To the Internal Revenue Service, the reasonableness of total
itemized deductions depends on the taxpayer's adjusted gross
income. Large deductions, which include charity and medical
deductions, are more reasonable for taxpayers with large adjusted
gross incomes. If a taxpayer claims larger than average itemized
deductions for a given level of income, the chances of an IRS audit
are increased. Data (in thousands of dollars) on adjusted gross
income and the average or reasonable amount of itemized deductions
follow.
Adjusted Gross
Income
($1,000s)
Itemized
Deductions
($1,000s)
22
9.6
27
9.6
32
10.1
48
11.1
65
11.5
85
15.7
120
23.5
a. Use the least squares method to develop the estimated
regression equation that can be used to predict itemized deductions
(in $1,000s) given the adjusted gross income (in $1,000s). (Round
your numerical values to three decimal places.)
ŷ =
b. Predict the reasonable level of total itemized deductions (in
$1,000s) for a taxpayer with an adjusted gross income of $47,500.
(Round your answer to two decimal places.)
$(blank)thousand