Southern California casinos were given “location values” based on how close they are to households of various income levels and the location of competing casinos.

A casino has a higher location value if potential customers with money to spend are nearby and there are fewer competing casinos. Data were also collected on the number of gaming devices (primarily slot machines) installed at each casino. These data are in Table 8.19.

a. Which variable would you consider to be the dependent variable?

b. Do you expect the relationship between these two variables to be positive, negative, or 0?

c. Estimate the linear relationship between these two variables, Y = α₁ + β₁X + ε₁.

d. Estimate the log-linear relationship between the natural logarithms of these two variables, ln[Y] = α₂ + β₂ln[X] + ε₂.

e. Which of these two estimated relationships seems to fit these data better?

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Table 8.19: Exercise 8.48 Gaming Location Gaming Location Gaming Location Devices Value Devices Value Devices Value 1,996 120.75 1,956 71.91 349 0.07 2,000 110.28 2,045 158.13 2,000 404.02 2,268 128.99 751 60.07 230 0.01 1,049 70.89 2,000 79.66 302 25.24 1,261 92.62 961 54.80 2,000 132.10 1,599 75.28 1,039 58.27 2,139 169.47