## 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.

## Sheet1

0.70 0.64 19.1

4.6

4.9

4.9

5.5

6.0

MAG | DEPTH | ||

0.70 | 7.2 | ||

0.74 | 2.2 | ||

0.64 | 13.9 | ||

0.39 | 1 | 5.5 | |

3.0 | |||

2.20 | 2.4 | ||

1.98 | 14.4 | ||

5.7 | |||

1.22 | 6.1 | ||

0.20 | 7.1 | ||

1.64 | 17.2 | ||

1.32 | 8.7 | ||

2.95 | 9.3 | ||

0.90 | 12.3 | ||

1.76 | 7.0 | ||

1.01 | 7.4 | ||

1.26 | 17.1 | ||

0.00 | 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 | 1 | 4.6 | |

1.28 | 4.9 | ||

0.83 | |||

1.34 | 9.9 | ||

0.54 | 16.1 | ||

1.25 | |||

0.92 | |||

1.00 | 16.3 | ||

0.79 | 14.0 | ||

4.2 | |||

1.44 | 5.4 | ||

5.9 | |||

2.24 | 15.6 | ||

2.50 | 7.7 | ||

1.79 | 16.4 | ||

15.4 | |||

1.49 | |||

0.84 | 8.1 | ||

1.42 | 7.5 | ||

14.1 | |||

11.1 | |||

16.0 | |||

1.35 | |||

0.93 | 7.3 | ||

3.1 | |||

1.39 |