For a certain data set the regression equation is y = 2 + 3.5x.The correlation coefficient between y and x in this data set ___.
A)must be 0
B)is negative
C)must be 1
D)is positive
E)must be 3

Question

Quizplus · Accepted Answer

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.
Since the regression equation is y = 2 + 3.5x, the slope of the line (3.5) is positive, indicating a positive linear relationship between y and x. Therefore, the correlation coefficient must also be positive. Option D is the best choice.

For a Certain Data Set the Regression Equation Is Y