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	25.5

(a)Develop a scatter diagram for these data with adjusted gross income as the independent variable.

A scatter diagram has 7 points plotted on it. The horizontal axis ranges from 0 to 140 and is labeled: Adjusted Gross Income ($1,000s). The vertical axis ranges from 0 to 30 and is labeled: Itemized Deductions ($1,000s). The 5 leftmost points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 20 to 70 on the horizontal axis and between 10 to 26 on the vertical axis. The other 2 points are between 80 to 120 on the horizontal axis and are both at approximately 10 on the vertical axis. The 5 leftmost points show little scatter, but are noticeably distant from the other 2 points.

A scatter diagram has 7 points plotted on it. The horizontal axis ranges from 0 to 140 and is labeled: Adjusted Gross Income ($1,000s). The vertical axis ranges from 0 to 30 and is labeled: Itemized Deductions ($1,000s). The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the diagram and are between 20 to 120 on the horizontal axis and between 9 to 26 on the vertical axis. The direction the points are plotted in becomes less steep as adjusted gross income increases. The points show little scatter.

A scatter diagram has 7 points plotted on it. The horizontal axis ranges from 0 to 140 and is labeled: Adjusted Gross Income ($1,000s). The vertical axis ranges from 0 to 30 and is labeled: Itemized Deductions ($1,000s). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 20 to 120 on the horizontal axis and between 9 to 26 on the vertical axis. The points show little scatter.

A scatter diagram has 7 points plotted on it. The horizontal axis ranges from 0 to 140 and is labeled: Adjusted Gross Income ($1,000s). The vertical axis ranges from 0 to 30 and is labeled: Itemized Deductions ($1,000s). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 20 to 120 on the horizontal axis and between 6 to 23 on the vertical axis. The points show little scatter.

(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.)=

(c)Predict the reasonable level of total itemized deductions (in $1,000s) for a taxpayer with an adjusted gross income of $47,500. (Round your answer to two decimal places.)$ thousandIf this taxpayer claimed itemized deductions of $20,600, would the IRS agent's request for an audit appear justified? Explain.

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.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. 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.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.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.