Question

Calculate the correlation coefficient between X and Y and comment on their relationship.

$\begin{array}{ccccccc}X& -3& -2& -1& 1& 2& 3\\ Y& 9& 4& 1& 1& 4& 9\end{array}$

Answer 1

$\begin{array}{ccccc}X& Y& XY& X^2& Y^2\\ -3& 9& -27& 9& 81\\ -2& 4& -8& 4& 16\\ -1& 1& -1& 1& 1\\ 1& 1& 1& 1& 1\\ 2& 4& 8& 4& 16\\ 3& 9& 27& 9& 81\\ \sum X=0& \sum Y=28& \sum XY=0& \sum X^2=28& \sum Y^2=196\end{array}$

$r=\frac{\sum XY-\frac{(\sum X)(\sum Y)}{N}}{\sqrt{\sum X^2-\frac{(\sum X{)}^2}{N}}\sqrt{\sum Y^2-\frac{(\sum Y{)}^2}{N}}}$

$=\frac{0-\frac{0\times 28}{6}}{\sqrt{28-\frac{(28{)}^2}{6}}\sqrt{196-\frac{(196{)}^2}{6}}}$

$=\frac{0}{\sqrt{28-\frac{(28{)}^2}{6}}\sqrt{196-\frac{(196{)}^2}{6}}}$

As the value of r is zero, so there is no linear correlation between X and Y.