Question

Given the following data, obtain a linear regression estimate of X for Y = 10, `bar x = 7.6, bar y = 14.8, sigma_x = 3.2, sigma_y = 16` and r = 0.7

Answer 1

Given, `bar x = 7.6, bar y = 14.8, sigma_x = 3.2, sigma_y = 16` and r = 0.7

`"b"_"XY" = "r" sigma_"X"/sigma_"Y" = 0.7 xx 3.2/16 = 0.14`

`"a"' = bar x - "b"_"XY"  bar y`

= 7.6 - 0.14 × 14.8 = 7.6 - 2.072 = 5.528

The regression equation of X on Y is

X = a' + b_XY Y

∴ X = 5.528 + 0.14 Y

For Y = 10

X = 5.528 + 0.14 × 10 = 5.528 + 1.4 = 6.928