Question

(A) Use a calculator to verify that Σx = 23.6, Σx2 = 82.20, Σy = 54.1, Σy2 = 469.57 and Σxy = 188.40.

Compute r. (Round to 3 decimal places.)

(B) Use a calculator to verify that Σx = 130, Σx² = 6808, Σy = 149, Σy² = 4743, and Σxy = 2900

Compute r. (Round your answer to three decimal places)

sorry! for the problem that starts with the decimal 23.6 there n=7

for the one that starts with 130 n=5

Answer 1

Q1:

Ʃx = 23.6, Ʃy = 54.1, Ʃxy = 188.4, Ʃx² = 82.2, Ʃy² = 469.57

n = 7

SSxx = Ʃx² - (Ʃx)²/n = 82.2 - (23.6)²/7 = 2.63429

SSyy = Ʃy² - (Ʃy)²/n = 469.57 - (54.1)²/7 = 51.45429

SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 188.4 - (23.6)(54.1)/7 = 6.00571

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 6.00571/√(2.63429*51.45429) = 0.516

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Q2:

Ʃx = 130, Ʃy = 149, Ʃxy = 2900, Ʃx² = 6808, Ʃy² = 4743

n = 5

SSxx = Ʃx² - (Ʃx)²/n = 6808 - (130)²/5 = 3428

SSyy = Ʃy² - (Ʃy)²/n = 4743 - (149)²/5 = 302.8

SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 2900 - (130)(149)/5 = -974   

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = -974/√(3428*302.8) = -0.956