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Question
Find correlation coefficient between x and y series for the following data.
n = 15, `bar"x"` = 25, `bar"y"` = 18, σx = 3.01, σy = 3.03, `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122
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Solution
here, n = 15, `bar"x"` = 25, `bar"y"` = 18, σx = 3.01, σy = 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) = `1/15 xx 122`
= 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
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