Question

4. The Transactional Records Access Clearinghouse at Syracuse University reported data showing the chance of an Internal Revenue Service (IRS) audit. The data in file IRSAudit.xlsx show the average adjusted gross income reported (in $ thousands) and the percent of the returns that were audited for 20 selected IRS districts.

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

1. Use XLSTAT to create a scatterplot with average adjusted gross income reported on the horizontal axis and percent of the returns that were audited on the vertical axis. Include the fitted simple linear regression line on the plot and include the plot in your answer. What does the scatterplot indicate about the relationship between the average adjusted gross income reported and the percent of the returns that were audited?

Hint: Select Visualizing data > Scatter plots, select cells B1:B21 for X and select cells C1:C21 for Y. Click “Options” and check “Regression lines.”

2. Use XLSTAT to estimate a simple linear regression model using least squares. Report the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported.

Hint: Select Modeling data > Linear regression, select cells C1:C21 for “Y / Dependent variables: Quantitative” and select cells B1:B21 for “X / Explanatory variables: Quantitative.”

3. Is there a significant linear relationship between the two variables based on a significance level α=0.05α=0.05?

Hint: You can use either a t-test or an F-test to answer this question. In your answer state the hypotheses, test statistic, p-value, decision, and conclusion.

4. Use the estimated regression equation to predict the percent audited for a district with an average adjusted gross income of $35,000.

Answer 1

Ans a ) The scatter plot is

the scatterplot indicate that there is a positive relationship between the average adjusted gross income reported and the percent of the returns that were audited.

b ) the output of regression analysis

we have

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.4659
R Square	0.2171
Adjusted R Square	0.1736
Standard Error	0.2088
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.2175	0.2175	4.9901	0.0384
Residual	18	0.7845	0.0436
Total	19	1.0020
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.4710	0.5842	-0.8061	0.4307	-1.6984	0.7565
Adjusted Gross Income	0.0387	0.0173	2.2339	0.0384	0.0023	0.0751

the estimated regression equation is

the percent audited for a district = -0.4710 +0.0387 * Adjusted Gross Income

c )let the null and alternative hypothesis

Ho:there is not a significant linear relationship between the two variables

Ha: there is a significant linear relationship between the two variables

the value of test stat is 4.99

p value = 0.0384

t since p value is less than 0.05 so we conclude that   there is a significant linear relationship between the two variables.

d ) for adjusted gross income of $35,000.

the percent audited for a district = -0.4710 +0.0387*35 = 0.8835