Find correlation coefficient between x and y series for the following data.n = 15, x¯ = 25, y¯ = 18, σx = 3.01, σy = 3.03, ∑(xi-x¯)(yi-y¯) = 122 - Mathematics and Statistics

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Sum

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) = `1/15xx122`

= 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

Concept: Concept of Correlation Coefficient
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Chapter 5: Correlation - Exercise 5.1 [Page 63]

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