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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.
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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