Fix assignment-Deliverable 6 - Analysis with Correlation and Regression
jeffro401
regressionandcorrelation.pptxCorrelation and Regression Inferential Statistics Submitted By: Jeff Rover
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.
Data Background
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. In this analysis the USGS, and determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes.
Scatterplot
From the scatterplot I did not see any linear relation between depended and independent variables.
DEPTH
y = 0.2306x + 9.5349 R² = 0.0007
0.7 0.74 0.64 0.39 0.7 2.2000000000000002 1.98 0.64 1.22 0.2 1.64 1.32 2.95 0.9 1.76 1.01 1.26 0 0.65 1.46 1.62 1.83 0.99 1.56 0.4 1.28 0.83 1.34 0.54 1.25 0.92 1 0.79 0.79 1.44 1 2.2400000000000002 2.5 1.79 1.25 1.49 0.84 1.42 1 1.25 1.42 1.35 0.93 0.4 1.39 6.6 2 15.3 17.2 3.2 2.2000000000000002 14.8 5.6 6.1 9.1 18.5 8.1 10 13.7 8 7 18.600000000000001 8.1999999999999993 5.7 18.899999999999999 13.7 4.5 8.3000000000000007 6 14.2 5.4 17.7 9.9 17.3 5.0999999999999996 5.3 15.9 13.7 4.2 5.7 5.9 15.1 8.5 14.7 16.399999999999999 4.7 8.6 8.1999999999999993 15.2 10.1 14.5 5.2 7.9 3.3 6.4
MAG
DEPTH
The value of the correlation coefficient r =0.027019729
: = 0 , , where = population correlation coefficient.
Test Statistic: T =
T-Critical= 2.0106347 (Using Excel command = TINV(alpha, Degree of freedom)
n=50
Degree of Freedom = n-2= 50-2= 48
R=0.027019729
T-test=0.143027184
Critical value of the test :
Where n= 50, alpha= 0.05.
Observed value of T= 0.1873
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.
𝛾=9.53487341+0.230642282x
Where x= Magnitude (MAG)
Y=Depth
Regression equation
From the R² = 0.0007 value we can conclude that good well of the model is 0.07% the equation is not a good model.
The best predicted depth of an earthquake with a magnitude of 2.0 is:
𝛾=9.53487341+0.230642282 (2)= 9.996157974
The best predicted depth of an earthquake with a magnitude of 2.0 is 9.99615797
Conclusion
As a junior analyst at the USGS, conclude that there is insufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes..
