Question

Using the following information you are requested to

1. obtain the linear regression of Y on X
2. Estimate the level of defective parts delivered when inspection expenditure amounts to ₹ 82
   ∑X = 424, ∑Y = 363, ∑X² = 21926, ∑Y² = 15123, ∑XY = 12815, N = 10.
   Here X is the expenditure on inspection, Y is the defective parts delivered.

Answer 1

Given ∑X = 424, ∑Y = 363, ∑X² = 21926, ∑Y² = 15123, ∑XY = 12815, N = 10.

`bar"X" = (sum"X")/"N" = 424/10` = 42.4

`bar"Y" = (sum"Y")/"N" = 363/10` = 36.3

Regression coefficient of Y on X is

b_yx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)`

= `(10(12815) - (424)(363))/(10(21926) - (424)^2)`

= `(128150 - 153912)/(219260 - 179776)`

= `(-25762)/39484`

= − 0.652

∴ Regression line of Y on X is

`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`

Y − 36.3 = − 0.652 (X − 42.4)

Y − 36.3 = − 0.652X + 27.645

Y = − 0.652X + 63.945

When X = 82, Y = − 0.652(82) + 63.945

Y = − 53.464 + 63.945

Y = 10.481

Y ≈ 10