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

The equations of two regression lines are2x + 3y − 6 = 0and 2x + 2y − 12 = 0 Find Correlation coefficient σXσY - Mathematics and Statistics

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प्रश्न

The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find 

  1. Correlation coefficient
  2. `sigma_"X"/sigma_"Y"`
बेरीज
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उत्तर

The given regression equations are
2x + 3y – 6 = 0 and 3x + 2y − 12 = 0

(i) 2x + 3y = 6

3y = – 2x + 6

`y = (– 2)/3x + 2`

`b_( yx)  = (-2)/3`

3x + 2y = 12

3x = – 2y = 12

`x = (-2)/3y + 4`

`b_(xy) = (-2)/3`

`b_( yx).b_(xy) = (-2)/3 xx (-2)/3 = 4/9 ∈ [0, 1]`

∴ Our assumption is correct.

∴ `r^2 = b_( yx).b_(xy)`

`r^2 = 4/9`

`r = ±2/3`

Since `b_( yx)` and `b_(xy)` are negative ∴ r =`(-2)/3`

(ii) `b_(xy) = (r . sigma_y)/sigma_x`

`(-2)/3 = (-2)/3 . sigma_x/sigma_y`

∴ `sigma_x/sigma_y = 1`

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Properties of Regression Coefficients
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Linear Regression - Exercise 3.3 [पृष्ठ ५०]

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