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

`barx = (sumx)/n = 170`,

`bary = (sumy)/n = 192`,

`b_(yx) = rσ_y/σ_x`

= `0.6 xx 20/60`

= 0.2

Regression equation y on x is

y − 192 = 0.2(x − 170)

`\implies` y − 192 = 0.2x − 34

`\implies` y = 0.2x + 158

Put x = 200

`\implies` y = 0.2(200) + 158 = 198

∴ Expenditure on food and entertainment = ₹ 198.