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Question
An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment (₹ y) gave the following results:
∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6
Estimate the expenditure on food and entertainment when expenditure on accommodation is Rs 200.
Solution
X = Expenditure on accommodation.
Y = Expenditure on food and entertainment
Given, ∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6, n = 50
∴ `bar x = (sum x)/"n" = 8500/50 = 170`
`bar y = (sum y)/"n" = 9600/50 = 192`
Now, `"b"_"YX" = "r" sigma_"Y"/sigma_"X" = 0.6 xx 20/60 = 0.2`
Also, `"a" = bar y - "b"_"YX" bar x`
= 192 - 0.2 × 170 = 192 - 34 = 158
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 158 + 0.2 X
For X = 200,
Y = 158 + 0.2 × 200 = 158 + 40 = 198
∴ The expenditure on food and entertainment is
₹ 198 when expenditure on accommodation is ₹ 200.
Notes
The answer in the textbook is incorrect.
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