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`

Answer 1

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