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?

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