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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.
Solution
`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.
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