**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.

**Instructions**

**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 the completed worksheet linked below and a series of PowerPoint slides you will create summarizing your findings.

**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

To get started, you will need to provide a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology.

**What to Submit**

To complete this assignment, you must first download the worksheet and then complete it by including the following items on the worksheet:

- calculations completed in a spreadsheet
- complete explanation of the reasoning behind your answers

You will also develop a PowerPoint presentation on these topics. Your boss has asked you to include the following slides:

**Slide 1: **Title slide

**Slide 2**: Describes correlation and regression

**Slide 3:** Describes the linear correlation coefficient *r* and the critical values of *r*

**Slide 4**: Explains how to determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables

**Slide 5: **Shows the formula for regression and lists what each variable in the formula represents

**Slide 6: **Explains how to determine whether the regression equation is a good model or not. If itâ€™s not a good model, what variable do we use to make a prediction?

**Slide 7: **Explains how to compute the best-predicted value

**Slide 8**: Provides your computed best-predicted value for the earthquake problem