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 adjus adjusted gross income and the average or reasonable amount of itemized deductions follow. Itemized Deductions ($1,000s) Adjusted Gross Income ($1,000s) 22 O 301 25 20 15 10 5 27 0 32 48 65 85 120 ... 9.6 (a) Develop a scatter diagram for these data with adjusted gross Income as the Independent variable. 9.6 10.1 x 11.1 15.5 17.7 27.5 20 40 60 80 100 120 140 Adjusted Gross Income ($1,000s) 30T 25 20 15- 10 5- 0 20 40 60 80 100 120 Adjusted Gross Income ($1,000s) 120 140 E 30 25 20- 15 10- 5- 0 ... 20 40 60 80 100 120 140 Adjusted Gross Income ($1,000s) (c) 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.) $ 13.08 x thousand If this taxpayer claimed itemized deductions of $20,400, would the IRS agent's request for an audit appear justified? Explain. O Since the predicted amount of itemized deductions is significantly greater than the actual claimed itemized deductions, the agent's request for an audit does not appear justified. O Since the predicted amount of itemized deductions is roughly the same as the actual claimed itemized deductions, the agent's request for an audit does not appear to be justified. be Deductions ( (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 places.) 94.155 +0.170x Since the predicted amount of itemized deductions is significantly less than the actual claimed itemized deductions, the agent's request for an audit appears to be justified. O Since the predicted amount of itemized deductions is roughly the same as the actual claimed itemized deductions, the agent's request for an audit appears to be justified. O Since the predicted amount of itemized deductions is significantly greater than the actual claimed itemized deductions, the agent's request for an audit appears to be justified. 30 25 20 13- 10- 5 0 80 100 120 120 140 20 40 60 Adjusted Gross Income ($1,000s)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 adjust
adjusted gross income and the average or reasonable amount of itemized deductions follow.
Itemized Deductions
($1,000s)
Adjusted Gross Income
($1,000s)
Itemized Deductions ($1,000s)
301
25
20
15
10
5
22
27
0 20
32
48
65
85
120
...
9.6
(a) Develop a scatter diagram for these data with adjusted gross Income as the Independent variable.
9.6
10.1
11.1
x
15.5
17.7
27.5
←
40 60 80 100 120 140
Adjusted Gross Income ($1,000s)
Remized Deductions ($1,000s)
30-
25
20-
15
10-
5-
0
20 40
Adjusted Gross Income ($1,000s)
60 80 100 120 140
emized Deductions ($1,00
30
25
20
15
10
5-
0
40 60 80 100 120
Adjusted Gross Income ($1,000s)
20
(c) 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.)
$ 13.08
x thousand
140
If this taxpayer claimed itemized deductions of $20,400, would the IRS agent's request for an audit appear justified? Explain.
O Since the predicted amount of itemized deductions is significantly greater than the actual claimed itemized deductions, the agent's request for an audit does not appear to be
justified.
O Since the predicted amount of itemized deductions is roughly the same as the actual claimed itemized deductions, the agent's request for an audit does not appear to be
justified.
O
Since the predicted amount of itemized deductions is significantly less than the actual claimed itemized deductions, the agent's request for an audit appears to be justified.
O Since the predicted amount of itemized deductions is roughly the same as the actual claimed itemized deductions, the agent's request for an audit appears to be justified.
O Since the predicted amount of itemized deductions is significantly greater than the actual claimed itemized deductions, the agent's request for an audit appears to be justified.
Itemized Deductions ($1,
ongno ino
30
20
15-
10-
5
0
(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 places.)
>= 4.155 +0.170x
...
20
80 100
60
40
Adjusted Gross Income ($1,000s)
120 140
Transcribed Image Text: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 adjust adjusted gross income and the average or reasonable amount of itemized deductions follow. Itemized Deductions ($1,000s) Adjusted Gross Income ($1,000s) Itemized Deductions ($1,000s) 301 25 20 15 10 5 22 27 0 20 32 48 65 85 120 ... 9.6 (a) Develop a scatter diagram for these data with adjusted gross Income as the Independent variable. 9.6 10.1 11.1 x 15.5 17.7 27.5 ← 40 60 80 100 120 140 Adjusted Gross Income ($1,000s) Remized Deductions ($1,000s) 30- 25 20- 15 10- 5- 0 20 40 Adjusted Gross Income ($1,000s) 60 80 100 120 140 emized Deductions ($1,00 30 25 20 15 10 5- 0 40 60 80 100 120 Adjusted Gross Income ($1,000s) 20 (c) 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.) $ 13.08 x thousand 140 If this taxpayer claimed itemized deductions of $20,400, would the IRS agent's request for an audit appear justified? Explain. O Since the predicted amount of itemized deductions is significantly greater than the actual claimed itemized deductions, the agent's request for an audit does not appear to be justified. O Since the predicted amount of itemized deductions is roughly the same as the actual claimed itemized deductions, the agent's request for an audit does not appear to be justified. O Since the predicted amount of itemized deductions is significantly less than the actual claimed itemized deductions, the agent's request for an audit appears to be justified. O Since the predicted amount of itemized deductions is roughly the same as the actual claimed itemized deductions, the agent's request for an audit appears to be justified. O Since the predicted amount of itemized deductions is significantly greater than the actual claimed itemized deductions, the agent's request for an audit appears to be justified. Itemized Deductions ($1, ongno ino 30 20 15- 10- 5 0 (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 places.) >= 4.155 +0.170x ... 20 80 100 60 40 Adjusted Gross Income ($1,000s) 120 140
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