Question

If x̄ = 30, ȳ = 50, r = 0.8 and the standard deviations of X and Y are 2 and 5 respectively, obtain the regression line of Y on X.

Answer 1

Here, x̄ = 30;

ȳ = 50; r = 0.8;

S_x = 2 and S_y = 5

Now, b =\(r.\frac{S_y}{S_x}\)

∴ b = 0.8 × \(\frac{5}{2}\) = 2

a = ȳ – bx̄

∴ a = 50 – 2(30)

= 50 – 60

= – 10

Regression line of Y on X is ŷ = a + bx

Putting a = – 10; b = 2 in ŷ = a + bx, the regression

line of Y on X obtained is ŷ = – 10 + 2x.