Question

The heights (in cm.) of a group of fathers and sons are given below.

Heights of Fathers:	158	166	163	165	167	170	167	172	177	181
Heights of Sons:	163	158	167	170	160	180	170	175	172	175

Find the lines of regression and estimate the height of son when the height of the father is 164 cm.

Answer 1

\(\bar{Y}=\frac{1690}{10}\) = 169

Regression equation of X on Y

Regression equation of Y on X 

Y - \(\bar{Y}\) = b_xy(X - \(\bar{X}\))

Y – 169 = 0.610 (X – 168.6) 

Y – 169 = 0.610X – 102.846 

Y = 0.610X – 102.846 + 169 

Y = 0.160X + 66.154 … (1) 

To get son’s height (Y) when the father height is X = 164 cm. 

Put X = 164 cm in equation (1) we get 

Son’s height = 0.610 × 164 + 66.154 

= 100.04 + 66.154 cm 

= 169.19 cm.