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

The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Find the value of the correlation coefficient (Given0.933=0.9667) - Mathematics and Statistics

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प्रश्न

The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Find the value of the correlation coefficient `("Given"  sqrt(0.933) = 0.9667)`

बेरीज
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उत्तर

r = `+-  sqrt("b"_(xy) * "b"_(yx))`

= `+-  sqrt((-7)/5 xx (-2)/3)`

= `+-  sqrt(0.933)`

= 0.9667

Since the values of bXY and bYX are negative,

r is also negative.

∴ r = – 0.9667

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Properties of Regression Coefficients
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.3: Linear Regression - Q.4

संबंधित प्रश्‍न

For bivariate data. `bar x = 53`, `bar y = 28`, byx = −1.2, bxy = −0.3. Find the correlation coefficient between x and y.


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bYX = 1.9 and bXY = - 0.25


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bYX = 2.6 and bXY = `1/2.6`


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Mean 25 20
S.D. 4 3

And r = 0.5. Estimate y when x = 10 and estimate x when y = 16


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Mean 40 6
S.D. 10 1.5

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For certain bivariate data the following information is available.

  X Y
Mean 13 17
S.D. 3 2

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For a bivariate data, `bar x = 53`, `bar y = 28`, byx = −1.5 and bxy = −0.2. Estimate y when x = 50.


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The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
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If byx < 0 and bxy < 0, then r is ______


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∴ y = `square`

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∴ x = `square`


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∴ byx = `square/square`

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`sum(x_i - barx)(y_i - bary)` = 1170


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