Question

The following sample observations were randomly selected.

x	5	3	6	3	4	4	6	8
y	13	15	7	12	13	11	9	5

  Click here for the Excel Data File

Determine the coefficient of correlation and the coefficient of determination. Interpret the association between x and y. (Round your coefficient of determination to 4 decimal places. Round all other answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

x	y		x−x¯x-x¯				y−y¯y-y¯				(x−x¯)2x-x¯2				(y−y¯)2y-y¯2				(x−x¯) (y−y¯)x-x¯ y-y¯
5	13							2.38				0.02				5.64				0.30
3	15							4.38				3.52				19.14
6	7			1.13								1.27				13.14				-4.08
3	12			-1.88								3.52				1.89
4	13			-0.88				2.38								5.64				-2.08
4	11			-0.88				0.38								0.14				-0.33
6	9			1.13				-1.63				1.27
8	5			3.13				-5.63				9.77								-17.58
39	85

x¯x¯

=

,

y¯y¯

=

,

Sx

=

Sy

=

,

r

=

The correlation coefficient of   indicates a  (Click to select)  no  very strong positive  strong inverse  moderate inverse  very strong negative   relationship between x and y. The coefficient of determination is   , found by squaring the value of  . x accounts for   % of the variation in y.

Answer 1

x	y	(x-x̅)	(x-x̅)	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
5	13	0.13	2.38	0.02	5.64	0.30
3	15	-1.88	4.38	3.52	19.14	-8.20
6	7	1.13	-3.63	1.27	13.14	-4.08
3	12	-1.88	1.38	3.52	1.89	-2.58
4	13	-0.88	2.38	0.77	5.64	-2.08
4	11	-0.88	0.38	0.77	0.14	-0.33
6	9	1.13	-1.63	1.27	2.64	-1.83
8	5	3.13	-5.63	9.77	31.64	-17.58
39	85	0.00	0.00	20.88	79.88	-36.38

xbar =4.88

ybar =10.63

sx =1.73

sy=3.38

r =-0.89

The correlation coefficient of -0.89 indicates a strong negative relationship between x and y. The coefficient of determination is 0.7935

found by squaring the value of r . x accounts for 79.35 % of the variation in y.