Data are given below on the adjusted gross income and the amount of itemized ded

Question

Data are given below on the adjusted gross income and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regressien oubeny" 468 t -16r, the point estimate of reasonable level of total itemiand deductiens for a taxpayer with adusted gross income of $52.5 thousand in the questions that follow, enter the dollar amounts equested. For eiample, the regression results provide a value 11-24 thousand. enter a1Ma as the dollar amount in the box. income of ssz soo (to the nearest whele normber). a. Develop a sown confidence interval for the amount of total itemiaed deductions for all taxpayer an aduated s 11735 income of ssa soo (to the nearest whole number) ted gross Develep. 9s% predictien interval for the amount of total emired deductions for taxpayer with an 16840 the particular taapayer referred to in part (b) claimedeotal itemized deductions of s20,400, would the IRS agent's request for an audit agpear to be justified? Ves becaure the deduction is larger than pected ndtunbed grass iseeme of s52.5000. to the .mevnt nemated deductions that would suggest an audit for a taxpaver with d. use your answer to part (b) to give the tous agent a guideln. suggest audit. limit of 10849 Any deductions .xceeding the upper

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Reasonable amount of itemized deductions (In $1000s)
Independent Variable: Adjusted Gross Income ($1000s)
Reasonable amount of itemized deductions (In $1000s) = 4.6767502 + 0.16131015 Adjusted Gross Income ($1000s)
Sample size: 7
R (correlation coefficient) = 0.97717395
R-sq = 0.95486894
Estimate of error standard deviation: 1.3715654

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

b. 95% prediction interval:

$ (9372, 16919)

d. $ 16919

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 4.6767502 1.0333943 0 5 4.5256204 0.0063 Slope 0.16131015 0.015683485 0 5 10.285351 0.0001

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