Question

10. X Data are given below on the adjusted gross income x and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation = 4.68 +.16 estimate of a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52.5 thousand is $13.08 thousand. 11. Adjusted Gross Income ($1000s) Reasonable Amount of Itemized Deductions ($1000s) 9.6 22 27 9.6 10.1 32 48 11.1 65 13.5 85 17.7 120 25.5 In the questions that follow, enter the dollar amounts requested. For example, if the regression results provide a value of 11.74 thousand, enter 11,740 as the dollar amount in the box. Use Table 1 of Appendix B. a. Develop a 95% confidence interval for the amount of total itemized deductions for all taxpayers with an adjusted gross income of $52,500 (to the nearest whole number). $ b. Develop a 95% prediction interval for the amount of total itemized deductions for a particular taxpayer with an adjusted gross income of $52,500 (to the nearest whole number). $ ) C. If the particular taxpayer referred to in part (b) claimed total itemized deductions of $20,400, would the IRS agent's request for an audit appear to be justified? Select x d. Use your answer to part (b) to give the IRS agent a guideline as to the amount of itemized deductions that would suggest an audit for a taxpayer with an adjusted gross income of $52,500. Any deductions exceeding the upper limit of $ could suggest an audit.

Answer 1

(a)

95% Confidence Interval
lower	upper
11717	14413

(b)

95% Prediction Interval
lower	upper
9290	16839

(c) Yes

(d) 16839

	r²	0.955
	r	0.977
	Std. Error	1.372
	n	7
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	199.0083	1	199.0083	105.79	.0001
Residual	9.4060	5	1.8812
Total	208.4143	6
Regression output				confidence interval
variables	coefficients	std. error	t (df=5)	p-value	95% lower	95% upper
Intercept	4.6768
x	0.1613	0.0157	10.285	.0001	0.1210	0.2016
Predicted values for: y
		95% Confidence Interval	95% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
52	13.0649	11717	14413	9290	16839	0.146