{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9e5b068f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8ae8924d",
   "metadata": {},
   "outputs": [],
   "source": [
    "score = pd.read_csv(r\"C:\\Users\\Teni\\Desktop\\Git-Github\\Datasets\\Linear Regression\\CGPA & SAT score.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fd818d67",
   "metadata": {
    "scrolled": true
   },
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT   GPA\n",
       "0  1714  2.40\n",
       "1  1664  2.52\n",
       "2  1760  2.54\n",
       "3  1685  2.74\n",
       "4  1693  2.83"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d44b8ec0",
   "metadata": {},
   "source": [
    "Visually assess is there's a linear relationship between SAT and the GPAs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "460da471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=score, x='GPA', y = 'SAT');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a7811808",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data=score, x='GPA', y = 'SAT');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cf4b732",
   "metadata": {},
   "source": [
    "Define the X and y Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8362c8f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = score['GPA']\n",
    "y = score['SAT']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30386620",
   "metadata": {},
   "source": [
    "**Say if someone had a GPA of 3.4, what is the predicted SAT Score**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0b07e2c6",
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>1936</td>\n",
       "      <td>3.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>1810</td>\n",
       "      <td>3.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>1987</td>\n",
       "      <td>3.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>1962</td>\n",
       "      <td>3.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>2050</td>\n",
       "      <td>3.81</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>84 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT   GPA\n",
       "0   1714  2.40\n",
       "1   1664  2.52\n",
       "2   1760  2.54\n",
       "3   1685  2.74\n",
       "4   1693  2.83\n",
       "..   ...   ...\n",
       "79  1936  3.71\n",
       "80  1810  3.71\n",
       "81  1987  3.73\n",
       "82  1962  3.76\n",
       "83  2050  3.81\n",
       "\n",
       "[84 rows x 2 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8d69a894",
   "metadata": {},
   "outputs": [],
   "source": [
    "# GPA = np.linspace(0, 10, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "cea5ebd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "GPA = 3.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6535d6d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1862.3806591060002"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_SAT = 245.21763914*GPA + 1028.64068603\n",
    "pred_SAT"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "141aabb2",
   "metadata": {},
   "source": [
    "This means the predicted SAT score will be 1862\n",
    "\n",
    "As displayed below, it shows that this is close to the real GPA score of those around 3.4 from the original data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2fe4277c",
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1925</td>\n",
       "      <td>3.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1824</td>\n",
       "      <td>3.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>1956</td>\n",
       "      <td>3.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT  GPA\n",
       "45  1925  3.4\n",
       "46  1824  3.4\n",
       "47  1956  3.4"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score[score['GPA'] == 3.4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2b39023",
   "metadata": {},
   "source": [
    "**Say if someone had a GPA of 2.91, what is the predicted SAT Score**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "77982264",
   "metadata": {},
   "outputs": [],
   "source": [
    "GPA = 2.91"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "d4a28063",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1742.2240159274002"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_SAT = 245.21763914*GPA + 1028.64068603\n",
    "pred_SAT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "3e139900",
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1764</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1764</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT  GPA\n",
       "6  1764  3.0\n",
       "7  1764  3.0"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score[(score['GPA'] <= 3.0) & (score['GPA']>= 2.92)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b052d310",
   "metadata": {},
   "source": [
    "Our predicted SAT score is not far from the real label in the data\n",
    "\n",
    "*Our model may not be spot on in comparism- but the residual difference is minimal.*"
   ]
  }
 ],
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