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Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficients.

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Question

The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficients.

Sum
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Solution

Let regression line of Y on X be,

2Y = 5 – X

Y = – 0.5X + 2.5

byx = – 0.5

i.e., byx = `-1/2`

Let regression line of X on Y be

2X = 8 – 3Y

X = – 1.5Y + 4

bxy = – 1.5

i.e., bxy = `-3/2`

Correlation coefficient (r) = `± sqrt("b"_"xy" xx "b"_"yx")`

= `± sqrt(1.5 xx 0.5)`

= – 0.866

Both bxy and byx is negative so take a negative sign.

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Regression Analysis
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Chapter 9: Correlation and Regression Analysis - Exercise 9.2 [Page 227]

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Samacheer Kalvi Business Mathematics and Statistics [English] Class 11 TN Board
Chapter 9 Correlation and Regression Analysis
Exercise 9.2 | Q 12 | Page 227

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