Fill the missing observations in the table below Show that R

Fill the missing observations in the table below. Show that R^2 = r^2, where r is the sample correlation coefficient.

Solution

(a)

Slope b-cap = r * ( S_y/S_x) = -0.2 * (6/4) = -0.3

Y intercept a-cap = y - bx = 18 - (-0.3*30)   = 27

Therefore ,

y-cap = 27 - 0.3 x-cap ------------------->Answer

(b)

Slope b-cap = r * ( S_y/S_x)

=> -2 = -0.6 * (4/S_x)

=> S_x = 1.2 Answer

Y intercept a-cap = y - bx

=> 30 = 18 - (-2)x

=> x-bar = 6 Answer