Question

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

Answer 1

Answer:

A. 0.75  

Step-by-step 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

$r =\frac{4\times1118-51\times84}{\sqrt{[4\times659-2601][4\times2216-7056]}}$

$r =\frac{4472-4284}{\sqrt{[2636-2601][8864-7056]}}$

$r =\frac{188}{\sqrt{35\times1808}}$

$r =\frac{188}{\sqrt{63280}}$

$r =\frac{188}{251.6}$

r = 0.747

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