Question

Calculate the coefficient of correlation from the following data:

$\begin{array}{cccccc}X& 30& 40& 60& 70& 100\\ Y& 90& 110& 140& 150& 160\end{array}$

Answer 1

$\begin{array}{ccccccc}X& \overline{X}=60& x^2& Y& \overline{Y}=130& y^2& xy\\ & x=X-\overline{X}& & y=Y-\overline{Y}& & & \\ 30& -30& 900& 90& -40& 1600& 1200\\ 40& -20& 400& 110& -20& 400& 400\\ 60& 0& 0& 140& +10& 100& 0\\ 70& +10& 100& 150& +20& 400& 200\\ 100& +40& 1600& 160& +30& 900& 1200\\ \sum X=300& \sum x=0& \sum x^2=3000& \sum Y=650& \sum y=0& \sum y^2=3400& \sum xy=3000\\ N=5& & & & & & \end{array}\overline{X}=\frac{\sum X}{N}=\frac{300}{5}=60;\overline{Y}=\frac{\sum Y}{N}=\frac{650}{5}=130.r=\frac{\sum (X-\overline{X})(Y-\overline{Y})}{\sqrt{\sum (X-\overline{X}{)}^2}\sqrt{\sum (Y-\overline{Y}{)}^2}}$

or $\frac{\sum xy}{\sqrt{\sum x^2}\sqrt{\sum y^2}}=\frac{3000}{\sqrt{3000}\sqrt{3400}}=\frac{3000}{3193.74}=0.94$