It is known that r_XY = 0.5, s_X² = 1, s_Y² = 1. A simple linear regression model is estimated. The regression line will have a slope of which one of the following? A) 0 B) 0.5 C) 0.5 or -0.5 D) 1 or -1 E) It depends on the values of $\bar{X}$ and $\bar{Y}$ .

Question

Quizplus · Accepted Answer

The slope of the regression line is given by:$$b = r_{XY} \frac{s_Y}{s_X}$$Substituting the given values, we get:$$b = 0.5 \frac{1}{1} = 0.5$$Therefore, the slope of the regression line is 0.5 or -0.5.

It Is Known That RXY = 0 Xˉ\bar{X}Xˉ And Yˉ\bar{Y}Yˉ

It Is Known That R_XY = 0 $\bar{X}$ And $\bar{Y}$