## 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.