Question

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

Answer 1

Answer:

Long answer short, its B: -0.24

Step-by-step explanation:

Answer 2

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,

$r=\frac{3(138)-440}{\sqrt{(38(3)-100)(3(936)-1936)}}$

$r= \frac{-26}{\sqrt{14 \times 872}}$

r= -0.24