In the context of regression, the statement 'the sample correlation between x and y is equal to the coefficient of determination' is

In the context of regression, the statement 'the sample correlation between x and y is equal to the coefficient of determination' is

• A. True
• B. False
• C. Depends on sample size
• D. Only for large samples

Answer: (B)

In simple linear regression, the amount of variation in the response explained by the predictor is captured by the coefficient of determination, R^2, which is the square of the Pearson correlation between x and y. That means R^2 = r^2, where r is the sample correlation. The correlation r can be negative or positive and lies between -1 and 1, while R^2 is always between 0 and 1 and is nonnegative. So the statement that the sample correlation equals the coefficient of determination is not correct in general; only the square of the correlation equals R^2. For example, if the correlation is 0.8, R^2 is 0.64.

In simple linear regression, the amount of variation in the response explained by the predictor is captured by the coefficient of determination, R^2, which is the square of the Pearson correlation between x and y. That means R^2 = r^2, where r is the sample correlation. The correlation r can be negative or positive and lies between -1 and 1, while R^2 is always between 0 and 1 and is nonnegative. So the statement that the sample correlation equals the coefficient of determination is not correct in general; only the square of the correlation equals R^2. For example, if the correlation is 0.8, R^2 is 0.64.