Question

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 15.5 85 19.7 120 27.5 (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.) ŷ = __ (C) Predict the reasonable level of total itemized deductions (in $1,000s) for a taxpayer with an adjusted gross income of $52,500. (Round your answer to two decimal places.) $ _ thousand

          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
15.5
85
19.7
120
27.5
(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.)
ŷ = __________
(C) Predict the reasonable level of total
itemized deductions (in $1,000s) for a taxpayer with an adjusted
gross income of $52,500. (Round your answer to two decimal
places.)
$ _________  thousand

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Added by Jacob S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jerelyn Nevil

05/16/2023

Step 1

First, we need to find the least squares regression line equation. To do this, we need to calculate the mean of the adjusted gross income (x) and the mean of the itemized deductions (y). Mean of x (Adjusted Gross Income): (22 + 27 + 32 + 48 + 65 + 85 + 120) / 7 = Show more…

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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 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 15.5 85 19.7 120 27.5 (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.) ŷ = __________ (C) Predict the reasonable level of total itemized deductions (in $1,000s) for a taxpayer with an adjusted gross income of $52,500. (Round your answer to two decimal places.) $ _________ thousand

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Transcript

00:01 I'm going to use excel, but you can use any type of free program out there to come up with your regression equation and for your scatter diagram.

00:10 You can go as far as also using paper and pencil.

00:14 However, with this type of problem, i'm assuming that you have some type of program or are using some type of a free program.

00:21 But in excel, i'll show you how you can answer this question.

00:25 So it says, to the internal revenue service, the reasonableness of a total itemized deductions depends on the taxpayer's adjusted gross income.

00:34 Large deductions, which include charity medical deductions, are more reasonable for taxpayers with large adjusted gross incomes.

00:41 If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an irs audit are increased.

00:52 Data in thousands of dollars on adjusted gross income in the average reasonableness amount of itemized deductions are as follows.

01:00 So develop, it wants you to develop a scatter diagram.

01:06 So i'm just gonna move this down.

01:10 And so here's, i'm gonna insert and i'm going to put in my scatter diagram and i'm going to insert a table, or i'm sorry, titles.

01:25 And so for the titles, i'm going to put in, let's see, so i have this and i'm going to, for my axes title, this one is called adjusted gross income.

01:44 And this is in the thousands of dollars.

01:48 And then for the reasonableness amount, reasonable amount of itemized deductions, and this is in the thousands.

02:11 Okay, and i'm just gonna make this bigger so that way it can kind of spread out a little bit.

02:16 All right, and let me bold this.

02:20 So i'm gonna bold this and make this bigger and bold this and make this bigger.

02:28 And actually we can add a title and we can call this the irs.

02:37 So deductions, irs deductions, okay...

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