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
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{(n\sum x^{2}-(\sum x)^{2})(n\sum y^{2}-(\sum y)^{2})}}}[/tex]
Now, we find term by term
[tex]\sum x = 1+3+7+6=17[/tex]
[tex]\sum y = 6+2+5+2=15[/tex]
[tex]\sum xy = 6+6+35+12=59[/tex]
[tex]\sum x^{2}= 1+9+49+36=95[/tex]
[tex]\sum y^{2}=36+4+25+4=69[/tex]
Substitute all the values in the formula,
[tex]r=\frac{4(59)-(17)(15)}{\sqrt{{(4(95)-(17)^{2})(4(69)-(15)^{2})}}}[/tex]
[tex]r=\frac{236-255}{\sqrt{{(380-289)(276-225)}}}[/tex]
[tex]r=\frac{-19}{\sqrt{{(91)(51)}}}[/tex]
[tex]r=\frac{-19}{\sqrt{4641}}[/tex]
[tex]r=\frac{-19}{68.12}[/tex]
[tex]r=-0.278[/tex]
[tex]r\approx -0.28[/tex]
Therefore, The correlation coefficient is -0.28.
So, Option D is correct.
