Question

12.3 Correlation Coefficient Calculation Based on the data shown below, calculate the correlation coefficient r (to three decimal places) 5 24 6 17 7 18 8 15 9 10 10 9 Get help: Read Points possible: 1 This is attempt 1 of 3. Message instructor about this question

Answer 1

Solution:

Given that,

x	y	x2	y2	xy
5	24	25	576	120
6	17	36	289	102
7	18	49	49	324
8	15	64	225	120
9	10	81	100	90
10	9	100	81	90
$\sum$x = 45	$\sum$y =93	$\sum$x2 =355	$\sum$y2 =1595	$\sum$xy =648

r = n ( $\sum$ xy )- ($\sum$x ) ($\sum$y) / $\sqrt{}$ n [ ( $\sum$ x² ) - ($\sum$ x )² ] $\sqrt{}$ [ n ($\sum$y² ) - ( $\sum$ y )²

^r = 6 (648) - (45 * 93 )$\sqrt{}$/ [ 6 * 355 - ( 45 ) ²  $\sqrt{}$ [ 6 * 1595 - ( 93 ) ² ]

r = 3888 - 4185/ $\sqrt{}$ 2130 - 2025  $\sqrt{}$9570- 8649

r = 297/  $\sqrt{}$105$\sqrt{}$921

r = 297 / 10.247 * 30.348

r = 297 / 310.9743

r = 0.955