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Question
Calculate the coefficient of correlation from the following data:
∑X = 50, ∑Y = – 30, ∑X2 = 290, ∑Y2 = 300, ∑XY = – 115, N = 10
Solution
∑X = 50, ∑Y = – 30, ∑X2 = 290, ∑Y2 = 300, ∑XY = – 115, N = 10
Coefficient of correlation
r(X, Y) = `("N"sum"XY" - (sum"X")(sum"Y"))/(sqrt("N"sum"X"^2 - (sum"X")^2) xx sqrt("N"sum"Y"^2 - (sum"Y")^2))`
= `(10(-115) - (50)(-30))/(sqrt(10(290) - (50)^2) xx sqrt(10(300) - (-30)^2))`
= `(-1150 + 1500)/((20)(sqrt2100))`
= `350/((20)(45.83))`
= `350/916.6`
r = 0.382
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