Question

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use

alphaαequals=​0.05.)

x	10	8	13	9	11	14	6	4	12	7	5
y	9.13	8.13	8.75	8.77	9.27	8.11	6.14	3.09	9.14	7.26	4.73

Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

The linear correlation coefficient is

r=______

​(Round to three decimal places as​ needed.)

Answer 1

Solution:

We are given a data set of size n = 11

To find r , we prepare a table.

	X	Y	XY	X^2	Y^2
	10	9.13	91.3	100	83.3569
	8	8.13	65.04	64	66.0969
	13	8.75	113.75	169	76.5625
	9	8.77	78.93	81	76.9129
	11	9.27	101.97	121	85.9329
	14	8.11	113.54	196	65.7721
	6	6.14	36.84	36	37.6996
	4	3.09	12.36	16	9.5481
	12	9.14	109.68	144	83.5396
	7	7.26	50.82	49	52.7076
	5	4.73	23.65	25	22.3729
Sum	99.00	82.52	797.88	1001.00	660.50

Putting n = 7 , = 797.88 , = 99.00, = 82.52 , = 1001.00 , = 660.50

we get ,

r = 0.817

The linear correlation coefficient is

r = 0.817