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.

Click here to view the data set.

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Click here to view the critical values table.

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

A.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 2. The following 5 points are plotted, listed here from left to right: (2, 4); (4, 8); (7, 12); (7, 14); (8, 18).

B.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 2. The following 5 points are plotted, listed here from left to right: (2, 18); (4, 14); (7, 12); (7, 8); (8, 4).

C.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 1. The following 5 points are plotted, listed here from left to right: (2, 4); (4, 8); (7, 12); (7, 9); (8, 18).

D.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 1. The following 5 points are plotted, listed here from left to right: (2, 18); (4, 9); (7, 12); (7, 8); (8, 4).

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

The correlation coefficient is r = ____________. ​(Round to three decimal places as​ needed.)

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

Because the correlation coefficient is _______________▼(positive/negative) and the absolute value of the correlation​ coefficient, _________ is _____________▼(not greater/greater) than the critical value for this data​ set, _______ is ______________▼(a negative, a positive, no) linear relation exists between x and y. ​(Round to three decimal places as​ needed.)

Data set

x	2	4	6	6	7
y	4	8	12	14	18

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
n

  

Answer 1

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