Question

Use a calculator to verify that Σx = 128, Σx2 = 6272, Σy = 150, Σy2 = 4778, and Σxy = 2966. Compute r. (Round your answer to three decimal places.)

Sample size n = 5

Answer 1

SOLUTION:

From given data,

Use a calculator to verify that Σx = 128, Σx2 = 6272, Σy = 150, Σy2 = 4778, and Σxy = 2966. Compute r. (Round your answer to three decimal places.)

Sample size n = 5

Σx = 128

Σx² = 6272

Σy = 150

Σy² = 4778

Σxy = 2966

Sample size = n = 5

r = Cov(x,y) / sqrt(Var(x))*sqrt(Var(y))

r = (1/n)*Σxy - / sqrt((1/n)*Σ(x-)²)*sqrt((1/n)*Σ(y-)²)

Where,

= Σx / n = 128/5 = 25.6

= Σy / n = 150/5 = 30

Similarly,

(1/n)*Σ(x-)² = (1/n)*Σ(x²+² - 2x )

= (1/n)*Σ(x²+² - 2 ²)

= (1/n)*Σ(x²-²)

= 6272/5 - (128/5)²

Similarly,

(1/n)*Σ(y-)² = (1/n)*Σ(y²+² - 2y )

= (1/n)*Σ(y²+² - 2 ²)

= (1/n)*Σ(y²-²)

= 4778/5 - (150/5)²

r = (1/n)*Σxy - / sqrt((1/n)*Σ(x-)²)*sqrt((1/n)*Σ(y-)²)

r = (1/5)*2966 - (128/5)*(150/5 ) / sqrt( (6272/5) - (128/5)²)*sqrt((4778/5) - (150/5)²)

r = 593.2 - 768 / sqrt( 1254.4 - 655.36)*sqrt(955.6 - 900)

r = -174.8 / (24.475293665*7.4565407529)

r = -174.8 / 182.50102465

r = - 0.9578028

r = - 0.957 (round to 3 decimal places)