Question

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter.

x	2.6	4.5	3.3	4.5	2.6	3.2	3.4
y	4.9	10.1	11.2	10.0	7.9	3.9	5.5

(b) Use a calculator to verify that Σx = 24.1, Σx² = 86.71, Σy = 53.5, Σy² = 459.33 and Σxy = 191.87.

Compute r. (Round to 3 decimal places.)

Answer 1

Solution :

X	Y	XY	X^2	Y^2
2.6	4.9	12.74	6.76	24.01
4.5	10.1	45.45	20.25	102.01
3.3	11.2	36.96	10.89	125.44
4.5	10	45	20.25	100
2.6	7.9	20.54	6.76	62.41
3.2	3.9	12.48	10.24	15.21
3.4	5.5	18.7	11.56	30.25

n	7
sum(XY)	191.87
sum(X)	24.10
sum(Y)	53.50
sum(X^2)	86.71
sum(Y^2)	459.33
Numerator	53.74
Denominator	96.10
r	0.5592
r square	0.3127
Xbar(mean)	3.4429
Ybar(mean)	7.6429
SD(X)	0.7890
SD(Y)	2.7410
b	2.0543
a	0.5703

r = 0.559