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Question
A survey was conducted to study the relationship between expenditure on accommodation (X) and expenditure on Food and Entertainment (Y) and the following results were obtained:
| Details | Mean | SD |
| Expenditure on Accommodation (₹) | 178 | 63.15 |
| Expenditure on Food and Entertainment (₹) | 47.8 | 22.98 |
| Coefficient of Correlation | 0.43 | |
Write down the regression equation and estimate the expenditure on Food and Entertainment, if the expenditure on accommodation is ₹ 200.
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Solution
`bar"X"` = 178, `bar"Y"` = 47.8, σx = 63.15, σy = 22.98, r = 0.43
byx = `"r"(sigma_"y")/(sigma_"x") = 0.43 xx 22.98/63.15` = 0.1565
Regression line of Y on X:
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y – 47.8 = 0.1565(X – 178)
Y = 0.1565X – 27.857 + 47.8
Y = 0.1565X + 19.94
When the expenditure on accommodation is ₹ 200 the expenditure on food and entertainments is,
Y = 0.1565X + 19.94
Y = 0.1565(200) + 19.94
= 31.3 + 19.94
= ₹ 51.24
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