Deliverable 6 – Analysis with Correlation and Regression
Assignment Content
- Competency
Determine the linear correlation and regression equation between two variables to make predictions for the dependent variable.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
- Deliverable 6 – Analysis with Correlation and Regression.xlsx
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.
Data and Questions
| MAG | DEPTH | |||
| 0.75 | 7.5 | |||
| 0.74 | 2.5 | |||
| 0.64 | 14.0 | |||
| 1.20 | 15.5 | |||
| 0.70 | 3.0 | |||
| 2.20 | 2.4 | |||
| 1.98 | 14.4 | |||
| 0.64 | 5.7 | |||
| 1.22 | 6.1 | |||
| 0.50 | 7.1 | |||
| 1.64 | 17.2 | |||
| 1.32 | 8.7 | |||
| 3.87 | 9.3 | |||
| 0.90 | 12.3 | |||
| 1.76 | 9.8 | |||
| 1.00 | 7.4 | |||
| 1.26 | 17.1 | |||
| 0.01 | 8.8 | |||
| 0.65 | 5.0 | |||
| 1.46 | 19.1 | |||
| 1.62 | 12.7 | |||
| 1.83 | 4.7 | |||
| 0.99 | 6.8 | |||
| 1.56 | 6.0 | |||
| 0.40 | 14.6 | |||
| 1.28 | 4.9 | r | ||
| 0.83 | 19.1 | CV | ||
| 1.34 | 9.9 | |||
| 0.54 | 16.1 | |||
| 1.25 | 4.6 | |||
| 0.92 | 4.9 | |||
| 1.25 | 16.3 | |||
| 0.79 | 14.0 | Slope | ||
| 0.79 | 4.2 | Y-intercept | ||
| 1.44 | 5.4 | Regression Equation | ||
| 1.00 | 5.9 | |||
| 2.24 | 15.6 | |||
| 2.50 | 7.7 | |||
| 1.79 | 16.4 | |||
| 1.25 | 15.4 | |||
| 1.49 | 4.9 | |||
| 0.84 | 8.1 | y-hat | ||
| 1.42 | 7.5 | y-bar | ||
| 1.00 | 14.1 | |||
| 1.25 | 11.1 | |||
| 1.42 | 14.8 | |||
| 1.35 | 4.6 | |||
| 1.45 | 7.1 | |||
| 0.40 | 3.1 | |||
| 1.39 | 5.3 | |||
Slide 3. Construct a Scatterplot Below.
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 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.
*Hint: You only need to find y-hat or y-bar (not both).
*Note: Refer to the deliverable instructions for a breakdown of the PowerPoint requirements.
