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# Homework #10 A baseball analyst would like to develop a model to predict the number of wins during the 2000 baseball season. The analyst collected...

Homework #10

A baseball analyst would like to develop a model to predict the number of wins during the 2000 baseball season. The analyst collected several variables: Wins, ERA, Runs Scored, Hits Allowed, Walks Allowed, Errors, and Saves from 30 professional baseball teams.

Summary Output Correlation Matrix
Regression Statistics Wins ERA
Win 1
Multiple R 0.9504
ERA -.6598 1
R squared 0.9032 Run Scored .6101 .0856
Standard Error 3.3463 Hits Allowed -.5520 .8600
Observations 30 Walks Allowed -.2261 .3105
Saves .5320 -.5985
Errors -.1308 .0540

ANOVA
df SS MS F Significance F
Regression 4 2611.92 652.98 58.3123 2.59E-12
Residual 25 279.95 11.198
Total 29 2891.97

Coefficient Standard Error t Stat P-value Lower 95% Upper 95%
Intercept b0 74.771 16.7626 4.4610 0.0002 40.2540 109.3003
ERA b1 -12.3206 3.2066 -3.8423 0.0007 -18.9247 -5.7166
Run Scored b2 0.08433 0.0079 10.6414 9.0114E-11 0.0680 0.1007
Hits Allowed b3 -.0107 0.0163 -0.6563 0.5176 -0.0441 0.0228
Saves b4 0.2731 0.1203 2.2703 0.0321 0.0254 0.5208
4) What is the estimated regression equation when using the four variables that have the highest correlation values?

5) Use the estimated regression equation to predict Wins when ERA is 5.2, Runs Scored are 938, Hits Allowed are 1596, and Saves are 30.

6) Calculate the residual for the observation described in question 5), if the original Wins for that observation were 72.

7) What is the 95% Confidence Interval for the true population slope between Wins and Saves?

8) What is the coefficient of multiple determination and interpret its meaning?

9) What is the standard error of the estimate and what are its units?

10) Determine if there is a significant relationship between Y and the explanatory variables in the model at alpha = .05. State the hypotheses, p-value, and the conclusion.

11) Which of the explanatory variables are significant predictors of Wins at alpha = .05?

12) On the basis of the results for question 9, which independent variables should be included in this model?

Homework #10 A baseball analyst would like to develop a model to predict the number of wins during the 2000 baseball season. The analyst collected several variables: Wins, ERA, Runs Scored, Hits Allowed, Walks Allowed, Errors, and Saves from 30 professional baseball teams. Summary Output Correlation Matrix Regression Statistics Wins ERA Win 1 Multiple R 0.9504 ERA -.6598 1 R squared 0.9032 Run Scored .6101 .0856 Standard Error 3.3463 Hits Allowed -.5520 .8600 Observations 30 Walks Allowed -.2261 .3105 Saves .5320 -.5985 Errors -.1308 .0540 ANOVA df SS MS F Significance F Regression 4 2611.92 652.98 58.3123 2.59E-12 Residual 25 279.95 11.198 Total 29 2891.97 Coefficient Standard Error t Stat P-value Lower 95% Upper 95% Intercept b 0 74.771 16.7626 4.4610 0.0002 40.2540 109.3003 ERA b 1 -12.3206 3.2066 -3.8423 0.0007 -18.9247 -5.7166 Run Scored b 2 0.08433 0.0079 10.6414 9.0114E-11 0.0680 0.1007 Hits Allowed b 3 -.0107 0.0163 -0.6563 0.5176 -0.0441 0.0228 Saves b 4 0.2731 0.1203 2.2703 0.0321 0.0254 0.5208 Part A: Correlation 1) Which variables are the dependent variables? 2) Which variables are the independent variables? 3) Which 4 variables have the highest correlation with Wins ?
Part B: Multiple Regression 4) What is the estimated regression equation when using the four variables that have the highest correlation values? 5) Use the estimated regression equation to predict Wins when ERA is 5.2, Runs Scored are 938, Hits Allowed are 1596, and Saves are 30. 6) Calculate the residual for the observation described in question 5), if the original Wins for that observation were 72. 7) What is the 95% Confidence Interval for the true population slope between Wins and Saves? 8) What is the coefficient of multiple determination and interpret its meaning? 9) What is the standard error of the estimate and what are its units? 10) Determine if there is a significant relationship between Y and the explanatory variables in the model at alpha = .05. State the hypotheses, p-value, and the conclusion. 11) Which of the explanatory variables are significant predictors of Wins at alpha = .05? 12) On the basis of the results for question 9, which independent variables should be included in this model? Part C: Residual Analysis 13) Perform a residual analysis of the plots of the residuals versus the predicted Y’s, and each of the independent variables? 14) Is this model a good fit for the data? Explain
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