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Question
Calculate the coefficient of correlation between X and Y series from the following data :
`n = 15 ,bar x = 25, bary = 18, σ_x = 3.01, σ_y = 3.03,`
`sum ("x"_i - bar x) ("y"_i - bar y) = 122`
Solution
Given that
n = 15 ; `bar x = 25, bary = 18 . σ_x = 3.01; σ_y = 3.03,`
`sum ("x"_1 - bar x) ("y"_1 - bar y) = 122`
r = `("Cov" (x , y))/[ (sigma x sigma y) ]`
= `[ sum ("x"_1 - bar x) ("y"_1 - bar y) ]/[ n . (sigma_x sigma_y) ]`
= `122/( 15 xx 3.01 xx 3.03)`
r = `[8.133]/[9.1203]`
Taking log of both sides we get,
log r = log 8.133 - log 9.1203
= 0.9103 - 0.9600
log r = `bar1 .9503`
r = antilog( `bar1 .9503` )
r = 0.8917
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