Determine and interpret the linear correlation coefficient, anduse linear regression to find a best fit line for a scatter plot ofthe data and make predictions. Scenario According to the U.S.Geological Survey (USGS), the probability of a magnitude 6.7 orgreater earthquake in the Greater Bay Area is 63%, about 2 out of3, in the next 30 years. In April 2008, scientists and engineersreleased a new earthquake forecast for the State of Californiacalled the Uniform California Earthquake Rupture Forecast (UCERF).As a junior analyst at the USGS, you are tasked to determinewhether there is sufficient evidence to support the claim of alinear correlation between the magnitudes and depths from theearthquakes. Your deliverables will be a PowerPoint presentationyou will create summarizing your findings and an excel document toshow your work. Concepts Being Studied • Correlation and regression• Creating scatterplots • Constructing and interpreting aHypothesis Test for Correlation using r as the test statistic Youare given a spreadsheet that contains the following information: •Magnitude measured on the Richter scale • Depth in km Using thespreadsheet, you will answer the problems below in a PowerPointpresentation. What to Submit The PowerPoint presentation shouldanswer and explain the following questions based on the spreadsheetprovided above. • Slide 1: Title slide • Slide 2: Introduce yourscenario and data set including the variables provided. • Slide 3:Construct a scatterplot of the two variables provided in thespreadsheet. Include a description of what you see in thescatterplot. • Slide 4: Find the value of the linear correlationcoefficient r and the critical value of r using ? = 0.05. Includean explanation on how you found those values. • Slide 5: Determinewhether there is sufficient evidence to support the claim of alinear correlation between the magnitudes and the depths from theearthquakes. Explain. • Slide 6: Find the regression equation. Letthe predictor (x) variable be the magnitude. Identify the slope andthe y-intercept within your regression equation. • Slide 7: Is theequation a good model? Explain. What would be the best predicteddepth of an earthquake with a magnitude of 2.0? Include the correctunits. • Slide 8: Conclude by recapping your ideas by summarizingthe information presented in context of the scenario. Along withyour PowerPoint presentation, you should include your Exceldocument which shows all calculations.
| MAG | DEPTH |
| 0.70 | 7.2 |
| 0.74 | 2.2 |
| 0.64 | 13.9 |
| 0.39 | 15.5 |
| 0.70 | 3.0 |
| 2.20 | 2.4 |
| 1.98 | 14.4 |
| 0.64 | 5.7 |
| 1.22 | 6.1 |
| 0.20 | 9.1 |
| 1.64 | 17.2 |
| 1.32 | 8.7 |
| 2.95 | 9.3 |
| 0.90 | 12.3 |
| 1.76 | 7.4 |
| 1.01 | 7.0 |
| 1.26 | 17.1 |
| 0.00 | 8.8 |
| 0.65 | 6.0 |
| 1.46 | 19.1 |
| 1.62 | 12.7 |
| 1.83 | 4.7 |
| 0.99 | 8.6 |
| 1.56 | 6.0 |
| 0.40 | 14.6 |
| 1.28 | 4.9 |
| 0.83 | 19.1 |
| 1.34 | 9.9 |
| 0.54 | 16.1 |
| 1.25 | 4.6 |
| 0.92 | 4.9 |
| 1.00 | 16.1 |
| 0.79 | 14.0 |
| 0.79 | 4.2 |
| 1.44 | 5.9 |
| 1.00 | 5.4 |
| 2.24 | 15.6 |
| 2.50 | 7.7 |
| 1.79 | 15.4 |
| 1.25 | 16.4 |
| 1.49 | 4.9 |
| 0.84 | 8.1 |
| 1.42 | 7.5 |
| 1.00 | 14.1 |
| 1.25 | 11.1 |
| 1.42 | 16.0 |
| 1.35 | 5.5 |
| 0.93 | 7.3 |
| 0.40 | 3.1 |
| 1.39 | 6.0 |
