Consider the following data: = 20,s_x = 2, = -5,s_y = 4,and b₁ = 0.40.The sample correlation coefficient,r_xy is equal to ____. A) −0.40 B) −0.20 C) 0.20 D) 0.40

Question

Quizplus · Accepted Answer

First, we need to determine the covariance between the two variables: Covariance (_xy) = [∑ (_{x - mean of _x)(y - mean of}y)] / (n-1) = [(20-9)(2-3) + (-5-9)(4-3)] / (2-1) = -60/1 = -60 Next, we need to determine the standard deviation of each variable: Standard deviation of _{x (s_{x) = sqrt([∑ (_{x - mean of _{x)^2] / (n-1))
= sqrt([(20-9)^2 + (-5-9)^2] / (2-1))
= sqrt[506]
= 22.5166605

Standard deviation of}y (s}y) = sqrt([∑ (}y - mean of}y)^2] / (n-1)) = sqrt([(2-3)^2 + (4-3)^2] / (2-1)) = sqrt[2] = 1.41421356 Finally, we can determine the sample correlation coefficient: r_xy = Covariance (_xy) / (s_{x * s}y) = -60 / (22.5166605 * 1.41421356) = -0.1980291 ≈ -0.20 Therefore, the best choice is C, 0.20.

Consider the Following Data: = 20,sx = 2

Consider the Following Data: = 20,s_x = 2