Multiple regression was used to forecast success in college (GPA) based upon SAT score, high school GPA, and hours spent on-line

Question

Use the regression output shown and comment on the overall fit of the model, the usefulness of each independent variable, and the value to an admissions department of using the model to make admission decisions. What is the model's forecast for an applicant having a high school GPA of 2.5 and an SAT score of 1000 that spends 20 hours a week on-line? What other variables do you feel would make good indicators of college GPA?

What will be an ideal response?

Answer 1

Answer: This model was created based on 10 observations so alas, the overall model is not statistically significant nor are any of the independent variables. The r-squared is 0.516, so the model explains over half of the variation in a student's college GPA. The independent variables with the lowest p-values are HS GPA (0.22) and SAT (0.18) so these may be of practical significance if not statistical significance. Perhaps more data could be collected; with power so low, it's tough to find significance.
For the applicant in question, the model predicts the following:

= 0.541 + 0.423 × 2.5 + 0.001 × 1000 + 0.01 × 20

= 2.7985

Not exactly Dean's List material but higher than my undergraduate GPA…
Answers may vary on other predictors but possibilities include the number of hours a week spent working and studying, socioeconomic background, parents' education, and many others.