EBK STATISTICS FOR BUSINESS & ECONOMICS
12th Edition
ISBN: 9780100460461
Author: Anderson
Publisher: YUZU
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Chapter 14.2, Problem 13E
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 ($1000s) | Reasonable Amount of Itemized Deductions ($1000s) |
| 22 | 9.6 |
| 27 | 9.6 |
| 32 | 10.1 |
| 48 | 11.1 |
| 65 | 13.5 |
| 85 | 17.7 |
| 120 | 25.5 |
- a. Develop a
scatter diagram for these data with adjusted gross income as the independent variable. - b. Use the least squares method to develop the estimated regression equation.
- c. Predict the reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52,500. If this taxpayer claimed itemized deductions of $20,400, would the IRS agent’s request for an audit appear justified? Explain.
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To the Internal Revenue Service (IRS), 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 larg
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 Itemized Deductions
($1,000s)
22
($1,000)
9.6
27
9.6
32
10.1
48
11.1
65
13.5
85
120
15.7
25.5
(a) Develop a scatter diagram for these data with adjusted gross income as the independent variable.
30
25
20
15
10
5
30
25
20
15
10
5+
30
25-
20-
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10-
..
5-
0
20 40 60
80 100 120 140
Adjusted Gross Income ($1,000s)
0
20 40 60 80 100 120 140
0
Adjusted Gross Income ($1,000s)
20 40 60 80 100 120 140
Adjusted Gross Income ($1,000s)
30
25
20
15
10
5-
0
20 40 60 80 100
Adjusted Gross Income ($1,000s)
120
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(b) Use the least squares method to…
To the Internal Revenue Service (IRS), 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 th
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)
22
Itemized Deductions
($1,000s)
9.6
27
9.6
32
10.1
48
11.1
65
11.5
85
120
19.7
23.5
(a) Develop a scatter diagram for these data with adjusted gross income as the independent variable.
30
25
20
15
•
10
5
Itemized Deductions ($1,000s)
0
20 40 60 80 100 120
Adjusted Gross Income ($1,000s)
140
30
25
20
15
10
5.
Itemized Deductions ($1,000s)
30
25
20
15
10
•
15
•
10
5-
0
20 40 60
80 100 120 140
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Adjusted Gross Income ($1,000s)
20 40 60 80 100…
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
13.5
85
19.7
120
27.5
(a)
Develop a scatter diagram for these data with adjusted gross income as the independent variable.
(b)
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…
Chapter 14 Solutions
EBK STATISTICS FOR BUSINESS & ECONOMICS
Ch. 14.2 - Given are five observations for two variables, x...Ch. 14.2 - Given are five observations for two variables, x...Ch. 14.2 - Given are five observations collected in a...Ch. 14.2 - The following data give the percentage of women...Ch. 14.2 - Elliptical trainers are becoming one of the more...Ch. 14.2 - The National Football League (NFL) records a...Ch. 14.2 - A sales manager collected the following data on...Ch. 14.2 - The American Association of Individual Investors...Ch. 14.2 - Using a global-positioning-system (GPS)-based...Ch. 14.2 - On March 31, 2009, Ford Motor Companys shares were...
Ch. 14.2 - Sporty cars are designed to provide better...Ch. 14.2 - Concur Technologies, Inc., is a large...Ch. 14.2 - To the Internal Revenue Service, the...Ch. 14.2 - PCWorld rated four component characteristics for...Ch. 14.3 - The data from exercise 1 follow. xi 1 2 3 4 5 yi 3...Ch. 14.3 - The data from exercise 2 follow. xi 3 12 6 20 14...Ch. 14.3 - The data from exercise 3 follow. xi 2 6 9 13 20 yi...Ch. 14.3 - The following data show the brand, price (), and...Ch. 14.3 - In exercise 7 a sales manager collected the...Ch. 14.3 - Bicycling, the worlds leading cycling magazine,...Ch. 14.3 - An important application of regression analysis in...Ch. 14.3 - Refer to exercise 5 where the following data were...Ch. 14.5 - The data from exercise 1 follow. xi 1 2 3 4 5 yi 3...Ch. 14.5 - The data from exercise 2 follow. xi 3 12 6 20 14...Ch. 14.5 - The data from exercise 3 follow. xi 2 6 9 13 20 yi...Ch. 14.5 - In exercise 18 the data on price () and the...Ch. 14.5 - The number of megapixels in a digital camera is...Ch. 14.5 - In exercise 8 ratings data on x = the quality of...Ch. 14.5 - Refer to exercise 21, where data on production...Ch. 14.5 - Prob. 30ECh. 14.5 - In exercise 20, data on x = weight (pounds) and y...Ch. 14.6 - The data from exercise 1 follow. xi 1 2 3 4 5 yi 3...Ch. 14.6 - The data from exercise 2 follow. xi 3 12 6 20 14...Ch. 14.6 - The data from exercise 3 follow. xi 2 6 9 13 20 yi...Ch. 14.6 - The following data are the monthly salaries y and...Ch. 14.6 - In exercise 7, the data on y = annual sales (...Ch. 14.6 - In exercise 13, data were given on the adjusted...Ch. 14.6 - Refer to exercise 21, where data on the production...Ch. 14.6 - Almost all U.S. light-rail systems use electric...Ch. 14.7 - The commercial division of a real estate firm is...Ch. 14.7 - Following is a portion of the computer output for...Ch. 14.7 - A regression model relating x, number of...Ch. 14.7 - Out-of-state tuition and fees at the top graduate...Ch. 14.7 - Automobile racing, high-performance driving...Ch. 14.8 - Given are data for two variables, x and y. xi 6 11...Ch. 14.8 - The following data were used in a regression...Ch. 14.8 - Data on advertising expenditures and revenue (in...Ch. 14.8 - Refer to exercise 7, where an estimated regression...Ch. 14.8 - Recent family home sales in San Antonio provided...Ch. 14.9 - Consider the following data for two variables, x...Ch. 14.9 - Consider the following data for two variables, x...Ch. 14.9 - Charity Navigator is Americas leading independent...Ch. 14.9 - Many countries, especially those in Europe, have...Ch. 14.9 - Prob. 54ECh. 14 - Does a high value of r2 imply that two variables...Ch. 14 - In your own words, explain the difference between...Ch. 14 - What is the purpose of testing whether 1 = 0? If...Ch. 14 - The Dow Jones Industrial Average (DJIA) and the...Ch. 14 - The following data show Morningstars Fair Value...Ch. 14 - One of the biggest changes in higher education in...Ch. 14 - Jensen Tire Auto is in the process of deciding...Ch. 14 - In a manufacturing process the assembly line speed...Ch. 14 - A sociologist was hired by a large city hospital...Ch. 14 - The regional transit authority for a major...Ch. 14 - A marketing professor at Givens College is...Ch. 14 - The Transactional Records Access Clearinghouse at...Ch. 14 - The Toyota Camry is one of the best-selling cars...Ch. 14 - You have been assigned to analyze the risk...Ch. 14 - As part of a study on transportation safety, the...Ch. 14 - Consumer Reports tested 166 different...Ch. 14 - Finding the Best Car Value When trying to decide...
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