Maharashtra State BoardHSC Commerce 12th Board Exam
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Given the following information about the production and demand of a commodity obtain the two regression lines: Coefficient of correlation between X and Y is 0.6. - Mathematics and Statistics

Sum

Given the following information about the production and demand of a commodity obtain the two regression lines:

  X Y
Mean 85 90
S.D. 5 6

The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.

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Solution

Given, `bar x = 85, bar y = 90, sigma_"X" = 5, sigma_"Y" = 6`, r =0.6

`"b"_"YX" = "r" sigma_"Y"/sigma_"X" = 0.6 xx 6/5 = 0.72`

`"b"_"XY" = "r" sigma_"X"/sigma_"Y" = 0.6 xx 5/6 = 0.5`

The regression equation of Y on X is

`("Y" - bar y) = "b"_"YX" ("X" - bar x)`

(Y - 90) = 0.72 (X - 85)

Y - 90 = 0.72 X - 61.2

Y = 0.72X - 61.2 + 90

Y = 28.8 + 0.72 X           ....(i)

The regression equation of X on Y is

`("X" - bar x) = "b"_"XY" ("Y" - bar y)`

(X - 85) = 0.5(Y - 90)

X - 85 = 0.5 Y - 45

X = 0.5 Y - 45 + 85

X = 40 + 0.5Y            ....(ii)

For Y = 100, from equation (ii) we get

X = 40 + 0.5(100) = 40 + 50 = 90

∴ The production is 90 when demand is 100.

Notes

[Note: Answer in the textbook is incorrect.]

Concept: Properties of Regression Coefficients
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