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	3.0	4.7	3.3	4.5	2.6	3.2	3.4
y	5.0	9.7	11.2	10.0	7.9	3.9	5.5

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 24.7, Σx² = 90.79, Σy = 53.2, Σy² = 452.40 and Σxy = 194.27.

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

Answer 1

	X	Y	X * Y
	3	5	15	9	25
	4.7	9.7	45.59	22.09	94.09
	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
Total	24.7	53.2	194.27	90.79	452.4

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