Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# You are given the following data: Details X Y Arithmetic Mean 36 85 Standard Deviation 11 8 If the Correlation coefficient between X and Y is 0.66, then find the two regression coefficients, the most - Business Mathematics and Statistics

Sum

You are given the following data:

 Details X Y Arithmetic Mean 36 85 Standard Deviation 11 8

If the Correlation coefficient between X and Y is 0.66, then find

1. the two regression coefficients,
2. the most likely value of Y when X = 10.

#### Solution

bar"X" = 36, bar"Y" = 85, σx = 11, σy = 8, r = 0.66

(i) The two regression coefficients are,

byx = "r"(sigma_"y")/(sigma_"x") = 0.66 xx 8/11 = 0.48

bxy = "r"(sigma_"x")/(sigma_"y") = 0.66 xx 11/8 = 0.9075 = 0.91

(ii) Regression equation of X on Y:

"X" - bar"X" = "b"_"xy"("Y" - bar"Y")

X – 36 = 0.91(Y – 85)

X – 36 = 0.91Y – 77.35

X = 0.91Y – 77.35 + 36

X = 0.91Y – 41.35

Regression line of Y on X:

"Y" - bar"Y" = "b"_"yx"("X" - bar"X")

Y – 85 = 0.48(X – 36)

Y = 0.48X – 17.28 + 85

Y = 0.48X + 67.72

The most likely value of Y when X = 10

Y = 0.48(10) + 67.72 = 72.52

Concept: Regression Analysis
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