ch8-exercises_with_solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Chapter 8: Practice Exercises with Solutions\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1:** The following regression output is for predicting the tail length (`length`, in centimeters) of kangaroos using their body weight (`weight`, in kilograms). The coefficients are estimated using a dataset of 200 kangaroos.\n",
    "\n",
    "| . | Estimate | Std. Error   |\n",
    "|------|------|------|\n",
    "|  (Intercept)  | -0.437   | 0.552   |\n",
    "|   weight  | 5.034    | 0.340|\n",
    "|   R-squared = 64.6%  |      |\n",
    "\n",
    "(A) Write out the linear model.\n",
    "\n",
    "(B) Interpret the intercept.\n",
    "\n",
    "(C) Interpret the slope.\n",
    "\n",
    "(D) Interpret the R-squared value.\n",
    "\n",
    "(E) Calculate the correlation coefficient."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answers:**\n",
    "\n",
    "(A) $\\hat{length}$ = -0.437 + 5.034 x $weight$\n",
    "\n",
    "(B) Expected tail length of kangaroos with 0 body weight is -0.437. This is obviously not a meaningful\n",
    "value, it just serves to adjust the height of the regression line.\n",
    "\n",
    "(C) For each additional kilogram in kangaroos' weights, we expect their tails to be longer by 5.034\n",
    "centimeters, on average.\n",
    "\n",
    "(D) Body weight explains 64.6% of the variability in lengths of kangaroos' tails.\n",
    "\n",
    "(E) $\\sqrt{0.646} = 0.8037$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**Exercise 2**: Many people believe that gender, weight, drinking habits, and many other factors are much more important in predicting blood alcohol content (BAC) than simply considering the number of drinks a person consumed. Here we examine data from sixteen student volunteers at Ohio State University who each drank a randomly assigned number of cans of beer. These students were evenly divided between men and women, and they differed in weight and drinking habits. Thirty minutes later, a police officer measured their blood alcohol content (BAC) in grams of alcohol per deciliter of blood. The regression table summarize the findings.\n",
    "\n",
    "| . | Estimate | Std. Error   | t value   | p-value  |\n",
    "|------|------|------|------|------|\n",
    "|  (Intercept)  | -0.0127   | 0.0126  | -1.00  | 0.3320  |\n",
    "|   beers  | 0.0180    | 0.0024| 7.48| 0.0000|  \n",
    "\n",
    "(A) Write out the linear model.\n",
    "\n",
    "(B) Interpret the intercept.\n",
    "\n",
    "(C) Interpret the slope.\n",
    "\n",
    "(D) Do the data provide strong evidence that drinking more cans of beer is associated with an increase in blood alcohol? State the null and alternative hypotheses, report the p-value, and state your conclusion.\n",
    "\n",
    "(E) The correlation coefficient for number of cans of beer and BAC is 0.89. Calculate ${R^2}$ and interpret it in\n",
    "context."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answers:**\n",
    "\n",
    "(A) $\\hat{BAC}$ = -0.0127 + 0.0180 x ${beers}$\n",
    "\n",
    "(B) Students who don't have any beer are expected to have a blood alcohol content of -0.0127. This is obviously not a meaningful value, it just serves to adjust the height of the regression line.\n",
    "\n",
    "(C) For each additional can of beer consumed, the model predicts an additional 0.0180 grams per deciliter BAC.\n",
    "\n",
    "(D) The hypotheses are as follows:\n",
    "\n",
    "$H_0$: The true slope coefficient of number of beers is zero ($\\beta_1 = 0$).\n",
    "\n",
    "$H_a$: The true slope coefficient of number of beers is different than zero ($\\beta_1 \\neq 0$).\n",
    "\n",
    "The p-value is approximately 0. With such a small p-value and since the data showed a positive relationship, we reject $H_0$ and conclude that the data provide convincing evidence that number of cans of beer consumed and blood alcohol content are positively correlated and the true slope parameter is greater than 0.\n",
    "\n",
    "(E) $R^2 = 0.89^2 = 0.79$\n",
    "\n",
    "Approximately 79% of the variability in blood alcohol content can be explained by number of cans of beer consumed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Baseball Player Statistics (MLB11)\n",
    "\n",
    "The movie [Moneyball](https://www.imdb.com/title/tt1210166/) focuses on the \"quest for the secret of success in baseball\". It follows a low-budget team, the Oakland Athletics, who believed that under-used statistics, such as a player's ability to get on base, better predict the ability to score runs than typical statistics like home runs, RBIs (runs batted in), and batting average. Obtaining players who excelled in these under-used statistics turned out to be much more affordable for the team.\n",
    "\n",
    "Data Source: https://www.mlb.com/\n",
    "\n",
    "The data set is available as a CSV file named `mlb11.csv` (Download from [here](https://raw.githubusercontent.com/imranture/practice_stats/main/datasets/mlb11.csv))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data shape = (30, 12)\n"
     ]
    },
    {
     "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>team</th>\n",
       "      <th>runs</th>\n",
       "      <th>at_bats</th>\n",
       "      <th>hits</th>\n",
       "      <th>homeruns</th>\n",
       "      <th>bat_avg</th>\n",
       "      <th>strikeouts</th>\n",
       "      <th>stolen_bases</th>\n",
       "      <th>wins</th>\n",
       "      <th>new_onbase</th>\n",
       "      <th>new_slug</th>\n",
       "      <th>new_obs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Texas Rangers</td>\n",
       "      <td>855</td>\n",
       "      <td>5659</td>\n",
       "      <td>1599</td>\n",
       "      <td>210</td>\n",
       "      <td>0.283</td>\n",
       "      <td>930</td>\n",
       "      <td>143</td>\n",
       "      <td>96</td>\n",
       "      <td>0.340</td>\n",
       "      <td>0.460</td>\n",
       "      <td>0.800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Boston Red Sox</td>\n",
       "      <td>875</td>\n",
       "      <td>5710</td>\n",
       "      <td>1600</td>\n",
       "      <td>203</td>\n",
       "      <td>0.280</td>\n",
       "      <td>1108</td>\n",
       "      <td>102</td>\n",
       "      <td>90</td>\n",
       "      <td>0.349</td>\n",
       "      <td>0.461</td>\n",
       "      <td>0.810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Detroit Tigers</td>\n",
       "      <td>787</td>\n",
       "      <td>5563</td>\n",
       "      <td>1540</td>\n",
       "      <td>169</td>\n",
       "      <td>0.277</td>\n",
       "      <td>1143</td>\n",
       "      <td>49</td>\n",
       "      <td>95</td>\n",
       "      <td>0.340</td>\n",
       "      <td>0.434</td>\n",
       "      <td>0.773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Kansas City Royals</td>\n",
       "      <td>730</td>\n",
       "      <td>5672</td>\n",
       "      <td>1560</td>\n",
       "      <td>129</td>\n",
       "      <td>0.275</td>\n",
       "      <td>1006</td>\n",
       "      <td>153</td>\n",
       "      <td>71</td>\n",
       "      <td>0.329</td>\n",
       "      <td>0.415</td>\n",
       "      <td>0.744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>St. Louis Cardinals</td>\n",
       "      <td>762</td>\n",
       "      <td>5532</td>\n",
       "      <td>1513</td>\n",
       "      <td>162</td>\n",
       "      <td>0.273</td>\n",
       "      <td>978</td>\n",
       "      <td>57</td>\n",
       "      <td>90</td>\n",
       "      <td>0.341</td>\n",
       "      <td>0.425</td>\n",
       "      <td>0.766</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  team  runs  at_bats  hits  homeruns  bat_avg  strikeouts  \\\n",
       "0        Texas Rangers   855     5659  1599       210    0.283         930   \n",
       "1       Boston Red Sox   875     5710  1600       203    0.280        1108   \n",
       "2       Detroit Tigers   787     5563  1540       169    0.277        1143   \n",
       "3   Kansas City Royals   730     5672  1560       129    0.275        1006   \n",
       "4  St. Louis Cardinals   762     5532  1513       162    0.273         978   \n",
       "\n",
       "   stolen_bases  wins  new_onbase  new_slug  new_obs  \n",
       "0           143    96       0.340     0.460    0.800  \n",
       "1           102    90       0.349     0.461    0.810  \n",
       "2            49    95       0.340     0.434    0.773  \n",
       "3           153    71       0.329     0.415    0.744  \n",
       "4            57    90       0.341     0.425    0.766  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "mlb11 = pd.read_csv('datasets/mlb11.csv')\n",
    "print(f'Data shape = {mlb11.shape}')\n",
    "mlb11.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**Exercise 3:** Compute the correlation of `runs` (number of runs) and `bat_avg` (batting average, which is the number of hits divided by at bats).\n",
    "\n",
    "**Hint**: Use [`corr()`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.corr.html) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation = 0.8100\n"
     ]
    }
   ],
   "source": [
    "print(f\"Correlation = {mlb11['runs'].corr(mlb11['bat_avg']):.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**Exercise 4:** Construct a simple linear model for `runs` as dependent variable and `bat_avg` as the independent variable. Find the slope, intercept, and R-squared values.\n",
    "\n",
    "**Hint**: Use [`statsmodels`](https://www.statsmodels.org/stable/regression.html) to fit the linear model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   runs   R-squared:                       0.656\n",
      "Model:                            OLS   Adj. R-squared:                  0.644\n",
      "Method:                 Least Squares   F-statistic:                     53.41\n",
      "Date:                Sun, 16 Jun 2024   Prob (F-statistic):           5.88e-08\n",
      "Time:                        17:21:05   Log-Likelihood:                -158.43\n",
      "No. Observations:                  30   AIC:                             320.9\n",
      "Df Residuals:                      28   BIC:                             323.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept   -642.8189    183.080     -3.511      0.002   -1017.841    -267.797\n",
      "bat_avg     5242.2291    717.282      7.308      0.000    3772.943    6711.515\n",
      "==============================================================================\n",
      "Omnibus:                        3.078   Durbin-Watson:                   1.891\n",
      "Prob(Omnibus):                  0.215   Jarque-Bera (JB):                1.837\n",
      "Skew:                           0.570   Prob(JB):                        0.399\n",
      "Kurtosis:                       3.410   Cond. No.                         85.0\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "# if you want to exclude the intercept, add \"-1\" to the formula:\n",
    "# that is, \"runs ~ bat_avg - 1\"\n",
    "formula_string = 'runs ~ bat_avg'\n",
    "\n",
    "model = sm.formula.ols(formula = formula_string, data = mlb11)\n",
    "model_fitted = model.fit()\n",
    "print(model_fitted.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept = -642.8189\n",
      "Slope = 5242.2291\n",
      "R-squared = 0.6561\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/6k/hgb80htj4jjctgq4scyrwwzm0000gn/T/ipykernel_99326/2421614329.py:1: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  print(f'Intercept = {model_fitted.params[0]:.4f}')\n",
      "/var/folders/6k/hgb80htj4jjctgq4scyrwwzm0000gn/T/ipykernel_99326/2421614329.py:2: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`\n",
      "  print(f'Slope = {model_fitted.params[1]:.4f}')\n"
     ]
    }
   ],
   "source": [
    "print(f'Intercept = {model_fitted.params[0]:.4f}')\n",
    "print(f'Slope = {model_fitted.params[1]:.4f}')\n",
    "print(f'R-squared = {model_fitted.rsquared:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**Exercise 5:** Summarize the relationship between these two variables by finding the line that best describes their relationship. In other words, plot `bat_avg` vs. `runs`, both actual `runs` (as a scatter plot) and predicted `runs` (as a line plot)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lZcaPH59LLrkkSdLY2JhJkya1OPb0008vHk+fPj1NTU2tPm5TU1NmzJjR4rXNnnnmmbz00kvFOr7xjW9sF1IlyYknnpgrrriixS0nAQBgbyeoAgAAyt5RRx2VcePGtXp+0KBB+Yu/+Ivi11OmTNmtx6uurs5pp52WJNm8eXMxjCgnF154Yfr27dvq+QkTJhSPW7sH1NaB31FHHZWTTjqp1fmGDBmS8ePHt7/QDnLyySena9euSZIXXnihxTEjR44sviYrV67M3LlzW53v+eefz+rVq5Mk+++/f4488sjtxmz9+px22mmtbjmZbFlRd8wxx+z8iQAAwF7G1n8AAEDZa21buveO+X//7/8lSd54442sXbs2PXv2bHX8unXr8sorr+Stt95KXV1dNm7cmEKhUDz/9ttvF49ff/31nHDCCbvxDN5/La182trgwYNTU1OTTZs2FZ9/c9DTbOsgpzm425HTTz99t0PCHWm+H9by5cuzYcOG7VYoVVRUFMc1NTWlsnLbz25WVlbm1FNPzQMPPJAkmTZtWkaNGtXiY2297d9pp51WnHtr7X19TjvttDz//PM7HQcAAHsTQRUAAFD2Dj/88J2OOeCAA7LPPvukrq4uhUIhr7/+eoshRPN9p2bNmtXmrdia70FULrp375799ttvh2MqKirSo0ePbNq0KUmyfv36bYKqpqamvPHGG8Wvd7RaqNmhhx6aioqKbQK/jjB16tT86le/yuLFi9s0vrGxMevXr28xqDzjjDOKQdXMmTPzhS98IV26dNlmTH19ffE+YknL2/6tWLFim5+Ltrw+bRkDAAB7G1v/AQAAZW9noUuzfv36FY/XrFmz3fkFCxbka1/7WqZNm9au+wVt2LChzWP3BN27d2/TuOrq//+zje+9t9SGDRvS2NhY/Hrr17Y1Xbt2bfNjt0WhUMhtt92W2267rc0hVbONGze2+P1DDjkkBx98cJIt4dyf/vSn7cbMnj27eP3QoUNz4IEHbjdm65CqtrZ2h6v3mu1oK0YAANhbWVEFAACUvdra2naPe29QsXnz5vzf//t/s27duiRJ7969c84552TUqFEZMGBAevbsmZqamuIWb1OnTs1tt92WJB2+QqiztbRNXXu99/Wrqalp03W1tbXF13h3TZkyJVOnTi1+PWbMmIwbNy5Dhw5N3759U1tbu03Ydtlll2X58uVJtqwIa81pp52Wu+++O8mW7f/eu03i1tv+tbSaKtn29WnPawMAAB80gioAAKDs1dfXp1u3bm0a1+y991uaNWtWli1blmTL6qAbbrghffr0aXWucltF1dHeG6ps2rRpu9e0JVv/Geyu5i36kuTiiy/ORRddtMPxbf0zO/300/Pv//7vKRQKeeaZZ7Ju3br06NEjyZaVeM33kaqsrGz13lNbvz7N2yfuTEe+NgAAUC5s/QcAAJS9d955p03jVqxYUTzu1avXNudeeOGF4vFf/MVf7DCkSlJcmfNB1b1791RVVRW/3vq1bc3GjRuzfv36Dnn8d955p7jdX48ePfKxj31sh+PXr1/f5pVc/fr1y4gRI5JsWWn31FNPFc9Nnz69uOXh0Ucf3erPyT777FM8rq+vz9q1a3f6uCtXrmxTfQAAsDcRVAEAAGVv3rx5Ox2zePHi4n2DKioqMmTIkG3Or1q1qnjc0j2H3uvFF1/c6Zhd2WKvI7blez9UVlYW7+WUJK+++upOr5k/f36HbZO49Z/XoEGDtgnNWvLSSy+167G33tJv2rRpLR63tu1fsuW+aVuHVW15fdoyBgAA9jaCKgAAoOw98cQTOx2z9b2MDjnkkPTs2XOb81sHRDvbqm3+/Pl57bXXdvqYXbp0KR43r8LpjGtKZeTIkcXjrQOc1mx9b6fd1Z4/rySZNGlSu+Y/+eSTi38WL774Yt55550sWbIkr7zySpItW/uNHTt2h3McddRRxeO2vD5tGQMAAHsbQRUAAFD2XnzxxcyYMaPV84sXL86DDz5Y/PpDH/rQdmMGDBhQPJ49e3arc9XX1+enP/1pm+raekVNW7d125VrSmX8+PHF4xdffDF//OMfWx37+uuvbxMW7q7+/fsXw6o333wzS5YsaXXsjBkz8vTTT7dr/u7du+f4449PkhQKhUybNm2boO3EE0/c6T25JkyYUDyeNm3aDldMPf3008V7XwEAwAeJoAoAACh71dXV+dGPftTiyqpXX301119/ferr65MkBxxwQItB1ZgxY4rHTzzxRB544IE0NTVtM2bJkiW5/vrrs2DBgtTW1u60rv79+xfHLV++vE1bu+3KNaVy8MEH55RTTil+/YMf/CAzZ87cbtxLL72UG264IU1NTamuru6Qx+7Vq1eGDRuWZEuQdMstt+Ttt9/eZkxTU1Meeuih/OAHP0hlZeU2q9Xa4r3b/7V1279mo0ePzvDhw4u13HjjjZkzZ85242bPnp3vf//77a4PAAD2Bh3zLwQAAIAS+uu//uv867/+a374wx/m3nvvzfDhw1NdXZ2FCxcWt2pLtmzXdtlll6Wmpma7OY477riMGDEic+fOTaFQyL/927/l4YcfztChQ9O9e/csWbIkL7/8cpqamtK3b9+cf/75ueuuu3ZYV2VlZU488cRiwHHdddfl2GOPzX777ZfKyi2fG+zZs2cuuuii3bqmlP7n//yfefXVV7N8+fLU19fne9/7XgYNGpRhw4alsrIyb731VnGbxI9+9KOZNWtWli9fniTF57OrLr744lx//fUpFApZsGBB/vZv/zZHHnlk+vfvn40bN+all14q3svq4osvzpQpU4qP3RajR4/OPvvsk7q6urz55pvF7/fu3TvHHHPMTq+vrKzMJZdckmuuuSZr167N6tWrc91112Xo0KE55JBD0tTUlPnz52fhwoVJkv/xP/5H7rjjjiTlc68yAADYXYIqAACg7J1//vlZu3Zt7r///ixdujRLly7dbkyfPn1yxRVXFFe4tOQrX/lKbrjhhixYsCBJsmzZsixbtmybMQceeGC++tWvtnml02c+85nMmTMnq1atSn19/Xbb4+2///7bhU67ck2p9O7dO9dee21uvPHGvPXWW0mSt99+e7vVTR/60Ifymc98JtOnTy9+b2db5+3M0UcfnS984Qu544470tjYmMbGxsyZM2ebVUsVFRX5xCc+kQsvvDBTpkxp1/zV1dU5+eSTM3ny5G2+P27cuFRVVbVpjsGDB+eb3/xmbr755rzzzjtJkgULFhR/xpprvOiii3LOOecUg6rdfW0AAKBcCKoAAIC9wsSJEzN69OhMnjy5uJKmqqoqAwYMyNixY3PeeeelR48eO5yjT58+uf766zNlypTMmDEjb731Vurr69O7d+8MGjQop5xySk4//fTU1ta2Oajab7/98t3vfjcPPfRQnnvuubz99tvZuHFjGhsbO/SaUurfv39uvPHGPProo5k+fXoWLlyYjRs3pk+fPjnssMNy9tlnF1cgrVu3LsmWcKZ79+67/djnnntujjzyyPzud78rhns1NTXp27dvRo0alQkTJmTo0KG7PP8ZZ5yxXVDVlm3/tnbooYfme9/7Xh5++OHMnDkzS5YsyebNm9O3b98ceeSROeecc3L44Yfn3XffLV6zs59VAADYW1QUCoVCqYsAAABg77d48eJcccUVSZJBgwbln//5n0tb0B7m+eefz/XXX58kOfbYY3P11VeXuCIAAOh8u7chOAAAALTRU089VTw+7LDDSljJnmnGjBnFY68PAAAfFIIqAAAAOt3y5cvzwAMPFL8+9dRTS1jNnue1117L448/Xvza6wMAwAeFoAoAAIDdcsstt2TmzJnZvHlzi+efffbZ/MM//EPx/lQHH3xwjjvuuPexwtL69re/neeeey5NTU3bnWtqasq0adNy/fXXF+9BNnr06Bx00EHvd5kAAFAS1aUuAAAAgPL26quv5qmnnkq3bt0ydOjQ7L///unSpUvWrl2bV199Ne+8805xbG1tbS6//PJUVn5wPjf53HPP5bnnnkvPnj1z6KGHpm/fvqmurs7q1aszb968rF69uji2d+/e+Zu/+ZsSVgsAAO8vQRUAAAAdYsOGDZk7d26r5wcMGJArr7wyQ4YMef+K2oOsXbs2zz//fKvnhwwZkr/9279N375938eqAACgtCoKhUKh1EUAAABQvpYtW5ZZs2blxRdfzLJly1JXV5e6urpUV1enV69eOfTQQzNmzJicdtppqa7+4H1e8q233srs2bPz8ssvZ/ny5amrq8vatWtTW1ub3r175/DDD8+JJ56YsWPHpqKiotTlAgDA+0pQBQAAAAAAQEl8cDYFBwAAAAAAYI8iqAIAAAAAAKAkBFUAAAAAAACUhKAKAAAAAACAkhBUAQAAAAAAUBKCKgAAAAAAAEpCUAUAAAAAAEBJCKoAAAAAAAAoCUEVAAAAAAAAJSGoAgAAAAAAoCQEVQAAAAAAAJSEoAoAAAAAAICSEFQBAAAAAABQEoIqAAAAAAAASkJQBQAAAAAAQEkIqgAAAAAAACgJQRUAAAAAAAAlIagCAAAAAACgJARVAAAAAAAAlMT/B/E/3lD6gKJlAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 859,
       "width": 853
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "plt.style.use('ggplot')\n",
    "plt.rcParams['figure.figsize'] = (10,10)\n",
    "\n",
    "x = mlb11['bat_avg']\n",
    "y = mlb11['runs']\n",
    "\n",
    "y_pred = model_fitted.predict(x)\n",
    "\n",
    "plt.scatter(x, y, color = 'crimson')\n",
    "plt.plot(x, y_pred, color = 'mediumblue')\n",
    "plt.title('Scatter Plot - Runs vs. Batting Avg')\n",
    "plt.xlabel('batting avg')\n",
    "plt.ylabel('runs')\n",
    "plt.show();"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "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": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}