Question

What is the correlation coefficient with the following data points:
(1,6), (3,2), (7,5), (6,2)?

A.) 0.27
B.) -0.27
C.) 0.28
D.) -0.28

Answer 1

Answer:

Option D → -0.28                                                                                Step-by-step explanation:

Given : Data points : (1,6), (3,2), (7,5), (6,2)

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

Solution :

Let x= 1,3,7,6

And y=6,2,5,2

N is the number of points i.e, N=4

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

$\sum x = 1+3+7+6=17$

$\sum y = 6+2+5+2=15$

$\sum xy = 6+6+35+12=59$

$\sum x^{2}= 1+9+49+36=95$

$\sum y^{2}=36+4+25+4=69$

Substitute all the values in the formula,

$r=\frac{4(59)-(17)(15)}{\sqrt{{(4(95)-(17)^{2})(4(69)-(15)^{2})}}}$

$r=\frac{236-255}{\sqrt{{(380-289)(276-225)}}}$

$r=\frac{-19}{\sqrt{{(91)(51)}}}$

$r=\frac{-19}{\sqrt{4641}}$

$r=\frac{-19}{68.12}$

$r=-0.278$

$r\approx -0.28$

Therefore, The correlation coefficient is -0.28.

So, Option D is correct.