The data in Table 8.20 are for 16 three-digit ZIP codes within 4 hours’ driving time of a Southern California casino. The driving time to the casino is in hours and the gambling activity is the total dollars lost at the casino by residents of the ZIP code divided by the median income, in thousands of dollars, in that ZIP code.

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 8.20: Exercise 8.49 Driving Gambling Driving Time Activity Time Gambling Activity Driving Gambling Driving Gambling Time Activity Time Activity 0.35 1.2897 1.35 0.0650 1.52 0.0462 1.67 0.0104 0.67 0.3783 1.35 0.0405 1.53 0.0026 1.90 0.0094 0.82 0.2332 1.35 0.0033 1.57 0.0340 2.00 0.0031 0.98 0.1299 1.37 0.0943 1.58 0.0173 2.35 0.0182 1.07 0.1198 1.38 0.0213 1.58 0.0153 2.55 0.0048 1.22 0.0318 1.43 0.0277 1.58 0.0130 2.78 0.0001 1.22 0.0503 1.47 0.0233 1.63 0.0059 3.02 0.0010 1.27 0.0075 1.52 0.0351 1.63 0.0379 3.65 0.0020