Question Background:

The admission committee of an MBA program at a Canadian university is considering using a psychometric test of self-esteem (SE) in addition to the IQ test they administer to MBA applicants to help in their selection process. They want to assess the influence of self-esteem on candidate bachelor's GPA above and beyond IQ and sex. Treat GPA as the response variable and IQ, and SE as explanatory variables. In the data file there are 77 samples, you have been given the R^2 for each of the regression tests. R^2 for the multiple regression test uses IQ & SE as Independent Variables, and GPA as the Dependent Variable. The two other R^2 values use IQ and SE as independent variables in seperate tests respectively, with GPA still being the dependent variable.

Using the output given, please answer the following question:

What percent of the total variation in GPAs can be explained by the straight-line relationship for each of the continuous explanatory variables separately? How much does self-esteem (SE) contribute to explaining GPA after the effect of IQ on GPA is taken into account?

R^2 for multiple regression: 0.5196

R^2 for single linear regression (IQ): 0.44128555

R^2 for single linear regression (SE): 0.32565864