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.