The proportion of variance in one variable explained by a second variable is equal to the square of which statistic?

• A. P-value
• B. Coefficient of determination
• C. Confidence interval
• D. Variance explained ratio

Answer: (B)

The amount of variability in one variable that is accounted for by another is captured by the coefficient of determination, R^2. This statistic represents the proportion of the variance in the dependent variable that can be explained by the independent variable. In simple linear regression, R^2 is the square of the Pearson correlation coefficient between the two variables, so it directly tells you what fraction of the outcome’s variance is explained by the predictor. For example, if the correlation is 0.8, then R^2 is 0.64, meaning 64% of the variance is explained. Other options measure different ideas: the P-value tests whether the observed relationship could occur by chance, the confidence interval describes a range for a population parameter, and “variance explained ratio” isn’t a standard term. The coefficient of determination is the standard measure of explained variance.