Question

For the accompanying data set, (a) draw a scatter diagram of the data, (b) by hand,complete 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	12	12	20

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

(a) Draw a scatter diagram of the data _______________________

(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 or negative) and the absolute value of the correlation coefficient________ is (greater or not greater)than the critical value for this data set,________,( a positive, a negative or no)linear relation exists between x and y. (Round to three decimal places as needed.)

   

   

Answer 1

(a) Draw a scatter diagram of the data

(b)

(b) BY hand , compute the correlation coefficient.

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

	X	Y	XBAR	YBAR	(X-XBAR)	(Y-YBAR)	(X-XBAR)(Y-YBAR)	(X-XBAR)^2	(Y-YBAR)^2
	2	4	5	11.2	-3	-7.2	21.6	9	51.84
	4	8	5	11.2	-1	-3.2	3.2	1	10.24
	6	12	5	11.2	1	0.8	0.8	1	0.64
	6	12	5	11.2	1	0.8	0.8	1	0.64
	7	20	5	11.2	2	8.8	17.6	4	77.44
						TOTAL	44	16	140.8
MEAN	X BAR=25/5=5	YBAR=56/5=11.2
		r=44/sqrt(16*140.8)
		r=0.9270248

correlation coefficient=r=0.927

Solutionc:

n=5

critical r=0.878

Because the correlation coefficient is (positive) and the absolute value of the correlation coefficient 0.927

is (not greater),than the critical value for this data set 0.878,

a positive)linear relation exists between x and y.