What does an r² value of 0.311 indicate in a regression analysis of college GPAs and high school GPAs?

An r² value of 0.311 signifies that 31.1% of the variance in college GPA can be explained by the variance in high school GPA. This means that there is a moderate relationship between the two variables; specifically, that high school GPA has a measurable impact on predicting college GPA, accounting for just over a third of the changes seen in college performance.

In regression analysis, the r² value represents the proportion of the variance for the dependent variable (in this case, college GPA) that can be attributed to the independent variable (high school GPA). A higher r² value generally indicates a stronger relationship. Although 31.1% suggests that while high school GPA does contribute to variations in college GPA, other factors also play significant roles in determining college performance, which are not captured by high school GPA alone.

Thus, understanding that 31.1% of the variance is explained helps in interpreting the strength and limitations of the relationship between these two variables in the context of the study.