Question

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 + .16x, the point 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.

AGI ($1000') Itemized Deductions ($1000s)
22 9.6
27 9.6
32 10.1
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 11740 as the dollar amount in the box.
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).
$ ( 11,735 , 14,425 )
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. 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

The confidence interval for itemized deductions was provided, but to calculate a prediction interval and guide the IRS agent on which itemized deductions might suggest an audit, additional statistical data such as standard deviation and sample size are required.

Step-by-step explanation:

To develop a 95% confidence interval for the amount of total itemized deductions for all taxpayers with an adjusted gross income of $52,500, we would typically need to conduct a statistical analysis using the given regression equation and an estimate of the standard error of the estimate. However, as you provided the confidence interval pre-computed, we will proceed to the next part.

To develop a 95% prediction interval for the amount of total itemized deductions for a particular taxpayer with an adjusted gross income of $52,500, we would use the estimated regression equation and add and subtract the value that corresponds to the t-distribution for the appropriate degrees of freedom and the standard error of the forecast. This requires more information than provided in your question.

For part C of your question, the IRS agent would be interested in deductions that exceed the upper limit of the prediction interval as that suggests a lower likelihood of such high deductions occurring by chance and therefore may warrant an audit. The precise values for the prediction interval cannot be supplied without additional statistical data such as the standard deviation of the residuals and the sample size.