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.
