Chapter 4.1, Problem 16P

Geology: Earthquakes 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. The following is based on information taken from the National Earthquake Information Service of the U.S. Geological Survey. Additional data may be found by visiting the web site for the service.

x	2.9	4.2	3.3	4.5	2.6	3.2	3.4
y	5.0	10.0	11.2	10.0	7.9	3.9	5.5

(a) Make a scatter diagram and draw the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong? positive or negative?

(c) Use a calculator to verify that $\sum x=24.1,\sum x^2=85.75,\sum y=53.5,\sum y^2=458.31,\text{and }\sum xy=190.18$. Compute r. As x increases, does the value of r imply that y should tend to increase or decrease? Explain.