Assuming a linear relationship between X and Y,if the coefficient of correlation (r)equals -0.75,this means that: A) there is very weak correlation. B) the slope b₁ is = -0.75. C) the value of X is always greater than the value of Y. D) None of these choices are true.

Question

Quizplus · Accepted Answer

The coefficient of correlation, r, measures the strength and direction of the linear relationship between two variables. If r = 0, there is no linear relationship. If r = +/- 1, there is a perfect linear relationship. In this case, r = 0.75, which indicates a strong, positive linear relationship.

The slope of the regression line, b, is given by: 
b = r(Sy/Sx)

where Sy is the standard deviation of Y and Sx is the standard deviation of X. So, if we know r, we can determine the slope of the regression line. In this case, b = (0.75)(Sy/Sx). So, choice B is true.

Choices A and C are not true, as we don't have enough information to make these assertions. Choice D is not true, as choice B is true.

Assuming a Linear Relationship Between X and Y,if the Coefficient