Unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression ________.
A) can be greater than 1
B) measures the percentage of variation explained by the regression line
C) indicates whether the slope of the regression line is positive or negative
D) is a proportion

Question

Quizplus · Accepted Answer

The sample correlation coefficient, also known as Pearson's r, indicates the direction (positive or negative) of the linear relationship between two variables, which is what choice C describes. Unlike the coefficient of determination (R^2), which measures the proportion of variance in the dependent variable that can be predicted from the independent variable, the correlation coefficient also provides information on the direction of the relationship. Choices A, B, and D are incorrect: A) the correlation coefficient cannot be greater than 1, B) it does not measure the percentage of variation explained by the regression line (that's the coefficient of determination), and D) while it is a measure of linear association, describing it merely as a proportion does not capture its essence or primary function.

Unlike the Coefficient of Determination, the Sample Correlation Coefficient in a Simple