Question

For the accompanying data​ set, (a) draw a scatter diagram of the​ data, (b) compute the correlation​ coefficient, and​ (c) determine whether there is a linear relation between x and y.

   Data set

x	7	6	6	7	9
y	3	2	6	9	5

Critical Values for Correlation Coefficient

n
3	0.997
4	0.950
5	0.878
6	0.811
7	0.754
8	0.707
9	0.666
10	0.632
11	0.602
12	0.576
13	0.553
14	0.532
15	0.514
16	0.497
17	0.482
18	0.468
19	0.456
20	0.444
21	0.433
22	0.423
23	0.413
24	0.404
25	0.396
26	0.388
27	0.381
28	0.374
29	0.367
30	0.361

Compute the correlation coefficient.

The correlation coefficient is

r=__?__.

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

Answer 1

a)

By using excel we can solve this question easily.

We have to find a scatter plot

-First, enter all data into excel

Select all data ----------> Click on Insert --------> Scatter ------->Click on first graph
We get

b)

Now we have to find the correlation coefficient (r).

Formula is

	x	y	xy	x^2	y^2
	7	3	21	49	9
	6	2	12	36	4
	6	6	36	36	36
	7	9	63	49	81
	9	5	45	81	25
Total	35	25	177	251	155

n = 5

The correlation coefficient is r = 0.149

c)

Now we have to check there is a linear relation between x and y or not.

The null and alternative hypothesis is

Sample size = n = 5

Degrees of freedom = n - 2 = 5 - 2 = 3

Critical value = 0.997

Critical value > correlation coefficient (r) we fail to reject null hypothesis.

Conclusion: There is no linear relationship between x and y.