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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.

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\(\bar{Y}=\frac{1690}{10}\) = 169

Regression equation of X on Y

Regression equation of Y on X 

Y - \(\bar{Y}\) = bxy(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.

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