Question

Determine the value of the coefficient of correlation, r, for the following data.

X	3	6	7	11	13	17	21
Y	18	13	13	8	7	7	5

(Round the intermediate values to 3 decimal places. Round your answer to 3 decimal places.)


r =

Answer 1

The provided data are shown in the table below

X	Y
3	18
6	13
7	13
11	8
13	7
17	7
21	5

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	3	18	54	9	324
	6	13	78	36	169
	7	13	91	49	169
	11	8	88	121	64
	13	7	91	169	49
	17	7	119	289	49
	21	5	105	441	25
Sum =	78	71	626	1114	849

The correlation coefficient r is computed using the following expression:

where

In this case, based on the data provided, we get that

Therefore, based on this information, the sample correlation coefficient is computed as follows

which completes the calculation.