# Calculate the correlation coefficient from the following data and interpret it. x 9 7 6 8 9 6 7 y 19 17 16 18 19 16 17 - Mathematics and Statistics

Sum

Calculate the correlation coefficient from the following data and interpret it.

 x 9 7 6 8 9 6 7 y 19 17 16 18 19 16 17

#### Solution

 xi yi xi2 yi2 xiyi 9 19 81 361 171 7 17 49 289 119 6 16 36 256 96 8 18 64 324 144 9 19 81 361 171 6 16 36 256 96 7 17 49 289 119 Total 52 122 396 2136 916

From the table, we have
n = 7, sum"x"_"i" = 52, sum"y"_"i" = 122, sum"x"_"i"^2 = 396, sum"y"_"i"^2 = 2136, sum"x"_"i""y"_"i" = 916

∴ bar"x" = (sum"x"_"i")/"n" = 52/7

bar"y" = (sum"y"_"i")/"n" = 122/7

∴ bar"x"bar"y"=(52xx122)/49 = 6344/49

Cov (X, Y) = 1/"n" sum"x"_"i""y"_"i" - bar"x" bar"y"

= 916/7-6344/49

= (6412-6344)/49

= 68/49

sigma_"x"^2 = (sum"x"_"i"^2)/"n" - (bar"x")^2

= 396/7 - (52/7)^2

= (8772-2704)/49

= 68/49

sigma_"y"^2 = (sum"y"_"i"^2)/"n" - (bar"y")^2

= 2136/7 - (122/7)^2

= (14952 - 14884)/49

= 68/49

∴ sigma_"x" sigma_"y" = sqrt(sigma_"x"^2 sigma_"y"^2)

= sqrt(68/49 xx 68/49)

= 68/49

r = ("Cov (X, Y)")/(sigma_"x" sigma_"y")

= ((68/49))/(68/49) = 1
∴ The value of r indicates perfect positive correlation between x and y.

Concept: Interpretation of Value of Correlation Coefficient
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