A baseball analyst would like to develop a model to predict the number of wins during the 2014 baseball season. The analyst collected several variables: Wins, ERA, Runs Scored, Hits and Saves from 27 professional baseball teams. The data is shows below.
Regression Statistics |
|
Multiple R |
0.9232 |
Observations |
27 |
ANOVA
|
df |
SS |
MS |
F |
Significance
F |
Regression |
?? |
469.348 |
?? |
?? |
0.000145539 |
Residual |
?? |
?? |
?? |
|
|
Total |
?? |
746.297 |
|
|
|
Variable |
Coefficient |
Standard
Error |
T value |
P value |
Lower 95% |
Upper 95% |
Intercept |
72.456 |
14.417 |
5.02573 |
0.00002 |
?? |
?? |
ERA |
-10.234 |
3.3201 |
?? |
0.0007 |
-17.1194 |
-3.348 |
Runs Scored |
0.0723 |
0.0086 |
8.40698 |
0.00123 |
0.05446 |
0.09013 |
Hits |
-0.0174 |
0.01132 |
?? |
0.0457 |
-0.04087 |
0.00607 |
Saves |
2.215 |
1.218 |
?? |
0.06234 |
?? |
?? |
1) Fill in the tables with the missing values? (You should have 14 different values you need to find)
2) What is the coefficient of determination?
3) What is the adjusted r2?
4) What is the standard error of the estimated regression line?
5) What is the estimated regression equation?
6) Use the estimated regression equation to predict Wins when ERA 6.6, Runs Score is 925, Hits Allowed is 1523 and Saves are 33.
7) Calculate the residual for the observed described in number 6), if the original Wins for that observation were 109.
8) What is the hypothesis scenario?
9) Is there evidence of a significant relationship between the OVERALL Wins and the independent variables? Use alpha = .05. (State the p-value and the conclusion)
10) Which of the independent variables are significant predictors of Wins? Which ones do you want to include in your model? Use alpha = .05
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