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   y
2   4
4   8
6   12
6   12
7   20

Data set

x	22	44	66	66	77
y	44	88	1212	1212	2020

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

​(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

▼

greater

not greater

than the critical value for this data​ set, __?__​,

▼

a positive

a negative

no linear relation exists between x and y.

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

Answer 1

a.

b.

X Values
∑ = 25
Mean = 5
∑(X - M_x)² = SS_x = 16

Y Values
∑ = 56
Mean = 11.2
∑(Y - M_y)² = SS_y = 140.8

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 44

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 44 / √((16)(140.8)) = 0.927

c. Here df=n-2=3

So critical value is 0.997

Because the correlation coefficient is positive and the absolute value of the correlation​ coefficient, r=0.927​,

is not greater than the critical value for this data​ set, 0.997​, a positive

linear relation exists between x and y.