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Question
For a bivariate data:
`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250
Find:
- byx
- bxy
- Correlation coefficient between x and y.
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Solution
Given the following values for a set of bivariate data:
`sum (x-barx)^2 = 1200`
`sum (y-bary)^2 = 300`
`sum (x-barx)(y-bary) = -250`
Regression Coefficients
`b_(yx) = (sum (x-barx)(y-bary))/(sum(x-barx)^2)`
`b_(xy) = (sum (x-barx)(y-bary))/(sum(y-bary)^2)`
`b_(yx) = (-250)/1200 = -25/120 = -0.2083`
`b_(xy) = (-250)/300 = -25/30 = -0.8333`
`r = sqrt(b_(yx)xxb_(xy)) = sqrt((-0.2083) xx (-0.8333)) = sqrt0.1736 = 0.4166`
r = −0.4166
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