Question

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

0.1
0.2
0.3
0.4

Answer 1

The correct answer is 0.3
Hope this helps you

Answer 2

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.