The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts. Develop the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported. At the .05 level of significance, determine whether the adjusted gross income and the percent audited are related. Did the estimated regression equation provide a good fit? District Adjusted Gross Income ($) Percent Audited Los Angeles 36,664 1.3 Sacramento 38,845 1.1 Atlanta 34,886 1.1 Boise 32,512 1.1 Dallas 34,531 1.0 Providence 35,995 1.0 San Jose 37,799 0.9 Cheyenne 33,876 0.9 Fargo 30,513 0.9 New Orleans 30,174 0.9 Oklahoma City 30,060 0.8 Houston 37,153 0.8 Portland 34,918 0.7 Phoenix 33,291 0.7 Augusta 31,504 0.7 Albuquerque 29,199 0.6 Greensboro 33,072 0.6 Columbia 30,859 0.5 Nashville 32,566 0.5 Buffalo 34,296 0.5
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
- The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts.
- Develop the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported.
- At the .05 level of significance, determine whether the adjusted gross income and the percent audited are related.
- Did the estimated regression equation provide a good fit?
|
District |
Adjusted Gross Income ($) |
Percent Audited |
|
Los Angeles |
36,664 |
1.3 |
|
Sacramento |
38,845 |
1.1 |
|
Atlanta |
34,886 |
1.1 |
|
Boise |
32,512 |
1.1 |
|
Dallas |
34,531 |
1.0 |
|
Providence |
35,995 |
1.0 |
|
San Jose |
37,799 |
0.9 |
|
Cheyenne |
33,876 |
0.9 |
|
Fargo |
30,513 |
0.9 |
|
New Orleans |
30,174 |
0.9 |
|
Oklahoma City |
30,060 |
0.8 |
|
Houston |
37,153 |
0.8 |
|
Portland |
34,918 |
0.7 |
|
Phoenix |
33,291 |
0.7 |
|
Augusta |
31,504 |
0.7 |
|
Albuquerque |
29,199 |
0.6 |
|
Greensboro |
33,072 |
0.6 |
|
Columbia |
30,859 |
0.5 |
|
Nashville |
32,566 |
0.5 |
|
Buffalo |
34,296 |
0.5 |
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