Question

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

x 2 4 6 6 7

y 4 8 11 13 18

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
n

(a) Draw a scatter diagram of the data. Choose the correct graph below.

​(b) By​ hand, compute the correlation coefficient.

The correlation coefficient is r= ___

​(c) Determine whether there is a linear relation between x and y.

Answer 1

	X	Y	X * Y
	2	4	8	4	16
	4	8	32	16	64
	6	11	66	36	121
	6	13	78	36	169
	7	18	126	49	324
Total	25	54	310	141	694

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 5.2697

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 5.2697 ) = 0.0133
Reject null hypothesis if P value < level of significance
P - value = 0.0133 < 0.05 ,hence we reject null hypothesis
Conclusion :- We reject H0

There is statistically linear correlation between two variables.