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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 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 it’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