The coefficient of determination is the square of which statistic?

• A. Pearson's correlation coefficient
• B. Spearman's rho
• C. Kendall's tau
• D. F-statistic

Answer: (A)

The coefficient of determination, R^2, is the square of the Pearson correlation coefficient in simple linear regression. It represents the proportion of the variance in the dependent variable that is explained by the independent variable. This comes from the fact that, for one predictor, the variability explained by the regression line corresponds to the strength of the linear relationship between x and y, as captured by Pearson r, and squaring that strength gives the fraction of total variance accounted for by the model. For example, if r is 0.8, R^2 is 0.64, meaning 64% of the variance is explained.

Spearman's rho and Kendall's tau are rank-based measures of association and do not directly quantify the variance explained by a linear fit, so their squares do not equal the coefficient of determination. The F-statistic tests whether the model adds predictive value beyond a baseline, and while it relates to R^2, R^2 itself is not the square of the F-statistic.