What is the correlation coefficient with the following data points: (1,14), (3,10), (5,16) 0.1 0.2 0.3 0.4

Question

asked Dec 13, 2019 13.9k views

2 Answers

KHibma · Answer 1 · 2019-12-17T18:34:47+0000

Answer:

Option 3 - 0.3

Explanation:

Given : Data points : (1,14), (3,10), (5,16).

To find : What is the correlation coefficient with the following data points?

Solution :

Let X= 1,3,5

And Y=14,10,16

N is the number of points i.e, N=3

The formula of correlation coefficient is

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

Now, we find term by term

$\sum x = 1+3+5=9$

$\sum y = 14+10+16=40$

$\sum xy =14+30+80=124$

$\sum x^(2)= 1+9+25=35$

$\sum y^(2)=196+100+256=552$

Substitute all the values in the formula,

$r=\frac{3(124)-(9)(40)}{\sqrt{{(3(35)-(9)^(2))(3(552)-(40)^(2))}}}$

$r=\frac{372-360}{\sqrt{{(105-81)(1656-1600)}}}$

$r=\frac{12}{\sqrt{{(24)(56)}}}$

r=(12)/(√(1344))

r=(12)/(36.66)

r=0.32

Therefore, The correlation coefficient is 0.3.

So, option 3 is correct.