Assignment:
Competency
Determine and interpret the linear correlation coefficient, and use linear regression to find a best fit line for a scatter plot of the data and make predictions.
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 using r as the test statistic
You are given a spreadsheet that contains the following information:
- Magnitude measured on the Richter scale
- Depth in km
Using the spreadsheet, you will answer the problems below in a PowerPoint presentation.
What to Submit
The PowerPoint presentation should answer and explain the following questions based on the spreadsheet provided above.
Slide 1: Title slide
Slide 2: Introduce your scenario and data set including the variables provided.
Slide 3: Construct a scatterplot of the two variables provided in the spreadsheet. Include a description of what you see in the scatterplot.
Slide 4: Find the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Include an explanation on how you found those values.
Slide 5: Determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes. Explain.
Slide 6: Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation.
Slide 7: 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.
Slide 8: Conclude by recapping your ideas by summarizing the information presented in context of the scenario.
Along with your PowerPoint presentation, you should include your Excel document which shows all calculations.
| MAG |
DEPTH |
| 0.70 |
6.6 |
| 0.74 |
2.0 |
| 0.64 |
15.3 |
| 0.39 |
17.2 |
| 0.70 |
3.2 |
| 2.20 |
2.2 |
| 1.98 |
14.8 |
| 0.64 |
5.6 |
| 1.22 |
6.1 |
| 0.20 |
9.1 |
| 1.64 |
18.5 |
| 1.32 |
8.1 |
| 2.95 |
10.0 |
| 0.90 |
13.7 |
| 1.76 |
8.0 |
| 1.01 |
7.0 |
| 1.26 |
18.6 |
| 0.00 |
8.2 |
| 0.65 |
5.7 |
| 1.46 |
18.9 |
| 1.62 |
13.7 |
| 1.83 |
4.5 |
| 0.99 |
8.3 |
| 1.56 |
6.0 |
| 0.40 |
14.2 |
| 1.28 |
5.4 |
| 0.83 |
17.7 |
| 1.34 |
9.9 |
| 0.54 |
17.3 |
| 1.25 |
5.1 |
| 0.92 |
5.3 |
| 1.00 |
15.9 |
| 0.79 |
13.7 |
| 0.79 |
4.2 |
| 1.44 |
5.7 |
| 1.00 |
5.9 |
| 2.24 |
15.1 |
| 2.50 |
8.5 |
| 1.79 |
14.7 |
| 1.25 |
16.4 |
| 1.49 |
4.7 |
| 0.84 |
8.6 |
| 1.42 |
8.2 |
| 1.00 |
15.2 |
| 1.25 |
10.1 |
| 1.42 |
14.5 |
| 1.35 |
5.2 |
| 0.93 |
7.9 |
| 0.40 |
3.3 |
| 1.39 |
6.4 |