14 77 A Baseball Analytics Specialist Wants To Determine Which Variables Are Important In Predicting A Team S Wins In A 1 (155.98 KiB) Viewed 26 times
14.77 A baseball analytics specialist wants to determine which variables are important in predicting a team's wins in a given season. He has collected data related to wins, earned run aver- age (ERA), and runs scored per game for the 2014 season (stored in Baseball). Develop a model to predict the number of wins based on ERA and runs scored per game. a. State the multiple regression equation. b. Interpret the meaning of the slopes in this equation. c. Predict the mean number of wins for a team that has an ERA of 4.50 and has scored 4.6 runs per game. d. Perform a residual analysis on the results and determine whether the regression assumptions are valid. e. Is there a significant relationship between the number of wins and the two independent variables (ERA and runs scored per game) at the 0.05 level of significance? f. Determine the p-value in (e) and interpret its meaning. g. Interpret the meaning of the coefficient of multiple determina- tion in this problem. h. Determine the adjusted r². i. At the 0.05 level of significance, determine whether each inde- pendent variable makes a significant contribution to the regres- sion model. Indicate the most appropriate regression model for this set of data. j. Determine the p-values in (i) and interpret their meaning. k. Construct a 95% confidence interval estimate of the population slope between wins and ERA. 1. Compute and interpret the coefficients of partial determination. m. Which is more important in predicting wins-pitching, as measured by ERA, or offense, as measured by runs scored per game? Explain.
Team Baltimore Boston Chicago White Sox Cleveland Detroit Houston Kansas City Los Angeles Angels Minnesota New York Yankees Oakland Seattle Tampa Bay Texas Toronto Arizona Atlanta Chicago Cubs Cincinnati Colorado Los Angeles Dodgers Miami Milwaukee New York Mets Philadelphia Pittsburgh San Diego San Francisco St. Louis Washington E.R.A. 3.66 4.41 4.68 4.03 4.35 4.46 3.85 3.89 4.80 4.10 3.53 3.42 3.86 4.77 4.23 4.58 3.69 4.36 3.78 5.05 3.81 4.16 4.06 3.81 4.24 3.90 3.56 3.79 3.72 3.43 Runs Scored per Game 4.35 3.91 4.07 4.13 4.67 3.88 4.02 4.77 4.41 3.91 4.50 3.91 3.78 3.93 4.46 3.80 3.54 3.79 3.67 4.66 4.43 3.98 4.01 3.88 3.82 4.21 3.30 4.10 3.82 4.23 League 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Saves atting Avera 0.256 0.244 0.253 0.253 0.277 0.242 0.263 0.259 0.254 0.245 0.244 0.244 0.247 0.256 0.259 0.248 0.241 0.239 0.238 0.276 0.265 0.253 0.25 0.239 0.242 0.259 0.226 0.255 0.253 0.253 53 36 36 40 41 31 53 46 38 48 31 51 37 33 45 35 54 37 44 24 47 42 45 42 40 48 41 46 55 45 HRs 211 123 155 142 155 153 95 155 128 147 146 136 117 111 177 118 123 157 131 186 134 122 150 125 125 156 109 132 105 152 WHIP 1.241 1.324 1.405 1.268 1.332 1.335 1.259 1.271 1.391 1.232 1.145 1.173 1.212 1.413 1.310 1.340 1.265 1.300 1.237 1.439 1.206 1.330 1.247 1.284 1.306 1.263 1.225 1.169 1.236 1.158 Wins 98 71 73 85 88 90 70 89 98 70 84 88 87 77 67 83 64 79 73 76 66 94 77 82 79 73 88 77 88 90 96
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