Question 1. To the Internal Revenue Service (IRS), 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 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)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.)=

(b)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.

Question 2. A landscaping company has collected data on home values (in thousands of $) and expenditures (in thousands of $) on landscaping with the hope of developing a predictive model to help marketing to potential new clients. Suppose the following table represents data for 14 households.

Home Value ($1,000)	Landscaping Expenditures ($1,000)
243	8.2
322	10.9
199	12.3
340	16.3
300	15.7
400	18.8
800	23.5
200	9.5
522	17.5
548	22.0
438	12.2
463	13.5
635	17.8
357	13.8

( a)Use the least squares method to develop the estimated regression equation. (Let x = home value (in thousands of $), and let y = landscaping expenditures (in thousands of $). Round your numerical values to five decimal places.) =

(b)For every additional $1,000 in home value, estimate how much additional will be spent (in $) on landscaping. (Round your answer to the nearest cent.)$

(c)Use the equation estimated in part (a) to predict the landscaping expenditures (in $) for a home valued at $375,000. (Round your answer to the nearest dollar.)$

Question 3. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow.

Brokerage	Speed	Satisfaction
Scottrade, Inc.	3.4	3.5
Charles Schwab	3.3	3.4
Fidelity Brokerage Services	3.4	3.9
TD Ameritrade	3.6	3.7
E*Trade Financial	3.2	2.9
Vanguard Brokerage Services	3.8	2.8
USAA Brokerage Services	3.8	3.6
Thinkorswim	2.6	2.6
Wells Fargo Investments	2.7	2.3
Interactive Brokers	4.0	4.0
Zecco.com	2.5	2.5

(a)Develop the least squares estimated regression equation. (Round your numerical values to three decimal places.)=

The slope gives the change in the overall satisfaction rating for every one point increase in the speed of execution rating.

(b)SupposeThinkorswimdeveloped new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of2.6to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating? (Round your answer to one decimal place.)