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.

Answer 1

`bar"X"` = 178, `bar"Y"` = 47.8, σ_x = 63.15, σ_y = 22.98, r = 0.43

b_yx = `"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