Simple regression model but needs improvement

#1
I have been working on trying to fit a linear regression line to try to predict college gpa where the the prediction variables are high school GPA(X1) , SAT(X2),ACT (X3), and whether your from a rural/urban area(qualitative variable) (X4). So far I have eliminated Act scores because that showed a weak correlation with college gpa. I've kept the rest of the others in the model.
View attachment 5144
This is the full step wise regression and X3 has a large p-value so I removed it from the model.
View attachment 5142
View attachment 5147

So I chose Y~X1+X2+X4 and show the plots of residuals of this model. From these plots I see the residuals vs each predictor look good to me (with a few outliers) as that is to be expected in this case. The residuals look randomly distributed around the x=0 line. The qq plot looks decent to me. I've tried adding in interaction terms but I get large p-values due to high multicollinearity possibly, which I think I should not add. I also do not think transformations would be appropriate in this case as the residuals show no signs of a trend. I'm trying to develop the best model I can and what I have above is the best I got so far . Any opinions would be great on what I can try would be great. Thanks.


Im not exactly sure why i get no postings. Its about the third time already....
 
Last edited: