Question

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

a) Use XLSTAT to compute a 95% confidence interval for the average percent audited of districts with an average adjusted gross income of $35,000. Interpret the interval in the context of the application.

b) Use XLSTAT to compute a 95% prediction interval for the percent audited of an individual district with an average adjusted gross income of $35,000. Interpret the interval in the context of the application.

c) Use the regression output in XLSTAT to calculate the coefficient of determination, r2r2 from the sum of squares due to regression (SSR) and the total sum of squares (SST). Interpret your calculated value of r2r2 in the context of the application.

Answer 1

District	Adjusted Gross Income (x)	Percent Audited	(x-x_)^2
Los Angeles	36.664	1.3	9.17
Sacramento	38.845	1.1	27.14
Atlanta	34.886	1.1	1.56
Boise	32.512	1.1	1.26
Dallas	34.531	1	0.80
Providence	35.995	1	5.57
San Jose	37.799	0.9	17.33
Cheyenne	33.876	0.9	0.06
Fargo	30.513	0.9	9.75
New Orleans	30.174	0.9	11.98
Oklahoma City	30.06	0.8	12.78
Houston	37.153	0.8	12.37
Portland	34.918	0.7	1.64
Phoenix	33.291	0.7	0.12
Augusta	31.504	0.7	4.54
Albuquerque	29.199	0.6	19.68
Greensboro	33.072	0.6	0.32
Columbia	30.859	0.5	7.71
Nashville	32.566	0.5	1.14
Buffalo	34.296	0.5	0.44
Total	672.71	16.60	145.38

SUMMARY OUTPUT
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

c)

r^2==SSR/SST= 0.2175/1.0020=0.2171

Interpretation: 21.71% variation of the model or response variable (percent audited) is explained by the explanatory variable (average adjusted gross income).