Question

The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer parts ​a-c.

Height (x)   Interval after (y)
140   75
130   71
115   59
140   73
112   64
110   56
100   54
120   68

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

α=0.05

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

Answer 1

Solution :

X	Y	XY	X^2	Y^2
140	75	10500	19600	5625
130	71	9230	16900	5041
115	59	6785	13225	3481
140	73	10220	19600	5329
112	64	7168	12544	4096
110	56	6160	12100	3136
100	54	5400	10000	2916
120	68	8160	14400	4624

n	8
sum(XY)	63623.00
sum(X)	967.00
sum(Y)	520.00
sum(X^2)	118369.00
sum(Y^2)	34248.00
Numerator	6144.00
Denominator	6520.51
r	0.9423
r square	0.8879
Xbar(mean)	120.8750
Ybar(mean)	65.0000
SD(X)	12.6984
SD(Y)	7.1570
b	0.5179
a	2.3973

linear correlation coefficient = r = 0.9423

Critical value = 0.707

There is not sufficient evidence to conclude that there is a linear correlation between the two​ variables .