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Question
Calculate the correlation coefficient from the following data:
∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520, N = 25
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Solution
Given ∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520, N = 25
Correlation coefficient
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))`
= `(25(520) - (125)(100))/(sqrt(25(650) - (125)^2) xx sqrt(25(436) - (100)^2))`
= `(13000 - 12500)/(sqrt(16250 - 15625) xx sqrt(10900 - 10000))`
= `500/(sqrt625 xx sqrt900)`
= `500/((25)(30))`
= `500/750`
r = 0.667
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