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 3.2 4.1 3.3 4.5 2.6 3.2 3.4

y 4.5 9.6 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 = 24.3, Σx2 = 86.75, Σy = 52.6, Σy2 = 445.72 and Σxy = 187.44.

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.

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

b.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

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

d. Given our value of r, y should tend to remain constant as x increases.