## Description

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 (ATTACHED) 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.

So for this one you should have the excel and a powerpoint you create.

__YOU MUST MEET THE BELOW REQUIREMENTS:__

All problems are solved correctly. |

Complete and detailed steps are provided to explain how to solve the problem. |

Explanations demonstrate a mastery of understanding of the statistical concepts and terminology. |

All variables, equations, and expressions are properly formatted. |

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## Explanation & Answer

Attached.

Analysis with Correlation and Regression

Presented by:

Course:

Professor:

Date:

Introduction

➢ Correlation and regression analysis help to determine a

relationship between two variables.

➢ The two variables analyzed in this case are magnitudes

and depths from the earthquakes.

➢ The dataset comprises of 50 observations recorded in

excel spreadsheet.

Scatter plot

➢ The data points are evenly

DEPTH VS. MAG

25.0

distributed.

➢ The appearance and

equation of the trend line in

indicate that there is a linear

relationship between depths

and magnitudes.

DEPTH

20.0

y = 0.1933x + 9.4225

R² = 0.0005

15.0

10.0

5.0

0.0

0.00

0.50

1.00

1.50

2.00

MAG

2.50

3.00

3.50

Linear correlation

➢ The value of linear correlation coefficient r

is 0.0231 whereas the critical value of r is

Regression Statistics

1.96.

➢ The linear correlation coefficient was

determined by conducting linear

regression in excel.

Multiple R

0.023100158

R Square

0.000533617

Adjusted R Square

Standard Error

Observations

➢ The critical value of r was calculated

using the z-table.

-0.020288599

4.965021178

50

E...