Question

For 5 observations of pairs (x, y) of variables X and Y, the following results are obtained:

∑x = 15, ∑y = 25, ∑x² = 55, ∑y² = 135, ∑xy = 83.

Calculate the value of b_xy and b_yx.

Answer 1

We have,

n = 5, ∑x = 15, ∑y = 25, ∑x² = 55, ∑y² = 135, ∑xy = 83

We know that,

b_xy = `(∑"xy" - (∑"x".∑"y")/"n")/(∑"y"^2 - (∑"y")^2/"n")`

or b_xy = `("n"∑"xy" - ∑"x". ∑"y")/("n"∑"y"^2 - (∑"y")^2)`

= `(5 xx 83 - 15 xx 25)/(5 xx 135 - (25)^2)`

= `(415 - 375)/(675 - 625)`

= `40/50`

= `4/5`

⇒ b_xy = 0.8

Now, b_yx = `("n"∑"xy" - ∑"x". ∑"y")/("n"∑"x"^2 - (∑"x")^2)`

= `(5 xx 83 - 15 xx 25)/(5 xx 55 - (15)^2)`

= `(415 - 375)/(275 - 225)`

= `40/50`

= `4/5`

= 0.8