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# Linear Regression

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The chairman of the marketing department at a large state university undertakes a study to relate starting salary after graduation for marketing majors to grade point average (GPA) in major courses. To do this, records of 7 recent marketing graduates are selected randomly and the results are shown in the table below.
Marketing Starting Salary
1 3.26 33.8
2 2.60 29.8
3 3.35 33.5
4 2.86 30.4
5 3.82 36.4
6 2.21 27.6
7 3.47 35.3

a) Determine the least squares regression line for predicting starting salary on the basis of GPA in major courses.

b) Based on a review of the coefficients of determination and correlation, comment on whether the independent variable chosen is a good predictor of the dependent variable in this example.

c) John Smith, a marketing major from this university with a GPA in major courses of 3.92, would like an estimate of his expected starting salary. Using the least squares regression line, what could he expect to receive?

2. A firm wishes to choose the location for a new factory in one of three possible locations. Profits obtained will depend upon whether a new railroad spur is constructed to serve the town in which the new factory will be located. The firm choosing the site for the new factory has no control on where the railroad spur is to be constructed, but has received some advanced information on the probability of where it may be constructed. The firm believes there is a 25% chance of the spur being constructed in location A, 35% chance in location B, and a 40% chance of the spur being constructed in location C.

Profits expected in millions of \$ are shown below based on whether or not a spur is constructed for each of the three possible factory locations.

Location Alternatives Spur Constructed Spur Constructed
Location A \$1 \$14
Location B \$2 \$10
Location C \$4 \$ 6

Based on the information, determine the decision to be made for:

a) A strategy of maximizing expected payoff.

b) A strategy of minimizing expected opportunity loss.