(1) The two regression equations
Regression equation y on x is
y = a + byx (x)
y = a + (-0.2) (x)
28 = a - 0.2(53)
28+10.6 = a
a = 38.6
y = 38.6 -0.2x
Regressionn equation x on y is
x = a (bxy) y
x = a + (bxy) y
53 = a + (-1.5)(28)
53 42.0 = a
95 = a
x = 95 -1.5y
(2) The coefficient of correlation
r2 = bxy × byx
r2 = (-1.5) × (-0.2)
=+0.30
r = √0.3 = 0.548
3) The most likely value of Y when X = 60
Find y, x = 60
y = 38.6 - 0.2x
y = 38.6 - 0.2(60)
y = 38.6 - 12 = 26.6
(4) The most likely value of X when Y = 20
Find x when y = 20
x = 95