26.46 (Optional topic) A lurking variable. Return to the data on selling price versus appraised value for beachfront condominiums that are the basis for the Check Your Skills Exercises 26.16 to 26.24. The data are in order by date of the sale, and the data table includes the number of months from the start of the data period. Here are the residuals from the regression of selling price on appraised value (rounded) ordered from left to right: DATA CONDRES

"44.54 "117.36 "162.48 "178.04 "51.17 "152.00 185.56 "35.93 "84.82 146.25 558.43 229.38 333.15 "105.04 "127.26 "218.57 "101.32 197.20 312.84 599.82 "212.40 "103.89 279.13 "152.20 1.33 "75.73 "96.51 "254.00 "587.00 "26.97 "93.23 "98.10 243.71 "6.01 "73.10 "173.33 "95.12 "145.05 298.23 "164.86 177.96 167.52 127.82 13.35 "240.66 88.59 16.46

(a) Plot the residuals against the explanatory variable (appraised value). To make the pattern clearer, use vertical limits "600 to 600. Does the pattern you see agree with the conditions of linear relationship and constant standard deviation needed for regression inference?

(b) Make a stemplot of the residuals. Are there strong deviations from Normality that would prevent regression inference?

(c) Next, plot the residuals against month. Are the positive and negative residuals randomly scattered, as would be the case if the conditions for regression inference are satisfied? (Comment: Suppose prices for beachfront property rise rapidly during any period. Because property is reassessed just once a year, selling prices might pull away from appraised values over time in the period, creating a pattern of many negative residuals followed by several positive residuals. As this example illustrates, it is often wise to plot residuals against important lurking variables as well as against the explanatory variable.)