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Correlation — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsCorrelation6 Marks
Question
Calculate the correlation coefficient between X and Y and comment on their relationship.
X
 1
3
4
5
7
8
Y
2
6
8
10
14
16
✓

Answer

$X$
$Y$
$XY$
$X^2$
$Y^2$
1
2
2
1
4
3
6
18
9
36
4
8
32
16
64
5
10
50
25
100
7
14
98
49
196
8
16
128
64
256
$\sum\text{X}=8$
$\sum\text{Y}=56$
$\sum\text{XY}=328$
$\sum\text{X}^2=164$
$\sum\text{Y}^2=656$
$\text{r}=\frac{\sum\text{XY}-\frac{\big(\sum\text{X}\big)\big(\sum\text{Y}\big)}{\text{N}}}{\sqrt{\sum\text{X}^2-\frac{\big(\sum\text{X}^2\big)}{\text{N}}}\sqrt{\sum\text{Y}^2-\frac{\big(\sum\text{Y}\big)^2}{\text{N}}}}$
$=\frac{328-\frac{28\times56}{6}}{\sqrt{164-\frac{(28)^2}{6}}\sqrt{656-\frac{(56)^2}{6}}}$
$=\frac{328-\frac{1568}{6}}{\sqrt{164-\frac{784}{6}}\sqrt{656-\frac{3136}{6}}}$
$=\frac{328-261.33}{\sqrt{164-130.67}\sqrt{656-522.67}}$
$=\frac{66.67}{\sqrt{33.33}\sqrt{133.33}}$
$=\frac{66.67}{5.77\times11.55}$
$=\frac{66.6}{66.6}$
$=1.00$
$=1$
As the correlation coefficient between the two variables is +1, so the two variables are perfectly positive correlated.

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