Question

To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer's adjusted gross income. Larga deductions, which incluce charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. It a taxpayer dalms larger than average Itemized deductions for a given level of income, the chances of an IRS audit are increased. Data in thousands of dollars) an adjusted gross income and the average or reasonable amount of loomized deductions follow. R Adjusted Gross Income ($1000s) onable Amount of Itemized Deductions ($1000s) 10.1 11.1 13.5 17.7 25.5 a. Which of the following scatter diagrams accurately represents the cata? 3 Scatter dingram 1 : 1. Compute by ord op (to 4 decimals). Complete the estimated regression equation to 2 decimals). c. Pruulist a rentable of total time w 3 thousand dollars ions for a lawyer with an a g ress in one of $52.5 thousand to 2 decimals). What is the value in dollars, of the deductions calculated in part (c) above to the reares: whole number)? If this taxpayer claimed itemized deductions of $20,000, would the IRS agent's request for an audit appear justified? Yes, $20,400 is higher than the estimated resonable level:

Answer 1

Answer: Adjusted Gross Income (x) 23 8.6 9.6 27 32 Reasonable amount of X2 Y XY: I temized deduction 02 484 73.96 189.2 729 92.16 259,2 1024 02.01 323.23 llele bat 2304 123.32_532.8 13.5. - 3025 182-25 742.5 17.7 7225 313.29 1504.5 25.5 14400 650.25 30 60 10.1 48 55 85 120 X = ?X 55,5714 Y = 13.7286 o = 1081.9592 Cov(x) = 2 - X Y = 6091.4 - 55.5714(13.7286)_ YHHAY COV(x,y) = 181-5682 b = Cov(1, - 0.1678 - 181.5682 1981.9592 bo Regression line Yon x is L-I = byn Cx-x) 1 - 3 + bx ( x - 3) 13.728 6 + 0.1678 X - 01078 (55.5714) X = 4.4037 + 0.1678 X Tbi= 01676 Ibo = 4.4037

for X- 52.5 Y = 4.4037 + 0.1078 (52.5) Y = 13.2132 Thousand dollars) = $13213.2 Tŷ = $13,213)