Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# 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: - Business Mathematics and Statistics

Sum

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.

#### 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

Concept: Regression Analysis
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Chapter 9: Correlation and Regression Analysis - Exercise 9.2 [Page 227]