Deliverable 7 - JBH Project Plan
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Deliverable6PPPresentation.pptxAnalysis of correlation and regression
Introduction of scenario and data set
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).
Data is provided for the magnitude of earthquake measured on the Richter scale and Depth of the earthquake measured in km.
Using the above data, I will carry out calculation to determine if there is any correlation between magnitudes and depths of earthquakes.
I will also use the data to plot scatter plot and also construct hypothesis test for the correlation using r as a test statistics.
Scatter Plot Analysis
From the figure of the scatter plot, magnitude of earthquake on Richter scale and depth of earthquake in km are clustered hence no linear relationship . This is confirmed by the scatter plot beside.
Linear correlation Coefficient (r) and critical value of r
Using the information data set on excel, plugging formula=Correl( magnitude: Depth)= 0.0231. This is the linear correlation coefficient
Taking the number of observations, n=50, and alpha 0.05. Then take n-2, which makes 50-2=48.
Read 48 against 0.05 on the Pearson coefficient table. Since there is no 48, I read 50 against 0.05 to get critical value as 0.273.
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Testing Significance of linear correlation
To test the claim, we carry out hypothesis testing;
H0 :Pxy=0, there is no linear correlation between magnitude and depth of earthquake.
H1:Pxy ≠0, there is linear correlation between magnitude and depth of earthquake,
Calculate the linear correlation coefficient or computed r, which in this case is equal to 0.0231.
The tabulate the critical r, which in this case, is equal to 0.273.
Decision rule: computed r (0.0231) ≤ critical value of r (0.273), therefore do not reject the null hypothesis.
Conclusion; there is no linear correlation between magnitude and depth of earthquake. This means there is no sufficient evidence to support the claim of linear correlation between magnitude and depth of earthquake.
Regression Equation
From the data set on the excel, Y(depth)=B0+B1(magnitude), the regression equation is equal to; Y(depth)=9.422+0.1933(Magnitude).
The intercept of regression equation is equal to 9.422.
The slope of the regression equation is equal to 0.1933.
Equation a good model
Equation of regression is not good model. This is because independent variable(MAG) is not statistically significant. MAG p-value 0.87>t-statistics=0.16.
Predicted depth of earthquake of magnitude of 2.0 would be, 0.1933+2.0*9.422=9.8086Km.
Therefore, the predicted depth of the earthquake is 9.81 km.
Summary
There is no evidence to support the claim of the linear correlation between depth and magnitude of earthquake. Therefore, there is no significant relationship between depth and magnitude of the earthquake forecast.
Regression equation is not a good model independent variable (MAG) is not statistically significant.
Critical value of linear correlation is greater than computed r, indicates no linear correlation between depth and magnitude of earthquake.
Regression equation of the model, Y(depth)=9.422+0.1933(MAG)
Predicted depth of earthquake, having magnitude of 2.0 is 9.81 km.
