In Figure 11.35, we discovered a potential multicollinearity problem. It appeared that home size was no longer a significant input given the presence of land area.

(a) Run a single regression based on just land area. What are the coefficients?

(b) What is the R2 value for this model? How does it compare with the adjusted R2 value for the multiple regression model shown in Figure 11.35? Which model appears to be a better predictor of the future of housing prices for this data set?

Figure 11.35

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F 1 Multiple Regression Using Data Analysis 2. 3 SUMMARY OUTPUT 5 Multiple R 6 R Square 7 Adjusted R Square 8 Standard Error 9 Observations 10 11 ANOVA Regression Statistics 0.936 0.876 0849 22.179 31,392.185 35,819.197 12 Signific ance F 0.000 Overall model is significant. 12 13 Regression 14 Residual 15 Total SS 2 31392.185 15696.093 31.910 9 4427.011 11 35819.197 af MS 491.890 16 Lower Upper Coeffi- Standard Enor 48.807 : Stat 2.047 P.value 95% 0.071 -10.490 210.329 0.352 -27.944 70.710 5.282 / 0.001 65.762 164.297 17 cients 95% 18 Intercept 19 (X1) Home size (000 sq ft) 21.383 20 02) Land area (acres) 99.919 21.805 0.981 95% confidence intervals for population slopes 115.030 21.779 Regression coefficients P.value of 0.352 indicates that home size is not significant given presence of land area in the model.