Question

Explain why the slope b of the least-squares line always has the same sign (positive or negative) as the sample correlation coefficient r. Choose the correct relationship between b and r, where sx and sy are the standard deviations of the x values and the y values, respectively.
a. b = 1/r(sx/sy)
b. b = r(sy/sx)
c. b = 1/r(sy/sx)
d. b = r(sx/sy)

Answer 1

Answer:

b = r(sy/sx)

Step-by-step explanation:

The sign of the slope Coefficient and the correlation are the same because both the slope and correlation Coefficient evaluates the changes in one variable with respect to the other . A decrease in y as x increases will result in a negative slope value and also a negative correlation Coefficient. While increase in x which results in the increase in y imvariable will result in a positive correlation Coefficient value and r value.

Slope, b = correlation Coefficient,r (Sy /Sx)

Sx = standard deviation of x values

Sy = standard deviation of Y Values