Data given below are on the adjusted gross income and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation y=4.68+0.16x , the point estimate of a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of 52,500 is 13,080. Click on the datafile to reference the data. Excel File: data14-37.xlsx Adjusted Gross Reasonable Amount of Itemized Income ($1000s) Deductions ($1000s) 22 9.6 27 9.6 32 10.1 48 11.1 65 13.5 85 17.7 120 25.5 Use the estimated regression coefficients rounded to 2 decimals in your calculations. Round all intermediate calculations to 2 decimal а. Develop a 95 confidence interval for the mean amount of total itemized deductions for all taxpayers with an adjusted gross income of 52,500 (to 2 decimals). $ thousand to $ thousand b. Develop a 95 prediction interval estimate for the amount of total itemized deductions for a particular taxpayer with an adjusted gross income of 52,500 (to 2 decimals). $ thousand to $ thousand d. Use your answer to part (b) to give the IRS agent a guideline as to the amount of total itemized deductions a taxpayer with an adjusted gross income of 52,500 should claim before an audit is recommended (to the nearest whole number). Any deductions exceeding the $ upper limit could suggest an audit.
Data given below are on the adjusted gross income and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation y=4.68+0.16x , the point estimate of a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of 52,500 is 13,080. Click on the datafile to reference the data.
Excel File: data14-37.xlsx
| Adjusted Gross | Reasonable Amount of Itemized | ||
| Income ($1000s) | Deductions ($1000s) | ||
| 22 | 9.6 | ||
| 27 | 9.6 | ||
| 32 | 10.1 | ||
| 48 | 11.1 | ||
| 65 | 13.5 | ||
| 85 | 17.7 | ||
| 120 | 25.5 |
Use the estimated regression coefficients rounded to 2 decimals in your calculations. Round all intermediate calculations to 2 decimal
а. Develop a 95 confidence interval for the mean amount of total itemized deductions for all taxpayers with an adjusted gross income of 52,500 (to 2 decimals).
$ thousand to $ thousand
b. Develop a 95 prediction interval estimate for the amount of total itemized deductions for a particular taxpayer with an adjusted gross income of 52,500 (to 2 decimals).
$ thousand to $ thousand
d. Use your answer to part (b) to give the IRS agent a guideline as to the amount of total itemized deductions a taxpayer with an adjusted gross income of 52,500 should claim before an audit is recommended (to the nearest whole number).
Any deductions exceeding the $ upper limit could suggest an audit.
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