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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.
Solution
`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300
`sum(x - overlinex)(y - overliney)` = – 250
cov (x, y) = `(sum(x - overlinex).(y - overliney))/n`
= `(-250)/n`
(σx)2 = `sqrt((sum(x - overlinex)^2)/n`
= `sqrt(1200/n)`
= `1200/n`
(σy)2 = `sqrt((sum(y - overliney)^2)/n`
= `sqrt(300/n)`
= `300/n`
byx = `(cov (x, y))/(σ_x)^2`
= `((-250)/n)/(1200/n)`
= `(-5)/60`
byx = `(-1)/12`
bxy = `(cov (x, y))/(σ_y)^2`
= `((-250)/n)/(300/n)`
bxy = `(-5)/6`
r = `±sqrt(b_(yx) . b_(xy))`
= `-sqrt((-1)/12 xx (-5)/6)`
= `-sqrt(5/72)`
= `-sqrt(0.07)`
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