Overview
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: 1) a PowerPoint presentation you will create that summarizes your findings, and 2) an Excel spreadsheet 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 spreadsheetLinks to an external site. 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 submit your Excel spreadsheet which shows all calculations.
| Deliverable 6 | ||
|---|---|---|
| Criteria | Ratings | Pts |
Slides 1-3 view longer description | 20 pts Excellent Slides 1-3: Clearly contains the introductory information and provides an image of the scatterplot and a thorough description of what is seen in the scatterplot.15 pts Good Slides 1-3: Contains the introductory information and provides an image of the scatterplot and an adequate description of what is seen in the scatterplot.10 pts Average Slides 1-3: Contains the introductory information, provides an image of the scatterplot, and provides a partial attempt at a description of what is seen in the scatterplot.5 pts Needs Improvement Slides 1-3: Contains missing introductory information and provides little to no attempt at a description of what is seen in the scatterplot.0 pts No Marks | / 20 pts |
Slides 4 & 5 view longer description | 20 pts Excellent Slides 4 and 5: Correctly utilizes the scatterplot to calculate the value of the linear correlation coefficient and critical value and thoroughly explains how those values were found. Thoroughly explains whether there is sufficient evidence to support the claim of a linear correlation.15 pts Good Slides 4 and 5: Correctly utilizes the scatterplot to calculate the value of the linear correlation coefficient and critical value and adequately explains how those values were found. Adequately explains whether there is sufficient evidence to support the claim of a linear correlation.10 pts Average Slides 4 and 5: Utilizes the scatterplot to calculate the value of the linear correlation coefficient and critical value and provides a partial attempt at explaining how those values were found. Provides a partial attempt at explaining whether there is sufficient evidence to support the claim of a linear correlation.5 pts Needs Improvement Slides 4 and 5: Incorrectly calculates the value of the linear correlation coefficient and critical value and provides little to no attempt at explaining how those values were found. Provides little to no attempt at explaining whether there is sufficient evidence to support the claim of a linear correlation.0 pts No Marks | / 20 pts |
Slides 6 & 7 view longer description | 20 pts Excellent Slides 6 and 7: Correctly finds the regression equation and correctly identifies the slope and y-intercept. Thoroughly explains whether the equation is a good model and correctly utilizes it to create a further prediction.15 pts Good Slides 6 and 7: Correctly finds the regression equation and correctly identifies the slope and y-intercept. Adequately explains whether the equation is a good model and correctly utilizes it to create a further prediction.10 pts Average Slides 6 and 7: Finds the regression equation and identifies the slope and y-intercept. Provides a partial explanation for whether the equation is a good model and utilizes it to create a further prediction.5 pts Needs Improvement Slides 6 and 7: Incorrectly finds the regression equation and the slope and y-intercept. Provides little to no explanation for whether the equation is a good model and does not utilize it to create a further prediction.0 pts No Marks | / 20 pts |
Slide 8 view longer description | 20 pts Excellent Slide 8: Summary is clear, detailed, and thorough.15 pts Good Slide 8: Summary is adequate.10 pts Average Slide 8: Partial attempt at creating a summary slide.5 pts Needs Improvement Slide 8: Little to no attempt at creating a summary slide.0 pts No Marks | / 20 pts |
Excel Workbook view longer description | 20 pts Excellent All calculations are clearly organized and identified on a separate Excel workbook.15 pts Good Most calculations are clearly organized and identified on a separate Excel workbook.10 pts Average Some calculations are clearly organized and identified on a separate Excel workbook.5 pts Needs Improvement No calculations were organized and identified on a separate Excel workbook.0 pts No Marks | / 20 pts |
| Total Points: 0 |