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 | 2.9 | 4.4 | 3.3 | 4.5 | 2.6 | 3.2 | 3.4 |
y | 4.9 | 10.3 | 11.2 | 10.0 | 7.9 | 3.9 | 5.5 |
(a) Make a scatter diagram of the data.
Submission Data |
Then visualize the line you think best fits the data.
(b) Use a calculator to verify that Σx = 24.3,
Σx^{2} = 87.47, Σy = 53.7,
Σy^{2} = 463.41 and Σxy = 193.21.
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 remain constant 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 decrease as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.
X | Y | X * Y | X^{2} | Y^{2} | |
2.9 | 4.9 | 14.21 | 8.41 | 24.01 | |
4.4 | 10.3 | 45.32 | 19.36 | 106.09 | |
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 | 24.3 | 53.7 | 193.21 | 87.47 | 463.41 |
r = 0.537
Given our value of r, y should tend to increase as x increases.
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