Answer :
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
[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+5=9[/tex]
[tex]\sum y = 14+10+16=40[/tex]
[tex]\sum xy =14+30+80=124[/tex]
[tex]\sum x^{2}= 1+9+25=35[/tex]
[tex]\sum y^{2}=196+100+256=552[/tex]
Substitute all the values in the formula,
[tex]r=\frac{3(124)-(9)(40)}{\sqrt{{(3(35)-(9)^{2})(3(552)-(40)^{2})}}}[/tex]
[tex]r=\frac{372-360}{\sqrt{{(105-81)(1656-1600)}}}[/tex]
[tex]r=\frac{12}{\sqrt{{(24)(56)}}}[/tex]
[tex]r=\frac{12}{\sqrt{1344}}[/tex]
[tex]r=\frac{12}{36.66}[/tex]
[tex]r=0.32[/tex]
Therefore, The correlation coefficient is 0.3.
So, option 3 is correct.