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.
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.