Question

Which of the following does not describe the correlation coefficient r?

A: it can be either positive or negative
B: It is a measure of the strength of the linear relationship between 2 variables
C: A value close to -1 indicates a strong linear relationship between 2 variables
D: It is the percentage of the varaiation in the response variable (y) that is explained by the linear relationship between the explanatory variable (x) and the response variable (y)

Answer 1

The incorrect description of the correlation coefficient r is the percentage of variation in the response variable y that is explained by the linear relationship with the explanatory variable x, which actually pertains to r².

Step-by-step explanation:

The statement that does not describe the correlation coefficient r is: "It is the percentage of the variation in the response variable (y) that is explained by the linear relationship between the explanatory variable (x) and the response variable (y)." This description is not accurate for r itself, but rather for the square of the correlation coefficient, known as the coefficient of determination, or r². The confusion here arises because while r measures the strength and direction of the linear relationship between two variables, r² actually represents the proportion of variance in the dependent variable that can be explained by the independent variable through the regression model.

.