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Question
The correlation coefficient from the following data N = 25, ∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520
Options
0.667
− 0.006
– 0.667
0.70
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Solution
0.667
Explanation:
r = `("N"sum"XY" - sum"X"sum"Y")/(sqrt("N"sum"X"^2 - (sum"X")^2) sqrt("N"sum"Y"^2 - (sum"Y")^2))`
= `(25(520) - 125 xx 100)/(sqrt(25 xx 650 - (125)^2) sqrt(25 xx 436 - (100)^2))`
= `(13000 - 12500)/(sqrt(16250 - 15625) sqrt(10900 - 10000))`
= `500/(sqrt625 sqrt900)`
= `500/(25 xx 30)`
= `2/3`
= 0.6666
= 0.667
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