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 2.8 3.9 3.3 4.5 2.6 3.2 3.4
y 4.7 9.6 11.2 10.0 7.9 3.9 5.5
(a) Make a scatter diagram of the data.
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Then visualize the line you think best fits the data.
(b) Use a calculator to verify that Σx = 23.7, Σx2 = 82.75, Σy = 52.8, Σy2 = 447.56 and Σxy = 184.28.
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.