linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "df =pd.read_csv(\"foodtruck.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        X        Y\n",
       "0  6.1101  17.5920\n",
       "1  5.5277   9.1302\n",
       "2  8.5186  13.6620\n",
       "3  7.0032  11.8540\n",
       "4  5.8598   6.8233"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(x=\"X\", y=\"Y\", style=\"o\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.159799999999999 5.839135051546393\n"
     ]
    }
   ],
   "source": [
    "x_mean = df[\"X\"].mean()\n",
    "y_mean = df[\"Y\"].mean()\n",
    "print(x_mean, y_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x*y</th>\n",
       "      <th>x^2</th>\n",
       "      <th>y^2</th>\n",
       "      <th>y_prediction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "      <td>-2.0497</td>\n",
       "      <td>11.752865</td>\n",
       "      <td>-24.089847</td>\n",
       "      <td>4.201270</td>\n",
       "      <td>138.129834</td>\n",
       "      <td>3.393774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "      <td>-2.6321</td>\n",
       "      <td>3.291065</td>\n",
       "      <td>-8.662412</td>\n",
       "      <td>6.927950</td>\n",
       "      <td>10.831108</td>\n",
       "      <td>2.698951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "      <td>0.3588</td>\n",
       "      <td>7.822865</td>\n",
       "      <td>2.806844</td>\n",
       "      <td>0.128737</td>\n",
       "      <td>61.197216</td>\n",
       "      <td>6.267196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "      <td>-1.1566</td>\n",
       "      <td>6.014865</td>\n",
       "      <td>-6.956793</td>\n",
       "      <td>1.337724</td>\n",
       "      <td>36.178600</td>\n",
       "      <td>4.459272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "      <td>-2.3000</td>\n",
       "      <td>0.984165</td>\n",
       "      <td>-2.263579</td>\n",
       "      <td>5.290000</td>\n",
       "      <td>0.968581</td>\n",
       "      <td>3.095158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.3829</td>\n",
       "      <td>11.8860</td>\n",
       "      <td>0.2231</td>\n",
       "      <td>6.046865</td>\n",
       "      <td>1.349056</td>\n",
       "      <td>0.049774</td>\n",
       "      <td>36.564576</td>\n",
       "      <td>6.105301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7.4764</td>\n",
       "      <td>4.3483</td>\n",
       "      <td>-0.6834</td>\n",
       "      <td>-1.490835</td>\n",
       "      <td>1.018837</td>\n",
       "      <td>0.467036</td>\n",
       "      <td>2.222589</td>\n",
       "      <td>5.023816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8.5781</td>\n",
       "      <td>12.0000</td>\n",
       "      <td>0.4183</td>\n",
       "      <td>6.160865</td>\n",
       "      <td>2.577090</td>\n",
       "      <td>0.174975</td>\n",
       "      <td>37.956257</td>\n",
       "      <td>6.338181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6.4862</td>\n",
       "      <td>6.5987</td>\n",
       "      <td>-1.6736</td>\n",
       "      <td>0.759565</td>\n",
       "      <td>-1.271208</td>\n",
       "      <td>2.800937</td>\n",
       "      <td>0.576939</td>\n",
       "      <td>3.842474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.0546</td>\n",
       "      <td>3.8166</td>\n",
       "      <td>-3.1052</td>\n",
       "      <td>-2.022535</td>\n",
       "      <td>6.280376</td>\n",
       "      <td>9.642267</td>\n",
       "      <td>4.090648</td>\n",
       "      <td>2.134527</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        X        Y       x          y        x*y       x^2         y^2  \\\n",
       "0  6.1101  17.5920 -2.0497  11.752865 -24.089847  4.201270  138.129834   \n",
       "1  5.5277   9.1302 -2.6321   3.291065  -8.662412  6.927950   10.831108   \n",
       "2  8.5186  13.6620  0.3588   7.822865   2.806844  0.128737   61.197216   \n",
       "3  7.0032  11.8540 -1.1566   6.014865  -6.956793  1.337724   36.178600   \n",
       "4  5.8598   6.8233 -2.3000   0.984165  -2.263579  5.290000    0.968581   \n",
       "5  8.3829  11.8860  0.2231   6.046865   1.349056  0.049774   36.564576   \n",
       "6  7.4764   4.3483 -0.6834  -1.490835   1.018837  0.467036    2.222589   \n",
       "7  8.5781  12.0000  0.4183   6.160865   2.577090  0.174975   37.956257   \n",
       "8  6.4862   6.5987 -1.6736   0.759565  -1.271208  2.800937    0.576939   \n",
       "9  5.0546   3.8166 -3.1052  -2.022535   6.280376  9.642267    4.090648   \n",
       "\n",
       "   y_prediction  \n",
       "0      3.393774  \n",
       "1      2.698951  \n",
       "2      6.267196  \n",
       "3      4.459272  \n",
       "4      3.095158  \n",
       "5      6.105301  \n",
       "6      5.023816  \n",
       "7      6.338181  \n",
       "8      3.842474  \n",
       "9      2.134527  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"x\"] = df[\"X\"] - x_mean\n",
    "df[\"y\"] = df[\"Y\"] - y_mean\n",
    "df[\"x*y\"] = df[\"x\"] * df[\"y\"]\n",
    "df[\"x^2\"] = df[\"x\"]**2\n",
    "df[\"y^2\"] = df[\"y\"]**2\n",
    "df[:10]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1715.2195285390003 1437.6958578599997 2914.8470516572247\n"
     ]
    }
   ],
   "source": [
    "summation_x_y = df[\"x*y\"].sum()\n",
    "summation_x_squared = df[\"x^2\"].sum()\n",
    "summation_y_squared = df[\"y^2\"].sum()\n",
    "print(summation_x_y, summation_x_squared, summation_y_squared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8378732325263412"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation = summation_x_y / (summation_x_squared * summation_y_squared)**0.5\n",
    "correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getMean(numbers):\n",
    "    if len(numbers) == 0:\n",
    "        return None\n",
    "    else:\n",
    "        current_sum = 0\n",
    "        for i in numbers:\n",
    "            current_sum += i\n",
    "            current_avg = current_sum/len(numbers)\n",
    "        return current_avg\n",
    "\n",
    "def getStandardDeviation(numbers):\n",
    "    if len(numbers) == 0:\n",
    "        return 0\n",
    "    else:\n",
    "        mean = getMean(numbers)\n",
    "        std_deviation = 0\n",
    "        for i in numbers:\n",
    "            std_deviation += (i - mean)**2\n",
    "        return (std_deviation/len(numbers))**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8498839959227156 5.48178525707763\n"
     ]
    }
   ],
   "source": [
    "std_deviation_x = getStandardDeviation(df[\"x\"].tolist())\n",
    "std_deviation_y = getStandardDeviation(df[\"y\"].tolist())\n",
    "print(std_deviation_x, std_deviation_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1930336441895941"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = correlation * (std_deviation_y / std_deviation_x)\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.8957808783118555"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = df[\"Y\"].mean() - m * df[\"X\"].mean()\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x*y</th>\n",
       "      <th>x^2</th>\n",
       "      <th>y^2</th>\n",
       "      <th>y_prediction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "      <td>-2.0497</td>\n",
       "      <td>11.752865</td>\n",
       "      <td>-24.089847</td>\n",
       "      <td>4.201270</td>\n",
       "      <td>138.129834</td>\n",
       "      <td>3.393774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "      <td>-2.6321</td>\n",
       "      <td>3.291065</td>\n",
       "      <td>-8.662412</td>\n",
       "      <td>6.927950</td>\n",
       "      <td>10.831108</td>\n",
       "      <td>2.698951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "      <td>0.3588</td>\n",
       "      <td>7.822865</td>\n",
       "      <td>2.806844</td>\n",
       "      <td>0.128737</td>\n",
       "      <td>61.197216</td>\n",
       "      <td>6.267196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "      <td>-1.1566</td>\n",
       "      <td>6.014865</td>\n",
       "      <td>-6.956793</td>\n",
       "      <td>1.337724</td>\n",
       "      <td>36.178600</td>\n",
       "      <td>4.459272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "      <td>-2.3000</td>\n",
       "      <td>0.984165</td>\n",
       "      <td>-2.263579</td>\n",
       "      <td>5.290000</td>\n",
       "      <td>0.968581</td>\n",
       "      <td>3.095158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.3829</td>\n",
       "      <td>11.8860</td>\n",
       "      <td>0.2231</td>\n",
       "      <td>6.046865</td>\n",
       "      <td>1.349056</td>\n",
       "      <td>0.049774</td>\n",
       "      <td>36.564576</td>\n",
       "      <td>6.105301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7.4764</td>\n",
       "      <td>4.3483</td>\n",
       "      <td>-0.6834</td>\n",
       "      <td>-1.490835</td>\n",
       "      <td>1.018837</td>\n",
       "      <td>0.467036</td>\n",
       "      <td>2.222589</td>\n",
       "      <td>5.023816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8.5781</td>\n",
       "      <td>12.0000</td>\n",
       "      <td>0.4183</td>\n",
       "      <td>6.160865</td>\n",
       "      <td>2.577090</td>\n",
       "      <td>0.174975</td>\n",
       "      <td>37.956257</td>\n",
       "      <td>6.338181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6.4862</td>\n",
       "      <td>6.5987</td>\n",
       "      <td>-1.6736</td>\n",
       "      <td>0.759565</td>\n",
       "      <td>-1.271208</td>\n",
       "      <td>2.800937</td>\n",
       "      <td>0.576939</td>\n",
       "      <td>3.842474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5.0546</td>\n",
       "      <td>3.8166</td>\n",
       "      <td>-3.1052</td>\n",
       "      <td>-2.022535</td>\n",
       "      <td>6.280376</td>\n",
       "      <td>9.642267</td>\n",
       "      <td>4.090648</td>\n",
       "      <td>2.134527</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        X        Y       x          y        x*y       x^2         y^2  \\\n",
       "0  6.1101  17.5920 -2.0497  11.752865 -24.089847  4.201270  138.129834   \n",
       "1  5.5277   9.1302 -2.6321   3.291065  -8.662412  6.927950   10.831108   \n",
       "2  8.5186  13.6620  0.3588   7.822865   2.806844  0.128737   61.197216   \n",
       "3  7.0032  11.8540 -1.1566   6.014865  -6.956793  1.337724   36.178600   \n",
       "4  5.8598   6.8233 -2.3000   0.984165  -2.263579  5.290000    0.968581   \n",
       "5  8.3829  11.8860  0.2231   6.046865   1.349056  0.049774   36.564576   \n",
       "6  7.4764   4.3483 -0.6834  -1.490835   1.018837  0.467036    2.222589   \n",
       "7  8.5781  12.0000  0.4183   6.160865   2.577090  0.174975   37.956257   \n",
       "8  6.4862   6.5987 -1.6736   0.759565  -1.271208  2.800937    0.576939   \n",
       "9  5.0546   3.8166 -3.1052  -2.022535   6.280376  9.642267    4.090648   \n",
       "\n",
       "   y_prediction  \n",
       "0      3.393774  \n",
       "1      2.698951  \n",
       "2      6.267196  \n",
       "3      4.459272  \n",
       "4      3.095158  \n",
       "5      6.105301  \n",
       "6      5.023816  \n",
       "7      6.338181  \n",
       "8      3.842474  \n",
       "9      2.134527  "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"y_prediction\"] = m * df[\"X\"] + c\n",
    "df[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot1 = plt.scatter(df[\"X\"], df[\"Y\"])\n",
    "plot2 = plt.scatter(df[\"X\"], df[\"Y\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.8391350515463945"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"y_prediction\"].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getSSR(df_pred):\n",
    "    result = 0\n",
    "    for i in range(len(df_pred)):\n",
    "        result += (df_pred[i] - df_pred.mean())**2\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2046.314604718041"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getSSR(df[\"y_prediction\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getSST(df_actual):\n",
    "    result = 0\n",
    "    for i in range(len(df_actual)):\n",
    "        result += (df_actual[i] - df_actual.mean())**2\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2914.8470516572247"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getSST(df[\"Y\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getSSE(df_actual, df_pred):\n",
    "    result = 0\n",
    "    for i in range(len(df_actual)):\n",
    "        result += (df_actual[i] - df_pred[i])**2\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "868.5324469391846"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getSSE(df[\"Y\"], df[\"y_prediction\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7020315537841402"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2 = correlation**2\n",
    "r2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7020315537841401"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2 = getSSR(df[\"y_prediction\"])/getSST(df[\"Y\"])\n",
    "r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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