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

For a bivariate data: ∑(x-x¯)2 = 1200, ∑(y-y¯)2 = 300, ∑(x-x¯)(y-y¯) = – 250 Find: byx bxy Correlation coefficient between x and y.

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प्रश्न

For a bivariate data:

`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

Find: 

  1. byx
  2. bxy
  3. Correlation coefficient between x and y.
बेरीज
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उत्तर

Given the following values for a set of bivariate data:

`sum (x-barx)^2 = 1200`

`sum (y-bary)^2 = 300`

`sum (x-barx)(y-bary) = -250`

Regression Coefficients

`b_(yx) = (sum (x-barx)(y-bary))/(sum(x-barx)^2)`

`b_(xy) = (sum (x-barx)(y-bary))/(sum(y-bary)^2)`

`b_(yx) = (-250)/1200 = -25/120 = -0.2083`

`b_(xy) = (-250)/300 = -25/30 = -0.8333`

`r = sqrt(b_(yx)xxb_(xy)) = sqrt((-0.2083) xx (-0.8333)) = sqrt0.1736 = 0.4166`

r = −0.4166

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Properties of Regression Coefficients
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