Question

Find correlation coefficient between x and y series for the following data.
n = 15, `bar"x"` = 25, `bar"y"` = 18, σ_x = 3.01, σ_y = 3.03, `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122

Answer 1

here, n = 15, `bar"x"` = 25, `bar"y"` = 18, σ_x = 3.01, σ_y = 3.03, and `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122

Since, Cov (x, y) = `1/"n" sum_("i"=1)^"n"("x"_"i"-bar"x")("y"_"i"-bar"y")`

∴ Cov (x, y) = `1/15xx122`

= 8.13
Since, r  = `("Cov"("x","y"))/(sigma_"x"sigma_"y")`

∴ = `8.13/(3.01 xx 3.03)`

= `8.13/9.1203`
∴ r = 0.89