Question

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

Answer 1

Answer:

Option 3 - 0.3

Step-by-step 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,

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

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

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

$r=\frac{12}{\sqrt{1344}}$

$r=\frac{12}{36.66}$

$r=0.32$

Therefore, The correlation coefficient is 0.3.

So, option 3 is correct.    

Answer 2

The correct answer is 0.3
Hope this helps you