1. Suppose that n=100 recent residential home sales in a city are used to fit a least squares straight-line model relating the
    sales price, P, to the square feet of living space, S. Homes in the sample range from 1,500 square feet to 4,000 square feet
    of living space, and the resulting least squares equation is

b. This homeowner is considering building an addition to his house. The contractor estimates that the cost per square foot to
    add on to the house is $55.60. The homeowner considers the home an investment when making the decision to add on and
    wants to maximize profits. Use the relevant information provided in this situation to propose a decision to the homeowner.
    Decision:         ___ Build the addition          ___ Do not build the addition
    Explain the decision. Be sure to use the relevant information.

c. Suppose a house currently contains 2000 square feet. Use the model to estimate the mean sales price. Show your work.
 

2. A car dealer is interested in modeling the relationship between the number of cars sold by the firm each week, C, and the
    number of salespeople who work on the showroom floor per week, S. The dealer believes the relationship between
    the two variables can best be described by a straight line. Using data supplied by the dealer the following model results

a. Interpret the 3.125 for the dealer who has not taken statistics and took algebra too long ago to recall technical terms (refer
    to test instructions).

b. The dealer, Ms. Thornapple, is considering hiring an additional salesperson at a base salary of $400 per week. She plans
    to constrain the bargains of the new salesperson so that the net revenue for her for each car this person sells is $100 (the
    $100 per car covers all costs except the base salary for the new employee--there are no hidden costs here that you
    need to consider). She wants to maximize profits. Use the relevant information provided in this situation to propose a
    decision for her.
    Decision:         ___ Hire the additional salesperson          ___ Do not hire an additional salesperson

    Explain the decision. Be sure to use the relevant information.
 

c. Suppose there are 6 salesperson in the force. Use the model to estimate the mean number of cars sold per week by this
    force. Show your work.
 
 
 

3. A factory manager believes he can approximate the relationship between output of parts per week, Q, and number of
    workers per week, W, with a linear production function for the levels of employment experienced over the last 45 weeks.
    Using data for these weeks, he estimates

a. Interpret the 30.8 for the manager who has not taken statistics and took algebra too long ago to recall technical terms (refer
    to test instructions).

b. The manager has learned of a robot that he believes will, on average, add 421.3 parts per week to production if set
    alongside the existing employees. The cost of the robot is $2000, but the parts are only guaranteed to last a week, so
    that robots must be replaced each week (replacement is cheaper than repairs and maintenance costs). If additional
    employees will cost $200 each per week and the manager can allocate $2000 more dollars, which should he add to the
    production line if he wants to maximize output?
    ___ One robot           ___ Ten new employees

    Explain the decision. Be sure to use the relevant information.
 

c. Use the estimated model to forecast the mean output if there are 200 employees working on the production process. Show
    your work.
 
 

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