Question

What is the correlation coefficient with the following data points: (15,36), (13,22), (12,6), (11,20)?

A.0.75

B.-0.75

C.0.65

D.-0.65

Answer 1

A. 0.75

Explanation:

The formula for the correlation coefficient r is

`r =\frac {n \sum{xy} - \sum{x}\sum{y}}{\sqrt{[n \sum{x^(2)}- (\sum{x})^(2)}][n \sum{y^(2)}- (\sum{y})^(2)]}`

It's easier to use a statistical calculator, but this question probably expects you to do it by hand.

Let’s write a table for easy calculation.

x y xy x² y²

15 36 540 225 1296

13 22 286 169 484

12 6 72 144 36

11 20 220 121 400

51 84 1118 659 2216

(Σx)² = 2601

(Σy)² = 7056

`r =(4*1118-51*84)/(√([4*659-2601][4*2216-7056]))`

`r =(4472-4284)/(√([2636-2601][8864-7056]))`

`r =(188)/(√(35*1808))`

`r =(188)/(√(63280))`

`r =(188)/(251.6)`

r = 0.747

The graph below shows that there is a poor correlation among the points.