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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

For bivariate data. x¯=53,y¯=28,bYX=-1.2,bXY=-0.3 Find estimate of Y for X = 50.

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प्रश्न

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.

बेरीज
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उत्तर

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

The regression equation of Y on X is

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

∴ (Y - 28) = (- 1.2)(X - 53)

∴ Y - 28 = - 1.2 X + 63.6

∴ Y = - 1.2 X + 63.6 + 28

∴ Y = - 1.2 X + 91.6

For X = 50

∴ Y = - 1.2(50) + 91.6 = - 60 + 91.6 = 31.6

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Properties of Regression Coefficients
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पाठ 3: Linear Regression - Exercise 3.2 [पृष्ठ ४७]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Linear Regression
Exercise 3.2 | Q 1.2 | पृष्ठ ४७

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