A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found $R ^ { 2 } = 0.311$. 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
A) I only
B) II only
C) III only
D) I and II
E) none of these

Question

Quizplus · Accepted Answer

III is correct because $R^2$ (the coefficient of determination) measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). In this case, it means that $31.1\%$ of the variance in college GPA can be explained by the model that includes high school GPA.

A Regression Analysis of Students' College Grade Point Averages (GPAs) R2=0.311R ^ { 2 } = 0.311R2=0.311

A Regression Analysis of Students' College Grade Point Averages (GPAs) $R ^ { 2 } = 0.311$