Question

If for a bivariate data `barx = 10,  bary = 12, V(X) = 9, σ_y = 4` and r = 0.6, estimate y  when x = 5.

Answer 1

Given : `barx = 10, bary = 12`, V(X) = 9
             `σ_y` and r = 0.6
∵ V(X) = 9
∴ `σ_x = sqrt ( V(X) ) = sqrt9 = 3`

`b_yx = r. (σ_y)/(σ_x)`

         = `0.6 xx 4/3`  = 0.8

Regression line of y on x is
`y - bary = b_(yx) ( x - barx )`

y - 12 = 0.8 ( x - 10 )

y = 12 + 0.8x - 8

y = 4 + 0.8x

If x = 5 then

y = 4 + 0.8 (5) 
y = 4 + 4 
y = 8