MAG	DEPTH
0.75	7.5
0.74	2.5
0.64	14.0
1.20	15.5
0.70	3.0
2.20	2.4
1.98	14.4
0.64	5.7
1.22	6.1
0.50	7.1
1.64	17.2
1.32	8.7
3.87	9.3
0.90	12.3
1.76	9.8
1.00	7.4
1.26	17.1
0.01	8.8
0.65	5.0
1.46	19.1
1.62	12.7
1.83	4.7
0.99	6.8
1.56	6.0
0.40	14.6
1.28	4.9
0.83	19.1
1.34	9.9
0.54	16.1
1.25	4.6
0.92	4.9
1.25	16.3
0.79	14.0
0.79	4.2
1.44	5.4
1.00	5.9
2.24	15.6
2.50	7.7
1.79	16.4
1.25	15.4
1.49	4.9
0.84	8.1
1.42	7.5
1.00	14.1
1.25	11.1
1.42	14.8
1.35	4.6
1.45	7.1
0.40	3.1
1.39	5.3

Scenario

According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF).

As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Your deliverables will be a PowerPoint presentation you will create summarizing your findings and an excel document to show your work.

Concepts Being Studied

• Correlation and regression
• Creating scatterplots
• Constructing and interpreting a Hypothesis Test for Correlation usingras the test statistic

You are given aspreadsheetthat contains the following information:

• Magnitude measured on the Richter scale
• Depth in km

PLEASE, SHOW ALL EXCEL FORMULAS USED! Thank you!

1. Construct a Scatterplot Below. (Show Steps on how you created this SCATTERPLOT) THANK YOU!

A. Find the value of the linear correlation coefficientrand the critical value ofrusing = 0.05. Include an explanation on how you found those values.

r=

CV=

B. Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation.

Slope=

Y-intercept=

Regression Equation=

C. Is the equation a good model? Explain. What would be the best predicted depth of an earthquake with a magnitude of 2.0? Include the correct units.

*Hint: You only need to find y-hat or y-bar (not both).

y-hat=

y-bar=