Question

Find the coefficient of correlation from the following data.

$x$	$-10$	$-5$	$0$	$5$	$10$
$y$	$5$	$9$	$7$	$11$	$13$

Answer 1

$n=5$

$x$	$y$	$x-\overline{x}$	$y-\overline{y}$	$(x-\overline{x})(y-\overline{y})$	$(x-\overline{x}{)}^2$	$(y-\overline{y}{)}^2$
$-10$	$5$	$-10$	$-4$	$40$	$100$	$16$
$-5$	$9$	$-5$	$0$	$0$	$25$	$0$
$0$	$7$	$0$	$-2$	$0$	$0$	$4$
$5$	$11$	$5$	$2$	$10$	$25$	$4$
$10$	$13$	$10$	$4$	$40$	$100$	$16$
$\sum x=0$	$\sum y=45$			$\sum (x-\overline{x})(y-\overline{y})=90$	$\sum (x-\overline{x}{)}^2=250$	$\sum (y-\overline{y}{)}^2=40$

$\overline{x}=\frac{\sum x}{n}=\frac{0}{5}=0$
$\overline{y}=\frac{\sum y}{n}=\frac{45}{5}=9$
Coefficient of correlation $r=\frac{\sum (x-\overline{x})(y-\overline{y})}{\sqrt{\sum (x-\overline{x}{)}^2}\sqrt{\sum (y-\overline{y}{)}^2}}$
$=\frac{\sqrt{90}}{\sqrt{250}\sqrt{40}}$
$=\sqrt{\frac{90}{10000}}$
$=\frac{90}{100}$
$=0.9$