### 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

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.

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