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

If for bivariate data x¯=10,y¯=12, v(x) = 9, σy = 4 and r = 0.6 estimate y, when x = 5.

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प्रश्न

If for bivariate data `bar x = 10, bar y = 12,` v(x) = 9, σy = 4 and r = 0.6 estimate y, when x = 5.

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उत्तर

Given, `bar x = 10, bar y = 12,` v(x) = 9, σy = 4, r = 0.6

∴ σx = 3

To estimate y, we should first find the regression equation of Y on X.

∴ `"b"_"YX" = "r" sigma_y/sigma_x = 0.6 xx 4/3 = 0.8`

Also, `"a" = bar "y" - "b"_"YX"  bar"x"`

= 12 - 0.8(10) = 12 - 8 = 4

The regression equation of Y on X is

Y = a + bYX X

∴ Y = 4 + 0.8 X

For X = 5,

Y = 4 + 0.8 (5) = 4 + 4 = 8

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पाठ 3: Linear Regression - Miscellaneous Exercise 3 [पृष्ठ ५४]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Linear Regression
Miscellaneous Exercise 3 | Q 4.03 | पृष्ठ ५४

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