# Analysis with Correlation and Regression

*label*Mathematics

*timer*Asked: Dec 13th, 2018

*account_balance_wallet*$25

**Question description**

**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.

## Tutor Answer

Hey, I am through with the assignment. Please review it and let me know if you need any clarification or editing

Correlation and Regression

Analysis to Determine if there is sufficient evidence to support the claim

of linear correlation

Mary Gibson

Introduction

• The objective of this analysis is to determine whether there is enough

evidence to support the claim of a linear correlation between the

magnitudes and depths from the earthquakes forecasted for the state

of California. The data sets are shown below:

x 25

28

35

39

44

48

52

65

55

72

y 0.5 0

0.8 1.6 1.8 3.1 4.3 4.6 3.5 7.2

• The variables used in this study are magnitude measured on he

Richter scale and depth in kilometers (km)

Scatterplot

Scatterplot for Magnitude and Depth

25.0

20.0

Depth (km)

• The scatterplot shows that the

points are scattered and most

are way off the line

• This means there is a weak

positive correlation between

magnitude and depth

• Large data occurs between

magnitude of 0.5 and 2.

• The linear model does not fit it

that well

15.0

10.0

5.0

0.0

0.00

0.50

1.00

1.50

2.00

Magnitude

2.50

3.00

3.50

Linear Correlation Coefficient

• From the spreadsheet, the linear

correlation coefficient betwee...

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