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	3.4	4.5	3.3	4.5	2.6	3.2	3.4
y	4.8	9.8	11.2	10.0	7.9	3.9	5.5

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 24.9, Σx² = 91.51, Σy = 53.1, Σy² = 452.39 and Σxy = 194.10.

Compute r. (Round to 3 decimal places.)


As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, we can not draw any conclusions for the behavior of y as x increases.Given our value of r, y should tend to remain constant as x increases.    Given our value of r, y should tend to decrease as x increases.Given our value of r, y should tend to increase as x increases.

Answer 1

Solution :

X	Y	XY	X^2	Y^2
3.4	4.8	16.32	11.56	23.04
4.5	9.8	44.1	20.25	96.04
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)	194.10
sum(X)	24.90
sum(Y)	53.10
sum(X^2)	91.51
sum(Y^2)	452.39
Numerator	36.51
Denominator	84.48
r	0.4322
r square	0.1868
Xbar(mean)	3.5571
Ybar(mean)	7.5857
SD(X)	0.6962
SD(Y)	2.7238
b	1.7758
a	1.2690

r = 0.432

Given our value of r, y should tend to increase as x increases.