What is the correlation coefficient with the following data points: (2,26), (3,2), (5,16) 0.14 -0.24 0.24 -0.14

Question

asked Jun 12, 2019 135k views

2 Answers

Nevermore · Answer 1 · 2019-06-16T10:03:19+0000

The correlation coefficient is calculated by the given formula

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

Here we have to find correlation coefficient for three ordered pairs, so n=3

$\sum x = 2+3+5=10$

$\sum y = 26+2+16=44$

$\sum xy = 52+6+80 =138$

$\sum x^(2) = 4+9+25 =38$

$\sum y^(2) =676+4+256 =936$

Substituting all the values in the above formula,

r=(3(138)-440)/(√((38(3)-100)(3(936)-1936)))

r= (-26)/(√(14 * 872))

r= -0.24