Analysis with Correlation and Regression

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.

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.