variables and the dependent variables. In high-dimensional datasets, this may not be the case, so linear regression may not be the best choice for many problems.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explanation and Theory <a class=\"anchor\" id=\"introduction-theory\"></a>\n",
    "\n",
    "**Assumptions and properties.** \n",
    "Suppose we have a data set that consists of n samples and m features\n",
    "\n",
    "\\begin{equation}\n",
    "\\label{eqn:samples}\n",
    "\\mathbf{X} = \\{\\mathbf{x_1}, \\mathbf{x_2}, \\ldots \\mathbf{x_n}\\}, \\quad   \\mathbf{x_i} \\in \\mathbb{R}^{m}\n",
    "\\end{equation}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{equation}\n",
    "\\label{eqn:features}\n",
    "\\mathbf{x_i} =  (x_i^{(1)}, x_i^{(2)}, \\ldots x_i^{(m)} ) ^T\n",
    "\\end{equation}\n",
    "\n",
    "The target variable is given by\n",
    "\\begin{equation}\n",
    "\\label{eqn:target}\n",
    "\\mathbf{Y}= \\{y_1, y_2 \\ldots y_n \\} \\quad where \\,\\,\\, y_j \\in (0,1)\n",
    "\\end{equation}\n",
    "\n",
    "**Algorithm and Training.** Linear regression takes the form of a linear model:\n",
    "\n",
    "$$f(i)=\\beta_0+\\beta_1x_{i}^{(1)}+...+\\beta_m x_{i}^{(m)} $$\n",
    "\n",
    "where $\\beta_0,...,\\beta_m$ are the regression coefficients or weights assigned to each feature $x$. For each data point $i$, a pseudo-variable $x_{0,i}=1$ is added to correspond to the intercept coefficient $\\beta_0$. This allows us to write the model in vector form as:\n",
    "$$f(i)=\\boldsymbol{\\beta}\\cdot\\boldsymbol{X_i}$$\n",
    "\n",
    "When we train the linear regression classifier, we are trying to find the best values of $\\beta$ to match the data i.e minimizes the following error functional or **objective function**:\n",
    "$$ \\frac{1}{2} \\sum_{i=1}^{n} (y_i - f(i))^2$$\n",
    "\n",
    "There are several techniques to do solve this minimization problem, such as [gradient descent](https://en.wikipedia.org/wiki/Gradient_descent)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data setup<a class=\"anchor\" id=\"setup\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we'll load the libraries that will be used throughout this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aAAH9q7UP_yy"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "dX7Hmgc5GnOt"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading data. In this notebook we should have cleaned and organized the data already, so we should simply have to import our data file into a dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#copy path of your file inside quotes\n",
    "df = pd.read_csv(\"lin_reg_educ_share.csv\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Unnamed: 0', 'male', 'literacy rate', 'years_educ1', 'years_educ2'], dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>male</th>\n",
       "      <th>literacy rate</th>\n",
       "      <th>years_educ1</th>\n",
       "      <th>years_educ2</th>\n",
       "      <th>years_educ3</th>\n",
       "      <th>years_educ4</th>\n",
       "      <th>years_educ5</th>\n",
       "      <th>years_educ6</th>\n",
       "      <th>years_educ7</th>\n",
       "      <th>years_educ8</th>\n",
       "      <th>hhsize</th>\n",
       "      <th>poverty rate</th>\n",
       "      <th>nkid06</th>\n",
       "      <th>nkid715</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Achham</td>\n",
       "      <td>0.461668</td>\n",
       "      <td>0.476151</td>\n",
       "      <td>0.080331</td>\n",
       "      <td>0.394979</td>\n",
       "      <td>0.224853</td>\n",
       "      <td>0.145161</td>\n",
       "      <td>0.099263</td>\n",
       "      <td>0.001059</td>\n",
       "      <td>0.050133</td>\n",
       "      <td>0.004221</td>\n",
       "      <td>6.322215</td>\n",
       "      <td>0.472</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>1.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Arghakhanchi</td>\n",
       "      <td>0.433736</td>\n",
       "      <td>0.652446</td>\n",
       "      <td>0.039106</td>\n",
       "      <td>0.298637</td>\n",
       "      <td>0.253662</td>\n",
       "      <td>0.189621</td>\n",
       "      <td>0.157736</td>\n",
       "      <td>0.000844</td>\n",
       "      <td>0.057360</td>\n",
       "      <td>0.003033</td>\n",
       "      <td>5.179200</td>\n",
       "      <td>0.288</td>\n",
       "      <td>0.458333</td>\n",
       "      <td>1.020833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Baglung</td>\n",
       "      <td>0.438207</td>\n",
       "      <td>0.647397</td>\n",
       "      <td>0.043599</td>\n",
       "      <td>0.301124</td>\n",
       "      <td>0.239773</td>\n",
       "      <td>0.186960</td>\n",
       "      <td>0.154035</td>\n",
       "      <td>0.000375</td>\n",
       "      <td>0.070341</td>\n",
       "      <td>0.003793</td>\n",
       "      <td>5.378669</td>\n",
       "      <td>0.229</td>\n",
       "      <td>0.716667</td>\n",
       "      <td>1.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Baitadi</td>\n",
       "      <td>0.464469</td>\n",
       "      <td>0.548497</td>\n",
       "      <td>0.058514</td>\n",
       "      <td>0.346258</td>\n",
       "      <td>0.259600</td>\n",
       "      <td>0.186120</td>\n",
       "      <td>0.114269</td>\n",
       "      <td>0.000787</td>\n",
       "      <td>0.030814</td>\n",
       "      <td>0.003637</td>\n",
       "      <td>6.748073</td>\n",
       "      <td>0.457</td>\n",
       "      <td>1.133333</td>\n",
       "      <td>1.416667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bajhang</td>\n",
       "      <td>0.477381</td>\n",
       "      <td>0.488333</td>\n",
       "      <td>0.073606</td>\n",
       "      <td>0.417432</td>\n",
       "      <td>0.219511</td>\n",
       "      <td>0.138940</td>\n",
       "      <td>0.112037</td>\n",
       "      <td>0.000483</td>\n",
       "      <td>0.034308</td>\n",
       "      <td>0.003682</td>\n",
       "      <td>6.945809</td>\n",
       "      <td>0.568</td>\n",
       "      <td>0.777778</td>\n",
       "      <td>1.583333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Unnamed: 0      male  literacy rate  years_educ1  years_educ2  \\\n",
       "0        Achham  0.461668       0.476151     0.080331     0.394979   \n",
       "1  Arghakhanchi  0.433736       0.652446     0.039106     0.298637   \n",
       "2       Baglung  0.438207       0.647397     0.043599     0.301124   \n",
       "3       Baitadi  0.464469       0.548497     0.058514     0.346258   \n",
       "4       Bajhang  0.477381       0.488333     0.073606     0.417432   \n",
       "\n",
       "   years_educ3  years_educ4  years_educ5  years_educ6  years_educ7  \\\n",
       "0     0.224853     0.145161     0.099263     0.001059     0.050133   \n",
       "1     0.253662     0.189621     0.157736     0.000844     0.057360   \n",
       "2     0.239773     0.186960     0.154035     0.000375     0.070341   \n",
       "3     0.259600     0.186120     0.114269     0.000787     0.030814   \n",
       "4     0.219511     0.138940     0.112037     0.000483     0.034308   \n",
       "\n",
       "   years_educ8    hhsize  poverty rate    nkid06   nkid715  \n",
       "0     0.004221  6.322215         0.472  0.750000  1.166667  \n",
       "1     0.003033  5.179200         0.288  0.458333  1.020833  \n",
       "2     0.003793  5.378669         0.229  0.716667  1.083333  \n",
       "3     0.003637  6.748073         0.457  1.133333  1.416667  \n",
       "4     0.003682  6.945809         0.568  0.777778  1.583333  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Write the code to display the first 5 rows of the dataframe\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qcwiA5EFVn8X"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>male</th>\n",
       "      <th>literacy rate</th>\n",
       "      <th>years_educ1</th>\n",
       "      <th>years_educ2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Achham</td>\n",
       "      <td>0.461668</td>\n",
       "      <td>0.476151</td>\n",
       "      <td>0.080331</td>\n",
       "      <td>0.394979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Arghakhanchi</td>\n",
       "      <td>0.433736</td>\n",
       "      <td>0.652446</td>\n",
       "      <td>0.039106</td>\n",
       "      <td>0.298637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Baglung</td>\n",
       "      <td>0.438207</td>\n",
       "      <td>0.647397</td>\n",
       "      <td>0.043599</td>\n",
       "      <td>0.301124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Baitadi</td>\n",
       "      <td>0.464469</td>\n",
       "      <td>0.548497</td>\n",
       "      <td>0.058514</td>\n",
       "      <td>0.346258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bajhang</td>\n",
       "      <td>0.477381</td>\n",
       "      <td>0.488333</td>\n",
       "      <td>0.073606</td>\n",
       "      <td>0.417432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Unnamed: 0      male  literacy rate  years_educ1  years_educ2\n",
       "0        Achham  0.461668       0.476151     0.080331     0.394979\n",
       "1  Arghakhanchi  0.433736       0.652446     0.039106     0.298637\n",
       "2       Baglung  0.438207       0.647397     0.043599     0.301124\n",
       "3       Baitadi  0.464469       0.548497     0.058514     0.346258\n",
       "4       Bajhang  0.477381       0.488333     0.073606     0.417432"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# write the code to display the first 5 columns of the data frame and first 5 rows\n",
    "df[df.columns[:5]].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "Spn6pMkxe3nv",
    "outputId": "166a3635-0a44-4dc7-a1f4-0dee17d90a0d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(71, 15)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Write the code to display the number of rows and columns of the dataframe\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rename the column 'Unnamed: 0' to 'district'\n",
    "df.rename(columns = {'Unnamed: 0': 'district'},inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>district</th>\n",
       "      <th>male</th>\n",
       "      <th>literacy rate</th>\n",
       "      <th>years_educ1</th>\n",
       "      <th>years_educ2</th>\n",
       "      <th>years_educ3</th>\n",
       "      <th>years_educ4</th>\n",
       "      <th>years_educ5</th>\n",
       "      <th>years_educ6</th>\n",
       "      <th>years_educ7</th>\n",
       "      <th>years_educ8</th>\n",
       "      <th>hhsize</th>\n",
       "      <th>poverty rate</th>\n",
       "      <th>nkid06</th>\n",
       "      <th>nkid715</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Achham</td>\n",
       "      <td>0.461668</td>\n",
       "      <td>0.476151</td>\n",
       "      <td>0.080331</td>\n",
       "      <td>0.394979</td>\n",
       "      <td>0.224853</td>\n",
       "      <td>0.145161</td>\n",
       "      <td>0.099263</td>\n",
       "      <td>0.001059</td>\n",
       "      <td>0.050133</td>\n",
       "      <td>0.004221</td>\n",
       "      <td>6.322215</td>\n",
       "      <td>0.472</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>1.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Arghakhanchi</td>\n",
       "      <td>0.433736</td>\n",
       "      <td>0.652446</td>\n",
       "      <td>0.039106</td>\n",
       "      <td>0.298637</td>\n",
       "      <td>0.253662</td>\n",
       "      <td>0.189621</td>\n",
       "      <td>0.157736</td>\n",
       "      <td>0.000844</td>\n",
       "      <td>0.057360</td>\n",
       "      <td>0.003033</td>\n",
       "      <td>5.179200</td>\n",
       "      <td>0.288</td>\n",
       "      <td>0.458333</td>\n",
       "      <td>1.020833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Baglung</td>\n",
       "      <td>0.438207</td>\n",
       "      <td>0.647397</td>\n",
       "      <td>0.043599</td>\n",
       "      <td>0.301124</td>\n",
       "      <td>0.239773</td>\n",
       "      <td>0.186960</td>\n",
       "      <td>0.154035</td>\n",
       "      <td>0.000375</td>\n",
       "      <td>0.070341</td>\n",
       "      <td>0.003793</td>\n",
       "      <td>5.378669</td>\n",
       "      <td>0.229</td>\n",
       "      <td>0.716667</td>\n",
       "      <td>1.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Baitadi</td>\n",
       "      <td>0.464469</td>\n",
       "      <td>0.548497</td>\n",
       "      <td>0.058514</td>\n",
       "      <td>0.346258</td>\n",
       "      <td>0.259600</td>\n",
       "      <td>0.186120</td>\n",
       "      <td>0.114269</td>\n",
       "      <td>0.000787</td>\n",
       "      <td>0.030814</td>\n",
       "      <td>0.003637</td>\n",
       "      <td>6.748073</td>\n",
       "      <td>0.457</td>\n",
       "      <td>1.133333</td>\n",
       "      <td>1.416667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bajhang</td>\n",
       "      <td>0.477381</td>\n",
       "      <td>0.488333</td>\n",
       "      <td>0.073606</td>\n",
       "      <td>0.417432</td>\n",
       "      <td>0.219511</td>\n",
       "      <td>0.138940</td>\n",
       "      <td>0.112037</td>\n",
       "      <td>0.000483</td>\n",
       "      <td>0.034308</td>\n",
       "      <td>0.003682</td>\n",
       "      <td>6.945809</td>\n",
       "      <td>0.568</td>\n",
       "      <td>0.777778</td>\n",
       "      <td>1.583333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       district      male  literacy rate  years_educ1  years_educ2  \\\n",
       "0        Achham  0.461668       0.476151     0.080331     0.394979   \n",
       "1  Arghakhanchi  0.433736       0.652446     0.039106     0.298637   \n",
       "2       Baglung  0.438207       0.647397     0.043599     0.301124   \n",
       "3       Baitadi  0.464469       0.548497     0.058514     0.346258   \n",
       "4       Bajhang  0.477381       0.488333     0.073606     0.417432   \n",
       "\n",
       "   years_educ3  years_educ4  years_educ5  years_educ6  years_educ7  \\\n",
       "0     0.224853     0.145161     0.099263     0.001059     0.050133   \n",
       "1     0.253662     0.189621     0.157736     0.000844     0.057360   \n",
       "2     0.239773     0.186960     0.154035     0.000375     0.070341   \n",
       "3     0.259600     0.186120     0.114269     0.000787     0.030814   \n",
       "4     0.219511     0.138940     0.112037     0.000483     0.034308   \n",
       "\n",
       "   years_educ8    hhsize  poverty rate    nkid06   nkid715  \n",
       "0     0.004221  6.322215         0.472  0.750000  1.166667  \n",
       "1     0.003033  5.179200         0.288  0.458333  1.020833  \n",
       "2     0.003793  5.378669         0.229  0.716667  1.083333  \n",
       "3     0.003637  6.748073         0.457  1.133333  1.416667  \n",
       "4     0.003682  6.945809         0.568  0.777778  1.583333  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two Dimensional Linear Regression<a class=\"anchor\" id=\"1dlinreg\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will begin by using linear regression to estimate poverty rates for each district using only one independent variable - literacy rate. Let's begin by making a scatter plot of the Poverty rate vs. Literacy rate to get a sense of how they depend on one another. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Poverty Rate vs. Literacy Rate in Districts of Nepal')"
      ]
     },
     "execution_count": 10,
     "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": [
    "plt.scatter(df['literacy rate'],df['poverty rate'])\n",
    "plt.xlabel('Literacy Rate')\n",
    "plt.ylabel('Poverty Rate')\n",
    "plt.title('Poverty Rate vs. Literacy Rate in Districts of Nepal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the Poverty rate is inversely related to Literacy rate in a somewhat linear way. We can quantify this relationship by finding the correlation between the two variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jjtIBs5tzFDC"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6798893910120695"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Write the code to find the pearson's correlation between literacy rate and poverty rate\n",
    "df['literacy rate'].corr(df['poverty rate'], method='pearson')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>district</th>\n",
       "      <th>male</th>\n",
       "      <th>literacy rate</th>\n",
       "      <th>years_educ1</th>\n",
       "      <th>years_educ2</th>\n",
       "      <th>years_educ3</th>\n",
       "      <th>years_educ4</th>\n",
       "      <th>years_educ5</th>\n",
       "      <th>years_educ6</th>\n",
       "      <th>years_educ7</th>\n",
       "      <th>years_educ8</th>\n",
       "      <th>hhsize</th>\n",
       "      <th>poverty rate</th>\n",
       "      <th>nkid06</th>\n",
       "      <th>nkid715</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Achham</td>\n",
       "      <td>0.461668</td>\n",
       "      <td>0.476151</td>\n",
       "      <td>0.080331</td>\n",
       "      <td>0.394979</td>\n",
       "      <td>0.224853</td>\n",
       "      <td>0.145161</td>\n",
       "      <td>0.099263</td>\n",
       "      <td>0.001059</td>\n",
       "      <td>0.050133</td>\n",
       "      <td>0.004221</td>\n",
       "      <td>6.322215</td>\n",
       "      <td>0.472</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>1.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Arghakhanchi</td>\n",
       "      <td>0.433736</td>\n",
       "      <td>0.652446</td>\n",
       "      <td>0.039106</td>\n",
       "      <td>0.298637</td>\n",
       "      <td>0.253662</td>\n",
       "      <td>0.189621</td>\n",
       "      <td>0.157736</td>\n",
       "      <td>0.000844</td>\n",
       "      <td>0.057360</td>\n",
       "      <td>0.003033</td>\n",
       "      <td>5.179200</td>\n",
       "      <td>0.288</td>\n",
       "      <td>0.458333</td>\n",
       "      <td>1.020833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Baglung</td>\n",
       "      <td>0.438207</td>\n",
       "      <td>0.647397</td>\n",
       "      <td>0.043599</td>\n",
       "      <td>0.301124</td>\n",
       "      <td>0.239773</td>\n",
       "      <td>0.186960</td>\n",
       "      <td>0.154035</td>\n",
       "      <td>0.000375</td>\n",
       "      <td>0.070341</td>\n",
       "      <td>0.003793</td>\n",
       "      <td>5.378669</td>\n",
       "      <td>0.229</td>\n",
       "      <td>0.716667</td>\n",
       "      <td>1.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Baitadi</td>\n",
       "      <td>0.464469</td>\n",
       "      <td>0.548497</td>\n",
       "      <td>0.058514</td>\n",
       "      <td>0.346258</td>\n",
       "      <td>0.259600</td>\n",
       "      <td>0.186120</td>\n",
       "      <td>0.114269</td>\n",
       "      <td>0.000787</td>\n",
       "      <td>0.030814</td>\n",
       "      <td>0.003637</td>\n",
       "      <td>6.748073</td>\n",
       "      <td>0.457</td>\n",
       "      <td>1.133333</td>\n",
       "      <td>1.416667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bajhang</td>\n",
       "      <td>0.477381</td>\n",
       "      <td>0.488333</td>\n",
       "      <td>0.073606</td>\n",
       "      <td>0.417432</td>\n",
       "      <td>0.219511</td>\n",
       "      <td>0.138940</td>\n",
       "      <td>0.112037</td>\n",
       "      <td>0.000483</td>\n",
       "      <td>0.034308</td>\n",
       "      <td>0.003682</td>\n",
       "      <td>6.945809</td>\n",
       "      <td>0.568</td>\n",
       "      <td>0.777778</td>\n",
       "      <td>1.583333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       district      male  literacy rate  years_educ1  years_educ2  \\\n",
       "0        Achham  0.461668       0.476151     0.080331     0.394979   \n",
       "1  Arghakhanchi  0.433736       0.652446     0.039106     0.298637   \n",
       "2       Baglung  0.438207       0.647397     0.043599     0.301124   \n",
       "3       Baitadi  0.464469       0.548497     0.058514     0.346258   \n",
       "4       Bajhang  0.477381       0.488333     0.073606     0.417432   \n",
       "\n",
       "   years_educ3  years_educ4  years_educ5  years_educ6  years_educ7  \\\n",
       "0     0.224853     0.145161     0.099263     0.001059     0.050133   \n",
       "1     0.253662     0.189621     0.157736     0.000844     0.057360   \n",
       "2     0.239773     0.186960     0.154035     0.000375     0.070341   \n",
       "3     0.259600     0.186120     0.114269     0.000787     0.030814   \n",
       "4     0.219511     0.138940     0.112037     0.000483     0.034308   \n",
       "\n",
       "   years_educ8    hhsize  poverty rate    nkid06   nkid715  \n",
       "0     0.004221  6.322215         0.472  0.750000  1.166667  \n",
       "1     0.003033  5.179200         0.288  0.458333  1.020833  \n",
       "2     0.003793  5.378669         0.229  0.716667  1.083333  \n",
       "3     0.003637  6.748073         0.457  1.133333  1.416667  \n",
       "4     0.003682  6.945809         0.568  0.777778  1.583333  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        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>district</th>\n",
       "      <th>male</th>\n",
       "      <th>literacy rate</th>\n",
       "      <th>years_educ1</th>\n",
       "      <th>years_educ2</th>\n",
       "      <th>years_educ3</th>\n",
       "      <th>years_educ4</th>\n",
       "      <th>years_educ5</th>\n",
       "      <th>years_educ6</th>\n",
       "      <th>years_educ7</th>\n",
       "      <th>years_educ8</th>\n",
       "      <th>hhsize</th>\n",
       "      <th>poverty rate</th>\n",
       "      <th>nkid06</th>\n",
       "      <th>nkid715</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>Syangja</td>\n",
       "      <td>0.428499</td>\n",
       "      <td>0.696740</td>\n",
       "      <td>0.024426</td>\n",
       "      <td>0.233124</td>\n",
       "      <td>0.248407</td>\n",
       "      <td>0.250872</td>\n",
       "      <td>0.179026</td>\n",
       "      <td>0.000864</td>\n",
       "      <td>0.060832</td>\n",
       "      <td>0.002448</td>\n",
       "      <td>5.298789</td>\n",
       "      <td>0.118</td>\n",
       "      <td>0.535714</td>\n",
       "      <td>0.869048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>Tanahu</td>\n",
       "      <td>0.437649</td>\n",
       "      <td>0.680704</td>\n",
       "      <td>0.035329</td>\n",
       "      <td>0.288172</td>\n",
       "      <td>0.265870</td>\n",
       "      <td>0.197444</td>\n",
       "      <td>0.146315</td>\n",
       "      <td>0.000844</td>\n",
       "      <td>0.061717</td>\n",
       "      <td>0.004310</td>\n",
       "      <td>5.192645</td>\n",
       "      <td>0.148</td>\n",
       "      <td>0.488095</td>\n",
       "      <td>1.107143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>Taplejung</td>\n",
       "      <td>0.468741</td>\n",
       "      <td>0.639603</td>\n",
       "      <td>0.043544</td>\n",
       "      <td>0.314855</td>\n",
       "      <td>0.265353</td>\n",
       "      <td>0.196421</td>\n",
       "      <td>0.146136</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.029723</td>\n",
       "      <td>0.003968</td>\n",
       "      <td>5.778622</td>\n",
       "      <td>0.270</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>Terhathum</td>\n",
       "      <td>0.463171</td>\n",
       "      <td>0.674394</td>\n",
       "      <td>0.024923</td>\n",
       "      <td>0.252844</td>\n",
       "      <td>0.243664</td>\n",
       "      <td>0.219448</td>\n",
       "      <td>0.211871</td>\n",
       "      <td>0.000688</td>\n",
       "      <td>0.045298</td>\n",
       "      <td>0.001265</td>\n",
       "      <td>5.536696</td>\n",
       "      <td>0.146</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>1.541667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>Udayapur</td>\n",
       "      <td>0.467240</td>\n",
       "      <td>0.614868</td>\n",
       "      <td>0.040798</td>\n",
       "      <td>0.290338</td>\n",
       "      <td>0.266224</td>\n",
       "      <td>0.183295</td>\n",
       "      <td>0.166718</td>\n",
       "      <td>0.000645</td>\n",
       "      <td>0.049024</td>\n",
       "      <td>0.002957</td>\n",
       "      <td>5.780472</td>\n",
       "      <td>0.259</td>\n",
       "      <td>0.791667</td>\n",
       "      <td>1.305556</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     district      male  literacy rate  years_educ1  years_educ2  years_educ3  \\\n",
       "66    Syangja  0.428499       0.696740     0.024426     0.233124     0.248407   \n",
       "67     Tanahu  0.437649       0.680704     0.035329     0.288172     0.265870   \n",
       "68  Taplejung  0.468741       0.639603     0.043544     0.314855     0.265353   \n",
       "69  Terhathum  0.463171       0.674394     0.024923     0.252844     0.243664   \n",
       "70   Udayapur  0.467240       0.614868     0.040798     0.290338     0.266224   \n",
       "\n",
       "    years_educ4  years_educ5  years_educ6  years_educ7  years_educ8    hhsize  \\\n",
       "66     0.250872     0.179026     0.000864     0.060832     0.002448  5.298789   \n",
       "67     0.197444     0.146315     0.000844     0.061717     0.004310  5.192645   \n",
       "68     0.196421     0.146136     0.000000     0.029723     0.003968  5.778622   \n",
       "69     0.219448     0.211871     0.000688     0.045298     0.001265  5.536696   \n",
       "70     0.183295     0.166718     0.000645     0.049024     0.002957  5.780472   \n",
       "\n",
       "    poverty rate    nkid06   nkid715  \n",
       "66         0.118  0.535714  0.869048  \n",
       "67         0.148  0.488095  1.107143  \n",
       "68         0.270  1.166667  2.000000  \n",
       "69         0.146  0.750000  1.541667  \n",
       "70         0.259  0.791667  1.305556  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Write the code to display the last 5 rows of the dataframe\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us remove Achham and Udayapur for now. We will use the model we created to predict the proverty rate of Accham and Udaypur.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Write the code to get rid of the first and last rows of the dataframe and call the new dataframe df_2d\n",
    "df_2d = df[1:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(69, 15)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_2d.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In two dimensions, the equation of the line is \n",
    "$$y=mx+b $$\n",
    "where b is the intercept and m is the slope of the line. So basically, linear regression algorithm gives us the most optimal value for the intercept and the slope (in two dimensions). The y and x variables remain the same, since they are the data features and cannot be changed. The values that we can control are the intercept(b) and slope(m). There can be multiple straight lines depending upon the values of intercept and slope. Basically what the linear regression algorithm does is it fits multiple lines on the data points and returns the line that results in the least error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ledhxsxyHcaw"
   },
   "outputs": [],
   "source": [
    "model= LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 193
    },
    "colab_type": "code",
    "id": "Odn3m5ZxHgEN",
    "outputId": "e574a320-b789-498c-d0e7-2884192342af"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Fill in the x and y values for fit (Note that we want to predict the poverty rates given the literacy rates)\n",
    "model.fit(df_2d[['literacy rate']], df_2d[['poverty rate']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.94631567]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "F93wA_XlHq4D"
   },
   "outputs": [],
   "source": [
    "#Fill in the x values for predict (Note that we want to predict the poverty rates given the literacy rates)\n",
    "predictions = model.predict(df_2d[['literacy rate']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OPR8C7RXTc7M"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/rosebay/Documents/adarsh/tensorflow-practice/.venv/lib/python3.6/site-packages/ipykernel_launcher.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "df_2d['predictions'] = predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>district</th>\n",
       "      <th>male</th>\n",
       "      <th>literacy rate</th>\n",
       "      <th>years_educ1</th>\n",
       "      <th>years_educ2</th>\n",
       "      <th>years_educ3</th>\n",
       "      <th>years_educ4</th>\n",
       "      <th>years_educ5</th>\n",
       "      <th>years_educ6</th>\n",
       "      <th>years_educ7</th>\n",
       "      <th>years_educ8</th>\n",
       "      <th>hhsize</th>\n",
       "      <th>poverty rate</th>\n",
       "      <th>nkid06</th>\n",
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       "      <th>predictions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Arghakhanchi</td>\n",
       "      <td>0.433736</td>\n",
       "      <td>0.652446</td>\n",
       "      <td>0.039106</td>\n",
       "      <td>0.298637</td>\n",
       "      <td>0.253662</td>\n",
       "      <td>0.189621</td>\n",
       "      <td>0.157736</td>\n",
       "      <td>0.000844</td>\n",
       "      <td>0.057360</td>\n",
       "      <td>0.003033</td>\n",
       "      <td>5.179200</td>\n",
       "      <td>0.288</td>\n",
       "      <td>0.458333</td>\n",
       "      <td>1.020833</td>\n",
       "      <td>0.204699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Baglung</td>\n",
       "      <td>0.438207</td>\n",
       "      <td>0.647397</td>\n",
       "      <td>0.043599</td>\n",
       "      <td>0.301124</td>\n",
       "      <td>0.239773</td>\n",
       "      <td>0.186960</td>\n",
       "      <td>0.154035</td>\n",
       "      <td>0.000375</td>\n",
       "      <td>0.070341</td>\n",
       "      <td>0.003793</td>\n",
       "      <td>5.378669</td>\n",
       "      <td>0.229</td>\n",
       "      <td>0.716667</td>\n",
       "      <td>1.083333</td>\n",
       "      <td>0.209476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Baitadi</td>\n",
       "      <td>0.464469</td>\n",
       "      <td>0.548497</td>\n",
       "      <td>0.058514</td>\n",
       "      <td>0.346258</td>\n",
       "      <td>0.259600</td>\n",
       "      <td>0.186120</td>\n",
       "      <td>0.114269</td>\n",
       "      <td>0.000787</td>\n",
       "      <td>0.030814</td>\n",
       "      <td>0.003637</td>\n",
       "      <td>6.748073</td>\n",
       "      <td>0.457</td>\n",
       "      <td>1.133333</td>\n",
       "      <td>1.416667</td>\n",
       "      <td>0.303067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bajhang</td>\n",
       "      <td>0.477381</td>\n",
       "      <td>0.488333</td>\n",
       "      <td>0.073606</td>\n",
       "      <td>0.417432</td>\n",
       "      <td>0.219511</td>\n",
       "      <td>0.138940</td>\n",
       "      <td>0.112037</td>\n",
       "      <td>0.000483</td>\n",
       "      <td>0.034308</td>\n",
       "      <td>0.003682</td>\n",
       "      <td>6.945809</td>\n",
       "      <td>0.568</td>\n",
       "      <td>0.777778</td>\n",
       "      <td>1.583333</td>\n",
       "      <td>0.360001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Bajura</td>\n",
       "      <td>0.485493</td>\n",
       "      <td>0.474538</td>\n",
       "      <td>0.093973</td>\n",
       "      <td>0.417503</td>\n",
       "      <td>0.233429</td>\n",
       "      <td>0.136786</td>\n",
       "      <td>0.093656</td>\n",
       "      <td>0.001517</td>\n",
       "      <td>0.019391</td>\n",
       "      <td>0.003744</td>\n",
       "      <td>6.564752</td>\n",
       "      <td>0.641</td>\n",
       "      <td>0.875000</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>0.373055</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       district      male  literacy rate  years_educ1  years_educ2  \\\n",
       "1  Arghakhanchi  0.433736       0.652446     0.039106     0.298637   \n",
       "2       Baglung  0.438207       0.647397     0.043599     0.301124   \n",
       "3       Baitadi  0.464469       0.548497     0.058514     0.346258   \n",
       "4       Bajhang  0.477381       0.488333     0.073606     0.417432   \n",
       "5        Bajura  0.485493       0.474538     0.093973     0.417503   \n",
       "\n",
       "   years_educ3  years_educ4  years_educ5  years_educ6  years_educ7  \\\n",
       "1     0.253662     0.189621     0.157736     0.000844     0.057360   \n",
       "2     0.239773     0.186960     0.154035     0.000375     0.070341   \n",
       "3     0.259600     0.186120     0.114269     0.000787     0.030814   \n",
       "4     0.219511     0.138940     0.112037     0.000483     0.034308   \n",
       "5     0.233429     0.136786     0.093656     0.001517     0.019391   \n",
       "\n",
       "   years_educ8    hhsize  poverty rate    nkid06   nkid715  predictions  \n",
       "1     0.003033  5.179200         0.288  0.458333  1.020833     0.204699  \n",
       "2     0.003793  5.378669         0.229  0.716667  1.083333     0.209476  \n",
       "3     0.003637  6.748073         0.457  1.133333  1.416667     0.303067  \n",
       "4     0.003682  6.945809         0.568  0.777778  1.583333     0.360001  \n",
       "5     0.003744  6.564752         0.641  0.875000  1.166667     0.373055  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_2d.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "4AygGy4qRUqk"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f6bc77b57b8>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+4u5pnV6qHMG30tFfHnfoaOlCim4fD488EspgH3dcGG3Uv3+YzBahbEpei+SKpIePmll74GzgHOBT4CHge8B+7n5k6ppaNwWCb6Wr7k6tF97ly8OoozvugM8+g549w5oJQ4dC69Ypa4OIJCepZLGZTQNeBVoCJ7n7AHd/1N1HEQrQ5ZR8qmWfrv7yoiKjY+tmdG7Xko6tm219992pU6hltGQJPPww7LBDeDLo3Bl+/nNYtCilbclW+fR3JYUnkZnFx7v7U9W2NXP3DZG2LI5kngjybYZs1v77vPlmmKQ2ZUoYjnr88aEQ3jHHhBXX8kzW/ncQqSKpriEze9vdD6xrW7okEwjycQx6VveXf/YZ3HlneC1fHmoejRoF55wTFtfJE/n4dyX5p0FdQ2a2k5n1AVqY2QFmdmDsdSShmyjn5OMY9Fq7bTJt553DEpqffAIPPggtW8KIEVBcDL/6FXxUUxmr3JOPf1dSWGrLERwH3ExYa/iPVV6/AH4TfdNST2PQM6RZs/AUMHMmvPZaGFn0pz+FNZj/53/ghRcgB2a4x8sD6O9Kcl2tXUOxSWRnuPtD6WtS7ZQjyBOlpaHLaOJE+PLLUPNo9Gg466zw5JBlavvbAfR3JVkv2RxBSbwPZ0Kyw0ezuk89jbLmPKxfH+Yi3HYbvPsutGsHw4bByJHQtWv62xNHXXmArDmfInEkW2sorxamyeo+9TTJqgqezZt/u4TmK6/A0UeHxXN69IBTTw3bsqDbqK48QLr/rjRcVVIpkUBwOjASeAWYFXtpRlcOq1yDuPLCVrpyHcMeLMlYITkgDCs9/HB47LGQRL70UnjxRfj+98PymvfdF54eMiSb8gBZFcglL9QZCNy9Rw2vjKxOJqmR9aNcunaF//s/WLoU7r47zEU491zo0gWuvDLkF9Ism2ocZWUgl5yWyMzilmZ2lZndFXvf08xOjL5pEpVsurutVcuWcP75MGdOGFn0ve+FANG9O5x+OsyYkbZuo2xaK7muQK5uI6mvRLqG7gPKgcNi75cB/5vIwc2sv5ktMLNFZnZ5Db8fbmb/MbN3zOzfZrZ3wi2XOsW7IGTT3W1CzMISmtOmhZIVv/gFPPtsCAzf/W6Yo7Ah+onu2ZJfqi2Qq9tIGiLhUUNmNtvdD4hte9fd96/jc42AhcCxQCkwkzAUdV6Vfdq4+1exnwcAI9y9f23HVdG5xNQ1VDbnR7msXRvWWR47FubPDzWPhg8Pr513znTrIlXbf9sVa8s1y1lqlOyooXIzawF47GC7AYncfh0ELHL3xe5eDkwGBlbdoTIIxLSq/A5JXl39yNlyd9tgrVqFi/7cueHp4LvfhTFjQn7hrLNCvaM8VVs3VdbnfyQrJRIIrgWeBrqY2UPA88CvE/hcZ8K6BZVKY9u2YmYjzexD4EZgdE0HMrMLzKzEzErKysoS+GpJ1wUh4/3RZnDssfDEE7BwYVgo54kn4JBD4OCD4aGHwnoJeSZeIM+Z/I9klURGDT0LnAIMBR4B+rr7S6lqgLvf7u67AZcBV8XZ5y537+vufTt27Jiqr85r6bggZF1/9O67w623hlFF48bBqlVw9tnQrRtcdx188cWWdqc6eGU8IMbUlv/JljZK9kkkR/AP4GFguruvTfjAZocC17r7cbH3VwC4+/Vx9i8CVrp729qOqxxBYtJRTiPrq25WVIRuo7Fj4Z//hKZN8dMHs+Sscznnnc0pOy/ZVrqkosL5cu0G1m+soJFBi6aNaNOsCR+UfZ01bZT0S7bExPcJk8pOICR8JwNPuHuts3vMrDEhWXw0YaTRTOBMd59bZZ+e7v5B7OeTgN/WVc5CgSBxUSeE07VCWkosXAjjx1Nx330Uff01JZ334v4+J/H0HoexU4fWSQWvbAuINQWmief04bZ/LeTZecuzoo2Sfkkli939ZXcfAewKTAR+DCyv/VPg7puAi4FngPnAFHefa2bXxUYIAVxsZnPN7B3gl8BPEvo3koREnRDOqf7oPfaAsWP5/L0P+N3Rw+iwdhXjp9/Iq3eex4CnHmDT5583+NCpyMekstumpoECF06axaA+XZJqo+SvxonsFBs1dBLhyeBA4IFEPhdb2eypatuuqfLzzxJuqWSdyv7o6t0NWTsfAWiyQzueO3YwDxx4IkcunsXQWf/g1688iO/3KJx5ZqiA+p3v1OuYlQGx+hNBogEx1V1L8QJT9f8uWRu0Je0SmVk8hXBH/wNgPLBbbL1iKXDZNNs2UZXBa5f22/HC7gfxm+E38+FLb8LQofDoo3DAAXDEEfDXv4bSFvU4ZkMn6KW6ZES8J7VOrZvlziRCSatEcgTHAf9y96x4hlSOQJIVN3eyciXcey+MHw9LloQ5CSNHhjIXO9RecDeZfEwqci1Vv79J4yK+Xr+JIfe+tdUTRs+O27Fy3cbcnUQoSUk2WdwEuAg4IrbpZeBOd9+Y0lYmSIFAIrd5c5iLcNttoQJqixZhGOqoUbDffin/umSTzfG6lnZs04x15broS5DszOI7gD7AhNjrwNg2kaxVU/I14YRso0YwcGAodDdnTggCkyZB795hvYS//z0EixSJqmtpcwW5O3Nc0iqRJ4Jt6golUmsoKnoiyG3pqHEU7w65WeOibbpL4uU0tmnn+jUU3ftnuP32UB67e/cwi/m882D77VPS5kx2LUn+S/aJYHOsvlDlwXYFsiJfILklXTOR490hf7zimxoTstWfFDZtqtimnUtozvIRP2PZrPdYPekRvGtX+NWvoHNnGDEiFL5LQjJDfes7jFczjKW6RALBpcCLZvaSmb0MvABcEm2zJB+lcnRMbRezeMMnWzZttM22ioptL/oLlq/h1ucWbDlGx+2a8cVX6zllwmv0++OrnLCsE+9P/gcVJbPCugj33gt77w0//GHILVRU1PvfJxn16VrKurIgkhUSmVD2PNCTUBBuFNDL3bd9DhWpQ6oK4dV1MYt3h/xN+eZttm126px8NfzI3bh06pxtA9ge+4QgsHQp/P73oRLqSSdBr14h0fzVV9RXfe7WK/f9bPU6dmzTjMdHHFbnMF6tbiY1SWQeQXPCmsXXAr8FLoptE6mXVM1ErutiFu8OuVv7lttsc/c6J19t36JJ7QGsY0f4zW/CkNPJk8PaCD//eeg2Gj06lLdIQH3u1qvvO2D8DFZ8Xc7ObVvU2rWkMtVSk0S6hh4E9gHGESaU7QNMirJRkp9StTJaXRezeBPdurdvtc22RCZffVO+ObEA1qTJt0tozpwJp5wCEyeGJ4Tjj4enn6612yhegPv8q/XbPCE09M4+p8qCSNokEgj2dffz3P3F2GsYIRiI1EuqZiIncjGrKfla07Z4wWmXti22tHP/Lm3rH8D69oUHHoBPPoHf/Q5mz4Yf/Qj22itMWFuzZpuPxAtwn65at80TQkPv7HNumVJJi0SGj/4FGO/ub8TeHwyMdPchaWjfNjR8VFJdmyeRoZtJD3stL4epU0Pu4K23oE0bOPfcMHN5992B+BPLrj5xby6cNGvL+2kj+gE0eBJazi9TKg2S7Mzi+UAv4JPYpq7AAmAT4O7eO4VtrZMCgUCOX8zefDOskTBlSpiYdsIJMHo0FT84mgXLt14z4IZBvbn5mQXMXrpqy8dnXHYUO7dtkVVrIEj2SzYQdKvt9+7+cRJtqzcFgvhy+uJYiD79FO68M7zKymCvvagYeTErBg2mvFlzzIxrp78Xdw0B/feW+kgqEGQbBYKaZdsqWVIPGzaEyqe33QZvvx1mKp93HhUXjWBByw4N/m+qQCFVKRAUgGxbJUsawB1eey0EhMcfB3f8pAGsHjactYd+j6ZNGid8MdeNgVSXbIkJyQEaH54HzKBfv5A7WLIELr8c+/erbH9ifzofeSgdH51E0fp1dR4GNHFM6keBIE9ofHieKS4Os5WXLoU//xmKimDYMOjSBS6/PGyvhW4MpD4UCPKExofnqRYtwjDT2bPh5ZfhqKPgppugRw847TR49dXQpVRNpm4MVNAuNylHkEeUHCwQH38Md9wBd90VVlX7zndCKYszzoDmofpLJnIEyktkNyWLRXJUrcH9m2/goYfCnIT33oMOHeCCC0JZ7M6d035joAEL2U3JYpEcVGcRupYtQ95gzhx4/vmQaL7++rBozuDBFL3xOh23a5q2VcqUl8hdCgSSV1LdR53K49X3WAmP/DGDH/wA/vY3WLQIfvazUOCuXz846KCwzOaGDQ1ud6I0YCF3RRoIzKy/mS0ws0VmdnkNv/+lmc0zszlm9nxds5hFapPqRVdSebyGHKtBd9i77go33wylpSGP8PXXMGQIdO0Kv/0tfPZZvdueKA1YyF2RBQIzawTcDvwI2Bs4w8z2rrbbbKBvrF7RVODGqNoj+S/VY+dTebyGHCupO+zttoPhw2HePHj22fBkMGYMdOsGZ58dCt+lWKqqy0r6RflEcBCwyN0Xu3s5MBkYWHWHWFnrb2Jv3wCKI2yP5LlU91Gn8ngNOVZK7rDN4Nhj4R//CAvkjBgB06fDwQfDoYfCI4+Eyqgpkszay5I5UQaCzkDVWS+lsW3xnAf8s6ZfmNkFZlZiZiVlZWUpbKLkk1T3UafyeA05VsrvsHffHf70J1i2LIw0WrECzjwzJJfHjIHly+s8hOSnrEgWm9nZQF/gppp+7+53uXtfd+/bsWPH9DZOckYyd9A1JXJT2efd0GNFcofdujWMGgXvvw9PPQX77w/XXBNmLQ8dGgrfSUGJbB6BmR0KXOvux8XeXwHg7tdX2+8YwjKY33f3Om9JNI9AatOQsfO1TYQCUjYWP6sn/C1YEFZOu//+kGDu1y9MUjv55LAEp+S8jEwoM7PGwELgaGAZMBM4093nVtnnAEKSuL+7f5DIcRUIJNU0EaqK1avhvvtg3DhYvBg6dw55hQsuCBPWJGdlZEKZu28CLgaeAeYDU9x9rpldZ2YDYrvdBGwHPGZm75jZ9KjaIxKPJkJV0bYt/PznIbE8fTrsuSdceWUognfeefDOO5luoUSgcZQHd/engKeqbbumys/HRPn9mZTV3QCylcpEbvUngoKeCNWoEZx0UnjNnRu6jR58EO69F444IkxaGzAAGkd6CZE0yYpkcb5J9cQmiVYuTYTKSHXPffYJk9NKS0Pl008+gUGDYLfdwvv//jf6NkikVHQuAupzzj258ASXSHXPtPx7bN4cuo3GjoWXXgqlss85JySX99kntd8lKaOic2mmPufckwsToeqanVzTk+j8z7/ii9XrUvv00KhRGE304ovw7rtw1lmh22jffeGYY0KQ2Ky/9VyiQBABFd+SKNR1g1FToLhw0iy+Wr+JK6fNiaZ7sndvuPvu0G10/fVhGOrAgdCzJ9xyC6xaldrvk0goEESgpj7nief0oaKiQqs2SYPVdYMRL1CsXreRnxzWg1ufWxDdmsXt24clND/6KKy5XFwMl1wS/jlyJMyfH833SkooEESgemmAh88/mNv+tZCDr39BiWNpsLqS2vECxYq15Vz21zkM6tOlwd2TCSepGzcOS2i+8kqYofzjH4c1l/feG447Dp58EioqGtQGiY6SxRFT4lhSqbZkcE3J5BsG9ebmZxYwe+kqpg4/lG7tW9X77y7pJSjLysKymhMmwKefhppHo0aFchZt2jTgLEhDKFmcQUocSyrVltSufBKdcuGhTB1+KFefuPeWIFDcrgWdWjdr0JDYpMtxd+wYJqUtWQKTJ0OnTmEeQufOYaTRwoX1bpOklgJBxJQ4lnQqKjJ2atOcVs0aM+aJeVuCwMRz+rBL2xYNGg0V72amMueV8JyGJk3g9NNhxgyYOTOMPLrzTujVC044AZ55Rt1GGaKuoYgl/Vgt0gCpnE9QtmYDV04LOYbtWzRh1bqNvL1kBQMOKObCSbOS+7v+/PPQbXTHHeHnXr1Ct9FPfhIW15GUyUjRuajkWiCA3JisJBLPpk0VvP/FGob/5duL/p1n92Hs8wt5dt63BYOTyn2Vl8Njj8Ftt4WnhTZtQm2jkSPDDGZJmnIEGZYLk5UkP0RRgmLluo1bggCEbqHhf5nFoD5dttovqdxX06ZhYtpbb8Hrr4euonHjwnyEAQPgX/+CHLtpzSUKBCJ5IqoaV/FyBNUTz/EOJB0AAAwLSURBVCnLfR1yCDz8MHz8MVx1FbzxRlhuc999YeJEWLs2+e+QrSgQiOSJpEf3xBFvwEOn1s2iLdS3yy5w3XWhyN0DD0Dz5jB8eJikdumlYRSSpIQCgUieiGqocryJbLu0bZG69ZRr07w5DBkCJSXw73/DD38It94acgennBIK36nbKCkqJi6SJ1K9rkLVQQ47tmnG4yMOY+Omiq0GPKR1UqRZWEKzXz9YujSMNLrrLpg2DfbbL8xJOOusUA1V6kVPBCJ5IpXrKlTPNwwYP4MVX5ezc9sW2THgoUsX+MMfQkC4554QJIYNC91GV1wRtjdQRtZ8yDANHxXJQg0dcpyqoco5VxrFPdQ3GjsW/va3EBhOPjk8JXzve+F9AvJ53o+Gj4rkkGRG/6RqqHKq8w2R32Wbwfe/D3/9KyxeDL/8ZRhyesQR0KcP3H8/rF9f52GiSrhnOwUCkSyT7otRTRfpVJZGSfvSrd26wY03hjUSJk4Mk9V++tPQnXTVVbBsWdyPFmptMAUCkSyTzotRvIt0uxZNUpZvyNhddqtWcMEF8J//wPPPw2GHhbxC9+5wxhlh4lq1rvFCrQ2mQCCSZdJ5MYp3kV65buNWa2okMzw043fZZvCDH8Df/w6LFoW8wT//GQLDQQfBpEmwYQOQ2oR7LlEgEMky6bwY1XaRbki+IepupqTtuiv88Y+h22jCBPj66zBHoVs3uPZaipZ/kbIAmEsiDQRm1t/MFpjZIjO7vIbfH2Fmb5vZJjM7Ncq2iOSK6ivcRXkxSkcuIJXdTCmz3XZw0UUwd24of923L/zud9C1K0VDzqHj+3MKqjZYZMNHzawRsBA4FigFZgJnuPu8Kvt0B9oAvwKmu/vUuo6r4aMiqZPK4ZK1DTlt36pp9lfg/eADGD8e7rsP1qwJNY9Gj4ZBg0JRvBxX2/DRKGcWHwQscvfFsUZMBgYCWwKBuy+J/U6rUYhkQNWnj2Qv0ol0M2W1nj1DGewxY8Jw03Hj4MwzYeedYcSIkHju1CnTrYxElF1DnYGq0/tKY9tEJIukau5BVuUCktGmTXgSWLAAnnwSeveGq68Ow0+HDoXZszPdwpTLiWSxmV1gZiVmVlJWVpbp5ohIDZJNcmddaYeiIjj+eHj6aZg/P5SwmDoVDjwQDj88LKSzaVNm25giUeYIDgWudffjYu+vAHD362vY937gCeUIRHJbMqUxcqK0w6pVIYcwfnyYwVxcHFZRGzYM2rfPdOtqlakSEzOBnmbWw8yaAoOB6RF+n4hkWEO7mXKmtMP228MvfgELF8L06WGN5SuuCAFh2DCYMyfTLWyQyAKBu28CLgaeAeYDU9x9rpldZ2YDAMzsu2ZWCpwGTDSzuVG1R0SyV8YnndVXo0Zw0kmhntF778FPfgIPPQT77w9HHRVKY2/O0rbXINIcgbs/5e57uPtu7v772LZr3H167OeZ7l7s7q3cvb277xNle0QkO+VqormiwinrujvLrr+FL+d/SMWNN8JHH4UFc3bbDW6+GVaubPix05QzyYlksYjkt/okmrMlqVx9At3/TJ7PgrMvpGLhB/D449CjR1hSs7g4LLE5N/EOj3QX6tN6BCKSFRJJNGdTUjmhNRvmzAlrJDz0UCiDfcwxYWjq8ceH7qVkjl1PWo9ARLJeIonmbEoqJ5TX6N07rKC2dClcfz28/z4MGAB77BHWXV69uuHHTiEFAhHJGdmUVK5XXqNDB7j88pA/mDIFdtklLJ7TuTNcfHEIEA09dgooEIhIzsimpHKDJtA1bgynnQavvgqzZoWf774b9toL+vcP5bErKtJeDls5AhHJGdmUI6hsT9LF9JYvh7vuCmWxP/ss1DwaNYqKc4awolHzlBXqqy1HoEAgIjklJRffbFReHkYbjR0bVk9r3TossTlqFOy+e9KHV7JYRPJGqorkZZ2mTWHwYHjtNXjrLRg4EO64IwSHiOmJQEQkW33+ObRoAW3bJn2oTK1HICIiydhpp7R8jbqGREQKnJ4IRESqyduEdBwKBCIiVWTbENV0UNeQiEgV2VTGIl0UCEREqsimMhbpokAgIlJFNpWxSBcFAhGRKtJd5ycbKFksIlJFUZHRa8fWTBvRT6OGREQKVWUZi0KhriERkQKnQCAiUuAUCERECpwCgYhIgVMgEBEpcAoEIiIFToFARKTA5dwKZWZWBnycga/uAHyZge/NBTo38enc1EznJb6ozk03d+9Y0y9yLhBkipmVxFvmrdDp3MSnc1MznZf4MnFu1DUkIlLgFAhERAqcAkHi7sp0A7KYzk18Ojc103mJL+3nRjkCEZECpycCEZECp0AgIlLgFAiqMbP+ZrbAzBaZ2eW17DfIzNzMCmIIXF3nxcyGmlmZmb0Te52fiXZmQiJ/M2b2YzObZ2ZzzezhdLcxUxL4u7m1yt/MQjNblYl2ZkIC56armb1oZrPNbI6ZHR9ZY9xdr9gLaAR8COwKNAXeBfauYb/WwCvAG0DfTLc7G84LMBQYn+m2Zum56QnMBtrF3nfKdLuz5dxU238UcG+m250t54aQNL4o9vPewJKo2qMngq0dBCxy98XuXg5MBgbWsN8Y4AZgfTobl0GJnpdClMi5GQbc7u4rAdx9eZrbmCn1/bs5A3gkLS3LvETOjQNtYj+3BT6NqjEKBFvrDCyt8r40tm0LMzsQ6OLuT6azYRlW53mJGRR7hJ1qZl3S07SMS+Tc7AHsYWYzzOwNM+ufttZlVqJ/N5hZN6AH8EIa2pUNEjk31wJnm1kp8BThiSkSCgT1YGZFwC3AJZluSxb6B9Dd3XsDzwEPZLg92aQxoXvoSMJd791mtn1GW5R9BgNT3X1zphuSRc4A7nf3YuB4YFLsGpRyCgRbWwZUvZMtjm2r1BrYF3jJzJYAhwDTCyBhXNd5wd1XuPuG2Nt7gD5palum1XluCHd70919o7t/BCwkBIZ8l8i5qTSYwukWgsTOzXnAFAB3fx1oTihIl3IKBFubCfQ0sx5m1pTwxzm98pfuvtrdO7h7d3fvTkgWD3D3ksw0N21qPS8AZrZzlbcDgPlpbF8m1XlugL8RngYwsw6ErqLF6WxkhiRybjCzPYF2wOtpbl8mJXJuPgGOBjCzvQiBoCyKxigQVOHum4CLgWcIF7Ip7j7XzK4zswGZbV3mJHheRseGRr4LjCaMIsp7CZ6bZ4AVZjYPeBG41N1XZKbF6VOP/58GA5M9NjymECR4bi4BhsX+n3oEGBrVOVKJCRGRAqcnAhGRAqdAICJS4BQIREQKnAKBiEiBUyAQESlwCgSSl8zs69g/dzGzqbGfvxNpBccI5GKbJfcoEEhec/dP3f3U2NvvEKbqJ8zMGqe+VfX6jnq3WaS+FAgkr5lZdzN7LzZ78zrg9Fjt+9PNrJWZ3Wtmb8Vqvg+MfWaomU03sxeA581sOzN73szeNrP/VO4X23dIrNDeu2Y2ycxam9lHZtYk9vs2Vd9X+dz9Znanmb0J3GhmB5nZ67F2vGZmverTZpFkRH63I5IN3L3czK4hrB9xMYCZ/QF4wd3PjRWBe8vM/hX7yIFAb3f/b+yO/WR3/ypWIuINM5tOqBF/FXCYu39pZju4+xozewk4gVBaYjDwuLtvrKFZxbHPbjazNsDh7r7JzI4B/uDugxJts7uvjeK8SWFQIJBC9kNggJn9Kva+OdA19vNz7v7f2M8G/MHMjgAqCOWCdwR+ADzm7l8CVNn/HuDXhEDwU8J6BDV5rEq1zbbAA2bWk1CHvkmcz8Rrc6HUdpIIKBBIITNgkLsv2Gqj2cFA1Tvss4COQB933xirPNs83kHdfUasS+pIoJG7vxdn16rfMQZ40d1PNrPuwEv1abNIMpQjkEKyhlBKvNIzwCgzMwAzOyDO59oCy2NB4CigW2z7C8BpZtY+9vkdqnzmQeBh4L4E29aWb8sQD01Bm0USpkAgheRFYO/KxCvhLrwJMMfM5sbe1+QhoK+Z/QcYArwP4O5zgd8DL8cqRN5S7TPtSLzG/o3A9WY2m62f1BvaZpGEqfqoSATM7FRgoLufk+m2iNRFOQKRFDOzccCP0Ph/yRF6IhARKXDKEYiIFDgFAhGRAqdAICJS4BQIREQKnAKBiEiB+3/Tqe+LUFxOfAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the regression line and the data in one graph\n",
    "sns.lineplot(x='literacy rate', y = 'predictions', data=df_2d, color='red')\n",
    "sns.scatterplot(x='literacy rate', y = 'poverty rate', data=df_2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As discussed earlier, linear regression model basically finds the best value for the intercept and slope, which results in a line that best fits the data. To see the value of the intercept and slope calculated by the linear regression algorithm for our dataset, execute the following code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8221182820384326\n",
      "-0.946315665100361\n"
     ]
    }
   ],
   "source": [
    "#To retrieve the intercept:\n",
    "b = model.intercept_[0]\n",
    "print(b)\n",
    "#For retrieving the slope:\n",
    "m = model.coef_[0][0]\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the equation of the line that best fits the data is \n",
    "$$ y = -0.94631567 x + 0.82211828 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "S9Mzg2kv1TYM"
   },
   "source": [
    "For Achham, the predicted poverty rate is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "yL4VP-_d2JPh"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.372"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(m*0.476151+b , 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "CGzyptQBhnB2"
   },
   "source": [
    "But, we know that the actual poverty rate was 0.472"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zFnuMP3xgE9x"
   },
   "source": [
    "For Udaypur, the predicted poverty rate is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70    0.614868\n",
       "Name: literacy rate, dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df['district']=='Udayapur']['literacy rate']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0wvwnFY2AsSf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70    0.24\n",
       "Name: literacy rate, dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Write the code for finding the poverty rate for Udaypur\n",
    "round(m*df[df['district']=='Udayapur']['literacy rate'] + b, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But, we know that the actual poverty rate was 0.259"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "v6W5oAtVwbxe"
   },
   "source": [
    "The accuracy or score of Linear Regression is tied to how well the data is correlated with each other. The coefficient of dertermination (R^2) for Linear Regression is the square of correlation.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scikit-Learn Linear Regression <a class=\"anchor\" id=\"sklearn-linreg\"></a>\n",
    "\n",
    "Scikit-Learn is one of the most popular Python machine learning library available. It contains a multitude of powerful tools the makes it an ideal choice for use in production environments. It provides a very robust, standardized API and comprehensive documentation, so once a user becomes familiar with the structure of building models with the package, it is fairly easy to apply it to other models.\n",
    "\n",
    "For this reason, we will utilize Scikit-Learn throughout the remainder of this workshop. \n",
    "\n",
    "Scikit-Learn's [LinearRegression](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html) model incorporates several different methods behind the scenes that help it to perform more reliably with different types of datasets.\n",
    "\n",
    "We will use four predictor variables - 'hh size', 'literacy rate', 'nkid06' and 'nkid715' and  to predict the 'poverty rate' where -\n",
    "\n",
    "* `literacy rate` -  ratio of literate population and total population in the district\n",
    "\n",
    "* `nkid06` - average share of kids of ages between 1 and 6 in the households of the district\n",
    "\n",
    "* `nkid715` - average share of kids of ages between 7 and 15 in the households of the district\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OYnbtSgho1S8"
   },
   "outputs": [],
   "source": [
    "df_predict = df[['literacy rate','district','nkid06','nkid715','hhsize']]\n",
    "df_y = df[['poverty rate']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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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>literacy rate</th>\n",
       "      <th>district</th>\n",
       "      <th>nkid06</th>\n",
       "      <th>nkid715</th>\n",
       "      <th>hhsize</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.476151</td>\n",
       "      <td>Achham</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>6.322215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.652446</td>\n",
       "      <td>Arghakhanchi</td>\n",
       "      <td>0.458333</td>\n",
       "      <td>1.020833</td>\n",
       "      <td>5.179200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.647397</td>\n",
       "      <td>Baglung</td>\n",
       "      <td>0.716667</td>\n",
       "      <td>1.083333</td>\n",
       "      <td>5.378669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.548497</td>\n",
       "      <td>Baitadi</td>\n",
       "      <td>1.133333</td>\n",
       "      <td>1.416667</td>\n",
       "      <td>6.748073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.488333</td>\n",
       "      <td>Bajhang</td>\n",
       "      <td>0.777778</td>\n",
       "      <td>1.583333</td>\n",
       "      <td>6.945809</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   literacy rate      district    nkid06   nkid715    hhsize\n",
       "0       0.476151        Achham  0.750000  1.166667  6.322215\n",
       "1       0.652446  Arghakhanchi  0.458333  1.020833  5.179200\n",
       "2       0.647397       Baglung  0.716667  1.083333  5.378669\n",
       "3       0.548497       Baitadi  1.133333  1.416667  6.748073\n",
       "4       0.488333       Bajhang  0.777778  1.583333  6.945809"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_predict.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "cAr_DnSQqv3f",
    "outputId": "d7618324-1a8f-4506-dfa1-c47bd4707a4c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(71, 5)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_predict.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 124
    },
    "colab_type": "code",
    "id": "V2Yy9BRTpFte",
    "outputId": "d1611102-e901-44b6-fa8e-14c9beea0941"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/rosebay/Documents/adarsh/tensorflow-practice/.venv/lib/python3.6/site-packages/ipykernel_launcher.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "df_predict.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 190
    },
    "colab_type": "code",
    "id": "VWEdBp97q4UK",
    "outputId": "060f8ac0-97e9-4e49-9fe3-23382b42d5c5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "literacy rate    False\n",
       "district         False\n",
       "nkid06           False\n",
       "nkid715          False\n",
       "hhsize           False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_predict.isnull().any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/rosebay/Documents/adarsh/tensorflow-practice/.venv/lib/python3.6/site-packages/pandas/core/frame.py:4117: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  errors=errors,\n"
     ]
    }
   ],
   "source": [
    "#Write the code to drop the column 'district' from the dataframe df_predict\n",
    "df_predict.drop(columns=['district'], inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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>literacy rate</th>\n",
       "      <th>nkid06</th>\n",
       "      <th>nkid715</th>\n",
       "      <th>hhsize</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.476151</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>6.322215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.652446</td>\n",
       "      <td>0.458333</td>\n",
       "      <td>1.020833</td>\n",
       "      <td>5.179200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.647397</td>\n",
       "      <td>0.716667</td>\n",
       "      <td>1.083333</td>\n",
       "      <td>5.378669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.548497</td>\n",
       "      <td>1.133333</td>\n",
       "      <td>1.416667</td>\n",
       "      <td>6.748073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.488333</td>\n",
       "      <td>0.777778</td>\n",
       "      <td>1.583333</td>\n",
       "      <td>6.945809</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   literacy rate    nkid06   nkid715    hhsize\n",
       "0       0.476151  0.750000  1.166667  6.322215\n",
       "1       0.652446  0.458333  1.020833  5.179200\n",
       "2       0.647397  0.716667  1.083333  5.378669\n",
       "3       0.548497  1.133333  1.416667  6.748073\n",
       "4       0.488333  0.777778  1.583333  6.945809"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_predict.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us split the data in training and testing set. The test_size parameter allows you to control the ratio of testing set you want to randomly capture from your data set. With the random_state parameter you can guarantee that the output of Run 1 will be equal to the output of Run 2, i.e. your split will be always the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "FycVICxhGv_Z"
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df_predict, df_y, test_size=0.20, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "velHrfoUAKhL",
    "outputId": "4416a7c9-a4b2-4d7c-8537-524eae80e938"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((56, 4), (15, 4), (56, 1), (15, 4))"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let us look at the shape our training and testing splits\n",
    "X_train.shape, X_test.shape, y_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ledhxsxyHcaw"
   },
   "outputs": [],
   "source": [
    "model= LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 193
    },
    "colab_type": "code",
    "id": "Odn3m5ZxHgEN",
    "outputId": "e574a320-b789-498c-d0e7-2884192342af"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "F93wA_XlHq4D"
   },
   "outputs": [],
   "source": [
    "predictions = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "-69fuFcmH2uv"
   },
   "outputs": [],
   "source": [
    "df_compare = X_test.reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zUvJlRdOH7x0"
   },
   "outputs": [],
   "source": [
    "df_compare['Actual'] = y_test.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "b_9KQbaEH__W"
   },
   "outputs": [],
   "source": [
    "df_compare['Predicted'] = predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "lX4yB-80IBqS",
    "outputId": "45299881-7ae3-4169-8e96-3e30bada688b"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "\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>literacy rate</th>\n",
       "      <th>nkid06</th>\n",
       "      <th>nkid715</th>\n",
       "      <th>hhsize</th>\n",
       "      <th>Actual</th>\n",
       "      <th>Predicted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.654978</td>\n",
       "      <td>0.700000</td>\n",
       "      <td>1.083333</td>\n",
       "      <td>5.236356</td>\n",
       "      <td>0.256</td>\n",
       "      <td>0.213130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.476151</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>6.322215</td>\n",
       "      <td>0.472</td>\n",
       "      <td>0.297400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.584571</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>1.812500</td>\n",
       "      <td>5.813340</td>\n",
       "      <td>0.322</td>\n",
       "      <td>0.363464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.488333</td>\n",
       "      <td>0.777778</td>\n",
       "      <td>1.583333</td>\n",
       "      <td>6.945809</td>\n",
       "      <td>0.568</td>\n",
       "      <td>0.328710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.631131</td>\n",
       "      <td>0.744444</td>\n",
       "      <td>1.283333</td>\n",
       "      <td>7.264983</td>\n",
       "      <td>0.173</td>\n",
       "      <td>0.224538</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   literacy rate    nkid06   nkid715    hhsize  Actual  Predicted\n",
       "0       0.654978  0.700000  1.083333  5.236356   0.256   0.213130\n",
       "1       0.476151  0.750000  1.166667  6.322215   0.472   0.297400\n",
       "2       0.584571  1.166667  1.812500  5.813340   0.322   0.363464\n",
       "3       0.488333  0.777778  1.583333  6.945809   0.568   0.328710\n",
       "4       0.631131  0.744444  1.283333  7.264983   0.173   0.224538"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_compare.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 15 entries, 0 to 14\n",
      "Data columns (total 6 columns):\n",
      "literacy rate    15 non-null float64\n",
      "nkid06           15 non-null float64\n",
      "nkid715          15 non-null float64\n",
      "hhsize           15 non-null float64\n",
      "Actual           15 non-null float64\n",
      "Predicted        15 non-null float64\n",
      "dtypes: float64(6)\n",
      "memory usage: 848.0 bytes\n"
     ]
    }
   ],
   "source": [
    "df_compare.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "colab_type": "code",
    "id": "4FvorrKoQ45s",
    "outputId": "44b48230-321f-4a60-edd6-892010690c90"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f6bc7690358>"
      ]
     },
     "execution_count": 44,
     "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": [
    "#Write a code to plot a scatterplot of the 'Actual' and the 'Predicted' values from df_compare\n",
    "sns.scatterplot('Actual', 'Predicted',data=df_compare)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The evaluation of Linear Regression can also be done by finding the residuals, which is the difference of the actual and the predicted values. The values of the residuals should be close to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_compare['residuals'] = df_compare['Actual'] - df_compare['Predicted']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "colab_type": "code",
    "id": "DVatMDiNaVTL",
    "outputId": "fcdac581-1ad7-466e-d4df-4baaf4c7582f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f6bc564b828>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GhdRmnsmjbmdQSKot51XUg0EhqZacg1IfDmZLqiXnoNSHPYouY1dc/cI5KPVhUHQRu+LqJ3NzUJrDwjko1fDQUxexK65+4hyU+rBH0UXsiqufOAelPgyKLmJXXP3GOSj14KGnLmJXXFIV7FF0EbvikqpgUHQZu+KSOs1DT5KkUpUERUS8MiK+EBHPFD9HFtnvoYj4fxHx+U7XKElqqKpHcQfwSGZuBh4pni/kXuBXOlaVJOkMVQXFdcCni+VPA+9YaKfMfAQ42qmiJElnqiooNmbmt4vlvwE2ruTNIuLWiJiIiInDhw+vvDpJ0iltO+spIv4c+AcLbLqz+UlmZkTkSj4rM+8H7gcYHx9f0XtJkk7XtqDIzCsX2xYRL0bEj2XmtyPix4DvtKsOSdLKVHXoaQ9wU7F8E/DHFdUhddTsbHL46AkOHXmJw0dPMDtrB1j1V9WEu7uBP4qIm4HngX8JEBHjwPsy818Xz78E/CRwbkRMAjdn5sMV1SytiJeJV7eKzN76i2Z8fDwnJiaqLkM6w+GjJ7j+Y4+ecVHH3Tu2OdtelYuIvZk5vtA2Z2ZLHeJl4tWtDAqpQ+YuE9/My8SrGxgUUod4mXh1K68eK3WIl4lXtzIopA7yMvHqRh56kiSVMigkSaUMCklSKYNCklTKoJAklTIoJEmlDApJUimDQpJUyqCQJJUyKCRJpQwKSVKpnrtxUUQcpnHXvLo5H/hu1UWsol5qTy+1BXqrPb3UFqh3ey7OzNGFNvRcUNRVREwsdveobtRL7emltkBvtaeX2gLd2x4PPUmSShkUkqRSBkXn3F91Aausl9rTS22B3mpPL7UFurQ9jlFIkkrZo5AklTIoJEmlDIpVEBFXR8T+iDgQEXcssP2NEbEvImYi4p3ztt0UEc8Uj5s6V/XCVtiWkxHxRPHY07mqF9dCe26PiG9ExJMR8UhEXNy0rdu+m7K2dON3876IeKqo+csRsbVp268Xr9sfEW/rbOULW257ImJTRBxv+n4+3vnqzyIzfazgAQwCzwKvAoaArwFb5+2zCbgM2AW8s2n9K4GDxc+RYnmkG9tSbPu7qr+PZbTnzcA5xfKvAn/Yxd/Ngm3p4u/mvKbla4GHiuWtxf5rgUuK9xns4vZsAr5e9XdS9rBHsXJXAAcy82BmTgMPANc175CZz2Xmk8DsvNe+DfhCZv5tZh4BvgBc3YmiF7GSttRRK+35Yma+VDx9DBgrlrvxu1msLXXUSnu+3/R0PTB35s11wAOZeSIzvwUcKN6vSitpT+0ZFCt3AfBC0/PJYl27X9sOK63nZRExERGPRcQ7Vre0ZVlqe24G/nSZr223lbQFuvS7iYj3R8SzwD3Av1nKaztsJe0BuCQivhoRfxkR/6S9pS7dmqoLUE+5ODMPRcSrgL+IiKcy89mqi2pFRNwIjAM/V3UtK7VIW7ryu8nM+4D7IuKXgd8AKh8rWolF2vNt4KLMnIqInwb+V0S8Zl4PpFL2KFbuEHBh0/OxYl27X9sOK6onMw8VPw8C/xt43WoWtwwttScirgTuBK7NzBNLeW0HraQtXfvdNHkAmOsJ1e27gRW0pziENlUs76Ux1vETbapzeaoeJOn2B41e2UEag2pzg1ivWWTf3+XMwexv0RgsHSmWX9mlbRkB1hbL5wPPMG8wr47tofEP5rPA5nnru+67KWlLt343m5uW3w5MFMuv4fTB7INUP5i9kvaMztVPYzD8UJX/ry3YvqoL6IUH8AvAXxe/pHcW6+6i8VcdwM/QOGZ5DJgCnm567XtpDMYdAN7TrW0B3gA8VfyCPAXcXHVbWmzPnwMvAk8Ujz1d/N0s2JYu/m4+CjxdtOWLzf/w0ug1PQvsB66pui0raQ/wz5vW7wPeXnVb5j+8hIckqZRjFJKkUgaFJKmUQSFJKmVQSJJKGRSSpFIGhTRP05VWvx4Rn42Ic1bwXm+KiM8Xy9cudFXRpn1fERE7lvEZ/yEifm25NUpnY1BIZzqemZdn5muBaeB9zRujYcm/O5m5JzPvLtnlFcCSg0JqN4NCKvcl4NXFPQP2R8Qu4OvAhRFxVUR8pbg/x2cj4lw4dV+Cb0bEPuCfzb1RRLw7Iv57sbwxInZHxNeKxxuAu4FLi97MvcV+H4yIx4t7THyk6b3ujIi/jogvA1s69l9DfcmLAkqLiIg1wDXAQ8WqzcBNmflYRJxP46JuV2bmsYj4EHB7RNwD7ATeQmNG9x8u8vb/FfjLzLw+IgaBc4E7gNdm5uXF519VfOYVQAB7IuKNNGbF3wBcTuN3eB+wd3VbL/2IQSGdaV1EPFEsfwn4JPDjwPOZ+Vix/mdp3EDn0YiAxvV9vgL8JPCtzHwGICJ+D7h1gc94C7AdIDNPAt+LiJF5+1xVPL5aPD+XRnAMA7uzuPdEXe5Yp95lUEhnOj73V/2cIgyONa+icWOjd83b77TXrVAA/ykzPzHvM/7tKn6GdFaOUUjL8xiwLSJeDRAR6yPiJ4BvApsi4tJiv3ct8vpHaNyulIgYjIiXA0dp9BbmPAy8t2ns44KI+PvAXwHviIh1ETFM40qkUtsYFNIyZOZh4N3AH0TEkxSHnTLzBzQONf1JMZj9nUXe4gPAmyPiKRrjC1uzcU+CR4vTcu/NzD8Dfh/4SrHf54DhzNxHY+zjazTuYvd42xoqgVePlSSVs0chSSplUEiSShkUkqRSBoUkqZRBIUkqZVBIkkoZFJKkUv8fW1M6QyQcE20AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x='Predicted', y = 'residuals', data=df_compare)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01710873855574724"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.mean_squared_error(df_compare['Actual'], df_compare['Predicted'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression Summary <a class=\"anchor\" id=\"summary\"></a>\n",
    "In this notebook, we have covered the basic concepts of a linear regression, and applied it to estimating poverty rates using several socio-economic variables. "
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Lab on Linear Regression",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}