Question

The data below shows the selling price​ (in hundred​ thousands) and the list price​ (in hundred​ thousands) of homes sold. Answer parts ​a-c.

Selling Price​ (x)	403	302	379	434	455	477	316	350	417	330
	List Price​ (y)	410	317	389	439	486	480	320	365	432

a. Find the value of the linear correlation coefficient r.

b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using

alpha=0.05

c. Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Answer 1

Solution:

a)

	X	Y	XY	X^2	Y^2
	302	410	123820	91204	168100
	379	317	120143	143641	100489
	434	389	168826	188356	151321
	455	439	199745	207025	192721
	477	486	231822	227529	236196
	316	480	151680	99856	230400
	350	320	112000	122500	102400
	417	365	152205	173889	133225
	330	432	142560	108900	186624
SUM	3460	3638	1402801	1362900	1501476

Putting value , we get

r = 0.1318

b)

n = 9

df = n - 2 = 9 - 2 = 7

= 0.05

Using the critical value table for Pearson correlation coefficient, (two tailed )

Critical value are  0.666

c)

r = 0.1318

| r | = | 0.1318| = 0.1318

r < 0.666

Fail to reject H₀

No significance correlation.

NO , there is NOT sufficient evidence to conclude that there is a linear correlation between the two​ variables.