1_SLR_SumSqs_R_fkingfisher.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aa13cd0f-de9a-4a9a-9177-7c53d9aea186",
   "metadata": {
    "tags": []
   },
   "source": [
    "The number of pounds of steam used per month at a plant is thought to be related to the average monthly ambient temperature. The past year’s usages and temperatures follow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "cd90d453-fe1f-44f2-a453-51c7779907ec",
   "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>Month</th>\n",
       "      <th>Temperature</th>\n",
       "      <th>Usage/l000</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Jan.</td>\n",
       "      <td>21</td>\n",
       "      <td>185.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Jul.</td>\n",
       "      <td>68</td>\n",
       "      <td>621.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Feb.</td>\n",
       "      <td>24</td>\n",
       "      <td>214.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Aug.</td>\n",
       "      <td>74</td>\n",
       "      <td>675.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Mar.</td>\n",
       "      <td>32</td>\n",
       "      <td>288.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Sep.</td>\n",
       "      <td>62</td>\n",
       "      <td>562.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Apr.</td>\n",
       "      <td>47</td>\n",
       "      <td>424.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Oct.</td>\n",
       "      <td>50</td>\n",
       "      <td>452.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>May</td>\n",
       "      <td>50</td>\n",
       "      <td>454.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Nov.</td>\n",
       "      <td>41</td>\n",
       "      <td>369.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Jun.</td>\n",
       "      <td>59</td>\n",
       "      <td>539.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Dec.</td>\n",
       "      <td>30</td>\n",
       "      <td>273.98</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Month  Temperature  Usage/l000\n",
       "0   Jan.           21      185.79\n",
       "1   Jul.           68      621.55\n",
       "2   Feb.           24      214.47\n",
       "3   Aug.           74      675.06\n",
       "4   Mar.           32      288.03\n",
       "5   Sep.           62      562.03\n",
       "6   Apr.           47      424.84\n",
       "7   Oct.           50      452.93\n",
       "8    May           50      454.68\n",
       "9   Nov.           41      369.95\n",
       "10  Jun.           59      539.03\n",
       "11  Dec.           30      273.98"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(12, 3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 12 entries, 0 to 11\n",
      "Data columns (total 3 columns):\n",
      " #   Column       Non-Null Count  Dtype  \n",
      "---  ------       --------------  -----  \n",
      " 0   Month        12 non-null     object \n",
      " 1   Temperature  12 non-null     int64  \n",
      " 2   Usage/l000   12 non-null     float64\n",
      "dtypes: float64(1), int64(1), object(1)\n",
      "memory usage: 416.0+ bytes\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "None"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Temperature</th>\n",
       "      <th>Usage/l000</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>12.000000</td>\n",
       "      <td>12.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>46.500000</td>\n",
       "      <td>421.861667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>17.344111</td>\n",
       "      <td>159.723460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>21.000000</td>\n",
       "      <td>185.790000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>31.500000</td>\n",
       "      <td>284.517500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>48.500000</td>\n",
       "      <td>438.885000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>59.750000</td>\n",
       "      <td>544.780000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>74.000000</td>\n",
       "      <td>675.060000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Temperature  Usage/l000\n",
       "count    12.000000   12.000000\n",
       "mean     46.500000  421.861667\n",
       "std      17.344111  159.723460\n",
       "min      21.000000  185.790000\n",
       "25%      31.500000  284.517500\n",
       "50%      48.500000  438.885000\n",
       "75%      59.750000  544.780000\n",
       "max      74.000000  675.060000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "dataset = pd.read_csv(\"https://raw.githubusercontent.com/forestwhite/Regression/main/data/212Table.csv\")\n",
    "display(dataset)\n",
    "\n",
    "# Shape of our dataset\n",
    "display(dataset.shape)\n",
    "\n",
    "# Info on our dataset\n",
    "display(dataset.info())\n",
    "\n",
    "# Describe our dataset\n",
    "display(dataset.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b0ddae9-7fe7-4246-8a4e-0e18da05c52b",
   "metadata": {
    "tags": []
   },
   "source": [
    "Generate a scatterplot of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a82ebcb5-6eb6-48d1-abe2-aebb34206c1e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate a scatterplot of the data.\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "dataset = pd.read_csv(\"https://raw.githubusercontent.com/forestwhite/Regression/main/data/212Table.csv\")\n",
    "\n",
    "# Import matplotlib and seaborn libraries to visualize the data\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns\n",
    "\n",
    "# Using pairplot we'll visualize the data for correlation\n",
    "sns.pairplot(dataset, x_vars=['Temperature'], \n",
    "             y_vars='Usage/l000', height=4, aspect=1, kind='scatter')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "028faa54-4f4a-45ac-abcc-5ecdfba2208c",
   "metadata": {
    "tags": []
   },
   "source": [
    "Fit a simple linear regression model to the data and generate the intercept and coefficient estimates.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b2caab6c-d127-404a-85bd-e96c34287949",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\JupyterLab\\resources\\jlab_server\\lib\\site-packages\\scipy\\stats\\stats.py:1541: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=12\n",
      "  warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>Usage/l000</td>    <th>  R-squared:         </th> <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>7.412e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 25 Mar 2022</td> <th>  Prob (F-statistic):</th> <td>1.10e-20</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:04:50</td>     <th>  Log-Likelihood:    </th> <td> -23.920</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    12</td>      <th>  AIC:               </th> <td>   51.84</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    10</td>      <th>  BIC:               </th> <td>   52.81</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>       <td>   -6.3321</td> <td>    1.670</td> <td>   -3.792</td> <td> 0.004</td> <td>  -10.053</td> <td>   -2.611</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Temperature</th> <td>    9.2085</td> <td>    0.034</td> <td>  272.255</td> <td> 0.000</td> <td>    9.133</td> <td>    9.284</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.719</td> <th>  Durbin-Watson:     </th> <td>   1.063</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.257</td> <th>  Jarque-Bera (JB):  </th> <td>   1.292</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.804</td> <th>  Prob(JB):          </th> <td>   0.524</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.972</td> <th>  Cond. No.          </th> <td>    147.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             Usage/l000   R-squared:                       1.000\n",
       "Model:                            OLS   Adj. R-squared:                  1.000\n",
       "Method:                 Least Squares   F-statistic:                 7.412e+04\n",
       "Date:                Fri, 25 Mar 2022   Prob (F-statistic):           1.10e-20\n",
       "Time:                        13:04:50   Log-Likelihood:                -23.920\n",
       "No. Observations:                  12   AIC:                             51.84\n",
       "Df Residuals:                      10   BIC:                             52.81\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "const          -6.3321      1.670     -3.792      0.004     -10.053      -2.611\n",
       "Temperature     9.2085      0.034    272.255      0.000       9.133       9.284\n",
       "==============================================================================\n",
       "Omnibus:                        2.719   Durbin-Watson:                   1.063\n",
       "Prob(Omnibus):                  0.257   Jarque-Bera (JB):                1.292\n",
       "Skew:                           0.804   Prob(JB):                        0.524\n",
       "Kurtosis:                       2.972   Cond. No.                         147.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "dataset = pd.read_csv(\"https://raw.githubusercontent.com/forestwhite/Regression/main/data/212Table.csv\")\n",
    "\n",
    "# Creating X and y\n",
    "X = dataset['Temperature']\n",
    "y = dataset['Usage/l000']\n",
    "\n",
    "# Add a list of ones with length of X to identify intercept terms in linear model\n",
    "x = sm.add_constant(X)\n",
    "results = sm.OLS(y,x).fit()\n",
    " \n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97408316-6354-48cc-8640-80ed191957c0",
   "metadata": {
    "tags": []
   },
   "source": [
    "Calculate the Sum of Squares Total (SST), the Sum of Squares of the Response (SSR), and the Sum of Squares of the Error/Residuals (SSE), and use them to find the coefficient of determination, R^2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8e5db4e8-fa47-459e-9d6b-242380f70907",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ybar: \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "421.8616666666667"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SS_total: \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "280627.4199666666"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SS_error: \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "37.85472832000013"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SS_regression: \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "280591.52670165343"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r_squared: \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9998720963724164"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "dataset = pd.read_csv(\"https://raw.githubusercontent.com/forestwhite/Regression/main/data/212Table.csv\")\n",
    "\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "# Creating X and y\n",
    "X = dataset['Temperature']\n",
    "y = dataset['Usage/l000']\n",
    "\n",
    "\n",
    "\n",
    "# calculate y_hat estimate and sample average for y\n",
    "yhat = 9.2085*X - 6.3321\n",
    "ybar = np.average(y)\n",
    "print(\"ybar: \")\n",
    "display(ybar)\n",
    "\n",
    "#Calculate the sum of squares values\n",
    "SS_total=sum(np.square(np.subtract(y,ybar)))\n",
    "print(\"SS_total: \")\n",
    "display(SS_total)\n",
    "SS_error=sum(np.square(np.subtract(y,yhat)))\n",
    "print(\"SS_error: \")\n",
    "display(SS_error)\n",
    "SS_regression=sum(np.square(np.subtract(yhat,ybar)))\n",
    "print(\"SS_regression: \")\n",
    "display(SS_regression)\n",
    "\n",
    "# calculate coefficient of determination, R^2\n",
    "r_squared=SS_regression/SS_total\n",
    "print(\"r_squared: \")\n",
    "display(r_squared)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cad2d31-8bcb-47e3-9797-53d00057cf86",
   "metadata": {
    "tags": []
   },
   "source": [
    "Plot the linear fit line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9fa8a834-8b15-48fc-935c-bdbab99e4cb0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "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": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Creating X and y\n",
    "X = dataset['Temperature']\n",
    "y = dataset['Usage/l000']\n",
    "\n",
    "plt.scatter(X,y)\n",
    " \n",
    "yhat = 9.2085*X - 6.3321\n",
    "fig = plt.plot(X, yhat, lw=4, c='orange', label = 'regression line')\n",
    " \n",
    "plt.xlabel('Temperature', fontsize = 20)\n",
    "plt.ylabel('Pounds of Steam/1000', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9144f5b5-270f-4610-ad28-b820934db3d4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}