CORRELATION AND REGRESSION BETWEEN MAGNITUDE AND THE DEPTH OF AN EARTHQUAKE

•Data about 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. 

•The data that I am using consist  a total of 50 sets of variable that represent the magnitude measured on the Richter scale and depth in km to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes.

CONCEPT

●Correlation – It’s a measure that gives information about the relationship between two variables (x and y). Goes from -1 to +1, the closest values to -1 shows a negative weak relationship, and a closest values to +1 indicates a strong positive relationship between x and y.

●Regression – It’s a mathematical model used to show the dependence level between a dependent variable “Y” and independent variable “X” for a simple linear regression model, and more than two variables in a multivariable regression model.

SCENARIO

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•The scatter plot tells us that the data is scattered and there is no linear relation between dependent and independent variables. This means there is no correlation.

Scatter Plot

➢The linear coefficient was calculated by using excel formula: Hypothesis Test for Correlation

=CORREL (x values, y values). 

So x values are MAG and the Y values are DEPTH

➢Within the parenthesis you are going to take all of the Mag variables then add a comma then add Depth variables and then close the parenthesis before hitting ‘enter’

➢So the equation in the excel looks like =CORREL(A:2:A51,B:2:B51)

➢R value equals to 0.0231

➢Using the 0.05 significance level, before analyzing the chart to find the answer, you must first count how many variables you have (50 variables). In the chart you shall find the number 50 and go over one slot which would be the 0.05 and that lists the CV value as 0.279.

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➢Since observed T-test value < critical value, we fail to reject H0 at 5% level of significance and conclude that there is insufficient evidence to support claim (Ha) that there is no linear correlation between the magnitudes and the depths from the earthquakes.

EVIDENCE