Analysis with Correlation and Regression

Anonymous
timer Asked: Dec 13th, 2018
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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.

MAG 0.70 0.74 0.64 0.39 0.70 2.20 1.98 0.64 1.22 0.20 1.64 1.32 2.95 0.90 1.76 1.01 1.26 0.00 0.65 1.46 1.62 1.83 0.99 1.56 0.40 1.28 0.83 1.34 0.54 1.25 0.92 1.00 0.79 0.79 1.44 1.00 2.24 2.50 1.79 1.25 1.49 0.84 1.42 1.00 1.25 1.42 1.35 0.93 0.40 1.39 DEPTH 7.2 2.2 13.9 15.5 3.0 2.4 14.4 5.7 6.1 9.1 17.2 8.7 9.3 12.3 7.4 7.0 17.1 8.8 6.0 19.1 12.7 4.7 8.6 6.0 14.6 4.9 19.1 9.9 16.1 4.6 4.9 16.1 14.0 4.2 5.9 5.4 15.6 7.7 15.4 16.4 4.9 8.1 7.5 14.1 11.1 16.0 5.5 7.3 3.1 6.0
Correlation and regression analysis Mary Gibson Introduction • The study focuses on determining whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. • The variables that are evaluated in this case include Magnitude measured on the Richter scale and Depth in km Scatterplot is spread out showing a low negative correlation. Large data occurs between magnitude of 0.5 and 2. Scatter plot 25.0 20.0 Depth • The scatterplot shows that the data 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 MAG MAG DEPTH From the linear correlation r = 0.0231. This shows that there is a weak positive relationship between magnitude and depth of the earthquakes. DEPTH 1 0.0231 1 Therefore in order to obtain tabulated values, n =50, alpha= 0.05, r = 0.0231 df = 50-2 = 48 T = +- 1.677 Evidence from the analysis • From the analysis the computed r = 0.0231 while the critical value is +1.677. • Thus r is found within the range of -1.677 and +1.677. we conclude that r is not significant hence there is no sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes Regression equation • The regression equation would be y= 9.4225 + 0.1933x • Y intercept = 9.4225 • slope = 0.1933 Intercept MAG Standard Coefficients Error 9.422496 1.593209 0.193332 1.20768 t Stat 5.914164 0.160085 P-value Lower 95% Upper 95% 3.39E-07 6.219136 12.62586 0.873486 -2.23487 2.621535 Is the equation a good model • The analysis shows that the regression equation mode is not a good fit considering that p = 0.873 which is greater than 0.05 • Predicting depth at magnitude 2. • y= 9.4225 + 0.1933(2) ANOVA Regression df SS MS 1 0.63175 0.63175 Residual 48 1183.269 24.65144 Total 49 1183.901 • Y = 9.8091 thus the depth = 9.8091 F 0.025627 Significance F 0.873486 Conclusion • The study sought to determine whether there is a linear relationship between magnitude and depth. The analysis determined that there was a weak positive linear relationship between the variables (r = 0.0231). The regression analysis determined that the regression model was not statistically significant predictor (p>0.05). References • Kutner, M. H., Nachtsheim, C., & Neter, J. (2004). Applied linear regression models. McGraw-Hill/Irwin. • Long, J. S., & Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54(3), 217-224.
DEPTH 7.2 2.2 13.9 15.5 3.0 2.4 14.4 5.7 6.1 9.1 17.2 8.7 9.3 12.3 7.4 7.0 17.1 8.8 6.0 19.1 12.7 4.7 8.6 6.0 14.6 4.9 19.1 9.9 16.1 4.6 4.9 16.1 14.0 4.2 5.9 5.4 15.6 7.7 15.4 16.4 4.9 8.1 7.5 14.1 11.1 16.0 5.5 7.3 3.1 6.0 25.0 20.0 Depth MAG 0.70 0.74 0.64 0.39 0.70 2.20 1.98 0.64 1.22 0.20 1.64 1.32 2.95 0.90 1.76 1.01 1.26 0.00 0.65 1.46 1.62 1.83 0.99 1.56 0.40 1.28 0.83 1.34 0.54 1.25 0.92 1.00 0.79 0.79 1.44 1.00 2.24 2.50 1.79 1.25 1.49 0.84 1.42 1.00 1.25 1.42 1.35 0.93 0.40 1.39 15.0 10.0 5.0 0.0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 MAG SUMMARY OUTPUT Regression Statistics Multiple R 0.0231 R Square 0.000534 Adjusted R Square -0.02029 Standard Error 4.965021 Observations 50 ANOVA df Regression Residual Total Intercept MAG SS MS F 1 0.63175 0.63175 0.025627 48 1183.269 24.65144 49 1183.901 Coefficients Standard Error t Stat P-value 9.422496 1.593209 5.914164 3.39E-07 0.193332 1.20768 0.160085 0.873486 MAG MAG DEPTH 3.00 3.50 Significance F 0.873486 Lower 95%Upper 95% Lower 95.0% Upper 95.0% 6.219136 12.62586 6.219136 12.62586 -2.23487 2.621535 -2.23487 2.621535 1 0.0231 DEPTH 1
DEPTH 7.2 2.2 13.9 15.5 3.0 2.4 14.4 5.7 6.1 9.1 17.2 8.7 9.3 12.3 7.4 7.0 17.1 8.8 6.0 19.1 12.7 4.7 8.6 6.0 14.6 4.9 19.1 9.9 16.1 4.6 4.9 16.1 14.0 4.2 5.9 5.4 15.6 7.7 15.4 16.4 4.9 8.1 7.5 14.1 11.1 16.0 5.5 7.3 3.1 6.0 25.0 20.0 Depth MAG 0.70 0.74 0.64 0.39 0.70 2.20 1.98 0.64 1.22 0.20 1.64 1.32 2.95 0.90 1.76 1.01 1.26 0.00 0.65 1.46 1.62 1.83 0.99 1.56 0.40 1.28 0.83 1.34 0.54 1.25 0.92 1.00 0.79 0.79 1.44 1.00 2.24 2.50 1.79 1.25 1.49 0.84 1.42 1.00 1.25 1.42 1.35 0.93 0.40 1.39 15.0 10.0 5.0 0.0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 MAG SUMMARY OUTPUT Regression Statistics Multiple R 0.0231 R Square 0.000534 Adjusted R Square -0.02029 Standard Error 4.965021 Observations 50 ANOVA df Regression Residual Total Intercept MAG SS MS F 1 0.63175 0.63175 0.025627 48 1183.269 24.65144 49 1183.901 Coefficients Standard Error t Stat P-value 9.422496 1.593209 5.914164 3.39E-07 0.193332 1.20768 0.160085 0.873486 MAG MAG DEPTH 3.00 3.50 Significance F 0.873486 Lower 95%Upper 95% Lower 95.0% Upper 95.0% 6.219136 12.62586 6.219136 12.62586 -2.23487 2.621535 -2.23487 2.621535 1 0.0231 DEPTH 1

Tutor Answer

Greaterthanall
School: Carnegie Mellon University

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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Anonymous
Thanks for the help.

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