Question

A survey of 50 families to study the relationships between expenditure on accommodation in (₹ x) and expenditure on food and entertainment (₹ y) gave the following results:

`sumx = 8500, sumy = 9600`, σ_x = 60, σ_y = 20, r = 0.6

Estimate the expenditure on food and entertainment when expenditure on accommodation is ₹ 200.

Answer 1

Given: `barx = (sumx)/n = 170`, `bary = (sumy)/n = 192`

r = 0.6, σ_x = 60, σ_y = 20

Regression coefficient of y on x:

`b_(yx) = rσ_y/σ_x`

= `0.6 xx 20/60`

= `0.6 xx 1/3`

= 0.2

Regression equation of y on x:

`y - bary = b_(yx)(x - barx)`

⇒ y – 192 = 0.2(x – 170)

⇒ y – 192 = 0.2x – 34

⇒ y = 0.2x + 158

Putting x = 200:

y = 0.2(200) + 158

= 40 + 158

= 198

∴ Expenditure on food and entertainment is ₹ 198.