# 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

**Competency**. **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.