To the internal revenue service the reasonableness of total...

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 14.5 85 18.7 120 24.5 (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). (c) Predict the reasonable level of total itemized deductions (in $1,000s) for a taxpayer with an adjusted gross income of $52,500. If this taxpayer claimed itemized deductions of $20,500, would the IRS agent's request for an audit appear justified? Explain.

Transcript

00:01 Okay, so i see that you need help with this question and it says, to the internal revenue service, the reasonableness of total itemized deductions depends on taxpayers ' adjusted gross income.

00:12 Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes.

00:20 If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an irs audit are increased.

00:30 Data and thousands of dollars on adjusted gross income and the average or reasonableness amount of itemized deductions follow.

00:40 So i took the information and i put it into a table.

00:45 And so a, it says, develop a scatter diagram for this data with adjusted gross income as the independent variable.

00:52 So i am using excel.

00:54 You do not have to use excel.

00:55 You could definitely use paper, pencil, graph paper.

00:58 If you do not have excel, you could use some other program.

01:01 You can follow along.

01:03 I'm using excel as a calculator and to make my graph.

01:09 And if you do not have excel and you're using graph paper, i am going to give you detailed directions on how to, how i got my answer.

01:18 So first thing i'm going to do is i'm going to insert my, my scattered plot or my scatter diagram, and i'm going to insert my trend line so that you can see, and i can display my equation right in here.

01:40 Now excel will automatically give me my equation.

01:45 However, if you need to come up with your equation yourself, there's a couple of different ways to go about that.

01:54 First of all, if you're making your equation on graph paper, you can count by 20s and then for your x -axis and your y -axis, you can count by fives.

02:04 Make sure your axes are labeled.

02:07 So for example, and just get rid of this part.

02:22 So adjusted gross income in thousands.

02:35 And then we have itemized deductions in thousands.

02:50 And this is, again, i'm just going to put in my trend line and my equation.

03:11 And okay.

03:16 So and for my chart title, you can pretty much call this whatever you want.

03:24 We can call this taxpayers.

03:29 Okay.

03:33 So for this, in order to get your linear regression equation, you can find the average of your x value, the average of your y value.

03:47 Then you can find the distance between each one of your x values and your mean of x.

03:55 Then you find your distance between each one of your y value and your mean of y...

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