Question

In: Statistics and Probability

For the accompanying data​ set, (a) draw a scatter diagram of the​ data, (b) by​ hand,...

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.

Solutions

Expert Solution

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.


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