Maharashtra State BoardHSC Commerce 12th Board Exam
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For bivariate data. x¯=53,y¯=28,bYX=-1.2,bXY=-0.3 Find estimate of X for Y = 25. - Mathematics and Statistics

Sum

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.

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Solution

Here, `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3`

The regression equation of X on Y is

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

∴ (X - 53) = (- 0.3)(Y - 28)

∴ X - 53 = - 0.3 Y + 8.4

∴ X = - 0.3 Y + 8.4 + 53

∴ X = - 0.3 Y + 61.4

For Y = 25

∴ X = - 0.3(25) + 61.4 = - 7.5 + 61.4 = 53.9

Concept: Properties of Regression Coefficients
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