Question

Calculate coefficient of correlation from the following data:

$x$	$y$
$3$	$15$
$10$	$17$
$8$	$4$
$6$	$5$
$8$	$4$

Answer 1

$x$	$y$	$x-\overline{x}$	$(y-\overline{y})$	$(x-\overline{x})(y-\overline{y})$	$(x-\overline{x}{)}^2$	$(y-\overline{y}{)}^2$
$3$	$15$	$-4$	$6$	$-24$	$16$	$36$
$10$	$17$	$3$	$8$	$24$	$9$	$64$
$8$	$4$	$1$	$-5$	$-5$	$1$	$25$
$6$	$5$	$-1$	$-4$	$4$	$1$	$16$
$8$	$4$	$1$	$-5$	$-5$	$1$	$25$

$\sum (x-\overline{x})(y-\overline{y})=-6,\sum (x-\overline{x}{)}^2=28$
$\sum x=35,\sum y=45$
$\sum (y-\overline{y}{)}^2=166$
$\overline{x}=7,\overline{y}=9$
$r_{xy}=\frac{\sum (x-\overline{x})(y-\overline{y})}{\sqrt{\sum (x-\overline{x}{)}^2}\sqrt{\sum (y-\overline{y}{)}^2}}$
$=\frac{-6}{\sqrt{28}\cdot \sqrt{166}}$
$=\frac{-6}{5.29\times 12.88}$
$=\frac{-6}{68.13}$
$=-0.088$ Approx.