Question

Find the coefficient of correlation from the following data.

$x$	$2$	$3$	$5$	$7$	$3$
$y$	$15$	$17$	$4$	$5$	$4$

Answer 1

$n=5$

$x$	$y$	$x-\overline{x}$	$y-\overline{y}$	$(x-\overline{x})(y-\overline{y})$	$(x-\overline{x}{)}^2$	$(y-\overline{y}{)}^2$
$2$	$15$	$-2$	$6$	$-12$	$4$	$36$
$3$	$17$	$-1$	$8$	$-8$	$1$	$64$
$5$	$4$	$1$	$-5$	$-5$	$1$	$25$
$7$	$5$	$3$	$-4$	$-12$	$9$	$16$
$3$	$4$	$-1$	$-5$	$5$	$1$	$25$
$\sum x=20$	$\sum y=45$			$\sum (x-\overline{x})(y-\overline{y})=-32$	$\sum (x-\overline{x}{)}^2=16$	$\sum (y-\overline{y}{)}^2=166$

$\overline{x}=\frac{\sum x}{n}=\frac{20}{5}=4$
$\overline{y}=\frac{\sum y}{n}=\frac{45}{5}=9$
Coefficient of correlation $r=\frac{\sum (x-\overline{x})(y-\overline{y})}{\sqrt{\sum (x-\overline{x}{)}^2}\sqrt{\sum (y-\overline{y}{)}^2}}$
$=\frac{-32}{\sqrt{16}\sqrt{166}}$
$=\frac{-32}{4\times 12.8841}$
$=\frac{-32}{51.5364}$
$=-0.64$.