A set of n = 5 pairs of X and Y values has SS_X = 16,SS_Y = 4 and SP = 2.For these data,what is the Pearson correlation ? A)r = 2/64 B)r = 2/8 C)r = $\surd$2/8 D)r = 64/64

Question

Quizplus · Accepted Answer

The formula for Pearson correlation is: 
r = (SSxy / √(SSxx * SSyy))
where SSxy is the sum of squares of the differences between each X and Y value, SSxx is the sum of squares of the differences between each X value and the mean of X, and SSyy is the sum of squares of the differences between each Y value and the mean of Y.

Using the given values:
SSxy = SSS1U1B1XS1U1B0 - ((SP * SSS1U1B1YS1U1B0)/n) = 16 - ((2 * 4)/5) = 14.2
SSxx = SSS1U1B0XS1U1B0 - ((SP * SP)/n) = 16 - ((2*2)/5) = 15.2
SSyy = SSS1U1B0YS1U1B0 - ((SP * SP)/n) = 4 - ((2*2)/5) = 3.2

Plugging in these values:
r = (14.2 / √(15.2 * 3.2)) = 2/8

Thus, the answer is B.

A Set of N = 5 Pairs of X and Y