20 Aug 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.

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 Click for more options

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.

Grading Rubric
F F C B A
0 1 2 3 4
Not Submitted No Pass Competence Proficiency Mastery
Not Submitted Did not correctly solve a majority of the problems or at least one problem left blank. Correctly solved a majority of the problems. Correctly solved almost all the problems. All problems are solved correctly.
Not Submitted Very few steps are provided to explain how to solve the problem OR the steps provided have several errors. Fairly complete and detailed steps are provided to explain how to solve the problem OR the steps provided have some errors. Mostly complete and detailed steps are provided to explain how to solve the problem. Complete and detailed steps are provided to explain how to solve the problem.
Not Submitted Explanations generally lack a basic understanding of the statistical concepts or lack of proper terminology. Explanations demonstrate a basic understanding of most of the statistical concepts and terminology, but some explanations may be incomplete or incorrect. Explanations demonstrate a proficient understanding of most of the statistical concepts and terminology, but with small errors. Explanations demonstrate a mastery of understanding of the statistical concepts and terminology.
Not Submitted The majority of variables, equations, and expressions are not properly formatted. The majority of variables, equations, and expressions are properly formatted. Almost all variables, equations, and expressions are properly formatted. All variables, equations, and expressions are properly formatted.