# Mathematics

**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.