The high desert area of Southern California is 80 to 90 miles from Newport Beach, Disneyland, and the Staples Center, and perhaps more significantly, 35–45 miles from jobs in the San Bernardino area. A study of the high desert housing market looked at the annual data in Table 8.21 on building permits for single-family homes and the ratio of the median home price in the high desert to the median home price in San Bernardino.

a. Which variable is 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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Year Table 8.21: Exercise 8.50 Price Ratio Building Permits 1997 0.844 152 1998 0.833 200 1999 0.741 315 2000 0.791 419 2001 0.690 655 2002 0.645 986 2003 0.519 2,102 2004 0.635 2,699 2005 0.649 2,258 2006 0.548 3,078 2007 0.625 1,090