A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found R²= 0.311. Which of these is true?
I. High school GPA accounts for 31.1% of college GPA.
II. 31.1% of college GPAs can be correctly predicted with this model.
III. 31.1% of the variance in college GPA can be accounted for by the model.

Question

Quizplus · Accepted Answer

R² is the proportion of variance in the dependent variable (college GPA) that can be explained by the independent variable (high school GPA) in a regression analysis. Therefore, option III is the correct choice. Option I implies causation, which cannot be inferred from a correlation coefficient. Option II is not technically correct as R² represents the proportion of variance that can be explained by the model, not the proportion that can be predicted.

A Regression Analysis of Students' College Grade Point Averages (GPAs)