13. A geographer compares residential lot sizes in four quadrants of a city To do this, he randomly samples 300 records from a city file on home residences and records the lot sizes (in thousands of square feet) by quadrant. The ANOVA table (Table 12.32) refers to a comparison of mean lot sizes for the northeast (NE), northwest (NW). southwest (SW). and southeast (SE) quadrants of the city.

TABLE 12.32 Sum of Mean Source Squares DF Square F Prob > F Quadiant 2700 3 1480 296 Total 4180 299

a) Find the F test statistic for Ho: 4 = 2=3=4, and report the P-value. Inter- pret.

b) Find the square root of the mean square in the "Error" row of the table, and interpret its value.

c) The sample mean lot sizes for the NE, NW. SW, and SE quadrants are 8, 15. 11, and 9, with n =100. n = 100, n3 = 50, n = 50. Illustrate simultaneous 94% confidence intervals for the pairwise differences in means by constructing the interval comparing the NE and NW quadrants. Would separate 94% confidence intervals for the differences be- tween each pair of means be wider, or narrower? Explain.

d) Set up dummy variables for a regression model with which one could conduct the ANOVA F test. State the regression model and interpret the parameters.