 # Question 3 4 Using the sample of 50 students from question #1, t...

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3a. Did the addition of gender allow for a significant increase in the explained variance in graduate GPA?. Perform the appropriate test to address this question and briefly explain what it means.

We can use the R²∆ F-test compare the R² from this model and the full model derived earlier.

where: R²(L) = R² from the larger model = .593
k(L) = number of predictors in larger model = 3
R²(S) = R² from the smaller model = .563
k(S) = number of predictors in smaller model = 2
N = number of subjects 50

F = ((0.593-0.563))/(3-2)/((1-0.593)/(50-3-1)) = 0.030/0.008847826 =3.390663391

looking at an F-table F(1,50, α = .05) = 4.034309707 so, this R²-change is not significant at the .05 level because the F calculated value is smaller than the F tabulated value. It means that the addition of gender variable in the regression model is not needed as it does not help in predicting the dependent variable.

3b. Test the overall regression equation (including the variables of GRE, undergraduate GPA, and gender) for statistical significance. Report the F value obtained from this test and briefly explain what it means.

For overall model, we have

Multiple R = .770
R Square    = .593
Standard Error = .064

R Square    = .593
Regression/Total = 0.593
Regression = 0.593*Total...

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