1. Let x, x2 and x3 be the excess of heights of father, mother and son respectively in 100 samples above their respective mean values in cm. A distribution of these variables gave the following correlation coefficients r, between x, and x; and standard deviations o; = v V(x) for i, j = 1, 2, 3; rij r12 = 0-3, 23 = 0-4, 31 = 0:5 O, = 3, 0, = 2, O3 = 4 Obtain a regression equation of x, on x, and x3, and estimate the excess of height of father when excess of heights of mother and son are 0-7 cm and 2-1 cm respectively.

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1. Let x1, x2 and x3 be the excess of heights of father, mother and son respectively in 100
samples above their respective mean values in cm. A distribution of these variables gave the following
correlation coefficients r, between x, and x; and standard deviations o; = v V(x) for i, j = 1, 2, 3;
rij
r12 = 0:3,
23 = 0-4,
131 = 0:5
0, = 3,
0, = 2,
Oz = 4
Obtain a regression equation of x, on x, and x3, and estimate the excess of height of father when excess
of heights of mother and son are 0-7 cm and 2·1 cm respectively.
Transcribed Image Text:1. Let x1, x2 and x3 be the excess of heights of father, mother and son respectively in 100 samples above their respective mean values in cm. A distribution of these variables gave the following correlation coefficients r, between x, and x; and standard deviations o; = v V(x) for i, j = 1, 2, 3; rij r12 = 0:3, 23 = 0-4, 131 = 0:5 0, = 3, 0, = 2, Oz = 4 Obtain a regression equation of x, on x, and x3, and estimate the excess of height of father when excess of heights of mother and son are 0-7 cm and 2·1 cm respectively.
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