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

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Question

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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Solution

Given:

`bar x = 53`,

`bar y = 28`,

byx = −1.2,

bxy = −0.3.

Correlation coefficient between x and y:

r = `+-sqrt("b"_"xy" * "b"_"yx")`

`= +- sqrt((-0.3)(-1.2))`

= `+- sqrt 0.36` 

= ± 0.6          ...[∵ byx and bxy are negative]

Since byx and bxy both are negative,

r is also negative.

∴ r = −0.6

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Properties of Regression Coefficients
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Chapter 3: Linear Regression - Exercise 3.2 [Page 47]

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