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# Using the Least Squares Method for Regression Analysis

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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.
Reasonable Amount of

Adjusted Gross Income (\$1000s) 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. Estimate a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of \$52,500 (2 decimals).

d. What is the value, in dollars, of the deductions calculated in part (c) above?