(30 pts) In assessing street stability, the "rate of rutting" was measured on 31 experimental asphalt pavements. Five independent or predictor variables were used to specify the conditions under which asphalt was prepared, while a sixth "dummy" variable was used to express the difference between the two separate "blocks" of runs into which the experiment was divided (15 in one block, 16 in the other). The equation used to fit the data was Y = B0 + B1X1 + B2X2 + B3X3 + B4X4 + B5X5 + B6X6 + E where Y = log(change of rut depth in inches per million wheel passes) X1 = log(viscosity of asphalt) X2 = percent asphalt in surface course X3 = percent asphalt in base course X4 = dummy variable to separate two sets of runs X5 = percent fines in surface course X6 = percent voids in surface course You may assume that the above equation is "complete" in the sense that it includes all the relevant terms. Your assignment is to select a suitable subset of these terms as the "best" regression equation under the circumstances. The residual sums of squares for all 64 of the possible regressions are given below, together with dummy indices for each X indicating whether the corresponding term is present in (1) or absent from (0) the model being fit. (note: n the number of observations=31; the number of models fit = 64.) The first row, with all Variables 0, is simply the constant fit. X1 X2 X3 X4 X5 X6 Residual Sum of Squares 0 0 0 0 0 0 11.0580 1 0 0 0 0 0 0.6070 0 1 0 0 0 0 10.7950 1 1 0 0 0 0 0.4990 0 0 1 0 0 0 10.6630 1 0 1 0 0 0 0.6000 0 1 1 0 0 0 10.1680 1 1 1 0 0 0 0.4980 0 0 0 1 0 0 1.5220 1 0 0 1 0 0 0.5820 0 1 0 1 0 0 1.2180 1 1 0 1 0 0 0.4500 0 0 1 1 0 0 1.4530 1 0 1 1 0 0 0.5810 0 1 1 1 0 0 1.0410 1 1 1 1 0 0 0.4410 0 0 0 0 1 0 9.9220 1 0 0 0 1 0 0.5970 0 1 0 0 1 0 9.4790 1 1 0 0 1 0 0.4770 0 0 1 0 1 0 9.8910 1 0 1 0 1 0 0.5820 0 1 1 0 1 0 9.3620 1 1 1 0 1 0 0.4750 0 0 0 1 1 0 1.3970 1 0 0 1 1 0 0.5690 0 1 0 1 1 0 1.0300 1 1 0 1 1 0 0.4130 0 0 1 1 1 0 1.3830 1 0 1 1 1 0 0.5610 0 1 1 1 1 0 0.9580 1 1 1 1 1 0 0.4120 0 0 0 0 0 1 9.1960 1 0 0 0 0 1 0.5760 0 1 0 0 0 1 9.1920 1 1 0 0 0 1 0.3670 0 0 1 0 0 1 8.8480 1 0 1 0 0 1 0.5670 0 1 1 0 0 1 8.8380 1 1 1 0 0 1 0.3650 0 0 0 1 0 1 1.5070 1 0 0 1 0 1 0.5580 0 1 0 1 0 1 1.1920 1 1 0 1 0 1 0.3230 0 0 1 1 0 1 1.4370 1 0 1 1 0 1 0.5550 0 1 1 1 0 1 0.9950 1 1 1 1 0 1 0.3110 0 0 0 0 1 1 7.6800 1 0 0 0 1 1 0.5740 0 1 0 0 1 1 7.6790 1 1 0 0 1 1 0.3640 0 0 1 0 1 1 7.6780 1 0 1 0 1 1 0.5610 0 1 1 0 1 1 7.6750 1 1 1 0 1 1 0.3640 0 0 0 1 1 1 1.3520 1 0 0 1 1 1 0.5530 0 1 0 1 1 1 1.0240 1 1 0 1 1 1 0.3130 0 0 1 1 1 1 1.3420 1 0 1 1 1 1 0.5450 0 1 1 1 1 1 0.9390 1 1 1 1 1 1 0.3070 a) The information provided in the above table is enough to fit plots of R^2, R^2_adj, and C_p for all of the models. Describe how. b) Produce plots using the above three criteria. If some of your values are excessively large, produce one plot including all values and another truncated so as to highlight those of interest. Include the line C_p = p in the C_p plot for visual reference. c) Produce a table of the corresponding values, in the form Variables R^2 R^2_adj C_p d) Choose the best 4 or 5 models based on the above. What variables do they have in common? Which variable values would you like to know?