Instructions: This is an open book test. You may use notes, text, other books and a calculator. Your presentations of statistical analysis will be marked for clarity of explanation. I expect you to explain what assumptions you are making and to comment if those assumptions seem unreasonable. The exam is out of 25.
data roofing; infile 'roofing.dat' ; input Sales Promo Active Compet Potent; proc glm data=roofing; model Sales = Promo Active Compet Potent; run ; proc glm data=roofing; model Sales = Promo Active Compet; run ; proc glm data=roofing; model Sales = Promo Active Potent; run ; proc glm data=roofing; model Sales = Promo Compet Potent; run ; proc glm data=roofing; model Sales = Active Compet Potent; run ; proc glm data=roofing; model Sales = Promo Active ; run ; proc glm data=roofing; model Sales = Promo Compet; run ; proc glm data=roofing; model Sales = Promo Potent; run ; proc glm data=roofing; model Sales = Active Compet ; run ; proc glm data=roofing; model Sales = Active Potent; run ; proc glm data=roofing; model Sales = Compet Potent; run ; proc glm data=roofing; model Sales = Promo ; run ; proc glm data=roofing; model Sales = Active ; run ; proc glm data=roofing; model Sales = Compet; run ; proc glm data=roofing; model Sales = Potent; run ;
Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 4 176777.06150 44194.26538 479.10 0.0001 Error 21 1937.13696 92.24462 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.989161 5.642757 9.6044061 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.59804 4510.59804 48.90 0.0001 ACTIVE 1 105117.72438 105117.72438 1139.55 0.0001 COMPET 1 67104.34254 67104.34254 727.46 0.0001 POTENT 1 44.39655 44.39655 0.48 0.4954 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 257.753913 257.753913 2.79 0.1094 ACTIVE 1 38269.428409 38269.428409 414.87 0.0001 COMPET 1 66682.540623 66682.540623 722.89 0.0001 POTENT 1 44.396549 44.396549 0.48 0.4954 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 178.3203403 13.76 0.0001 12.96031930 PROMO 1.8070643 1.67 0.1094 1.08103934 ACTIVE 3.3178334 20.37 0.0001 0.16289176 COMPET -21.1849842 -26.89 0.0001 0.78793899 POTENT 0.3245124 0.69 0.4954 0.46776444 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 3 176732.66495 58910.88832 654.06 0.0001 Error 22 1981.53351 90.06970 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.988912 5.575839 9.4905060 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.59804 4510.59804 50.08 0.0001 ACTIVE 1 105117.72438 105117.72438 1167.07 0.0001 COMPET 1 67104.34254 67104.34254 745.03 0.0001 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 228.908656 228.908656 2.54 0.1252 ACTIVE 1 49843.667563 49843.667563 553.39 0.0001 COMPET 1 67104.342537 67104.342537 745.03 0.0001 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 179.8442849 14.25 0.0001 12.62132900 PROMO 1.6772431 1.59 0.1252 1.05209332 ACTIVE 3.3693924 23.52 0.0001 0.14323065 COMPET -21.2165097 -27.30 0.0001 0.77729880 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 3 110094.52088 36698.17363 11.77 0.0001 Error 22 68619.67758 3119.07625 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.616037 32.81208 55.848691 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.59804 4510.59804 1.45 0.2419 ACTIVE 1 105117.72438 105117.72438 33.70 0.0001 POTENT 1 466.19846 466.19846 0.15 0.7028 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 190.680080 190.680080 0.06 0.8070 ACTIVE 1 74129.881595 74129.881595 23.77 0.0001 POTENT 1 466.198464 466.198464 0.15 0.7028 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT -79.72317175 -1.57 0.1297 50.64582944 PROMO 1.55420109 0.25 0.8070 6.28590108 ACTIVE 4.45836475 4.88 0.0001 0.91451733 POTENT 1.04982923 0.39 0.7028 2.71547768 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 3 138507.63309 46169.21103 25.26 0.0001 Error 22 40206.56537 1827.57115 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.775023 25.11643 42.750101 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.59804 4510.59804 2.47 0.1305 COMPET 1 122378.39935 122378.39935 66.96 0.0001 POTENT 1 11618.63570 11618.63570 6.36 0.0194 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 3866.54364 3866.54364 2.12 0.1599 COMPET 1 102542.99381 102542.99381 56.11 0.0001 POTENT 1 11618.63570 11618.63570 6.36 0.0194 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 318.3828110 6.51 0.0001 48.89801708 PROMO 6.8154836 1.45 0.1599 4.68567717 COMPET -25.3644484 -7.49 0.0001 3.38617636 POTENT 4.6714561 2.52 0.0194 1.85272878 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 3 176519.30759 58839.76920 589.77 0.0001 Error 22 2194.89087 99.76777 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.987718 5.868349 9.9883816 170.20769 Source DF Type I SS Mean Square F Value Pr > F ACTIVE 1 109524.08874 109524.08874 1097.79 0.0001 COMPET 1 66979.66755 66979.66755 671.36 0.0001 POTENT 1 15.55129 15.55129 0.16 0.6968 Source DF Type III SS Mean Square F Value Pr > F ACTIVE 1 41878.218139 41878.218139 419.76 0.0001 COMPET 1 66615.466790 66615.466790 667.71 0.0001 POTENT 1 15.551292 15.551292 0.16 0.6968 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 186.1147426 14.80 0.0001 12.57591387 ACTIVE 3.3797683 20.49 0.0001 0.16496353 COMPET -21.1735255 -25.84 0.0001 0.81940907 POTENT 0.1891620 0.39 0.6968 0.47912158 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 2 109628.32242 54814.16121 18.25 0.0001 Error 23 69085.87604 3003.73374 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.613428 32.19968 54.806329 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.59804 4510.59804 1.50 0.2328 ACTIVE 1 105117.72438 105117.72438 35.00 0.0001 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 104.23367 104.23367 0.03 0.8539 ACTIVE 1 105117.72438 105117.72438 35.00 0.0001 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT -76.02301958 -1.56 0.1330 48.80506813 PROMO 1.13159365 0.19 0.8539 6.07459320 ACTIVE 4.63122881 5.92 0.0001 0.78286879 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 2 126888.99739 63444.49870 28.16 0.0001 Error 23 51825.20107 2253.26961 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.710011 27.88864 47.468617 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.59804 4510.59804 2.00 0.1705 COMPET 1 122378.39935 122378.39935 54.31 0.0001 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 2886.95904 2886.95904 1.28 0.2693 COMPET 1 122378.39935 122378.39935 54.31 0.0001 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 385.6567000 8.48 0.0001 45.49998215 PROMO 5.8703132 1.13 0.2693 5.18617945 COMPET -27.1183132 -7.37 0.0001 3.67973775 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 2 35964.639285 17982.319642 2.90 0.0755 Error 23 142749.559177 6206.502573 Corrected Total 25 178714.198462 R-Square C.V. Root MSE SALES Mean 0.201241 46.28543 78.781359 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.598039 4510.598039 0.73 0.4027 POTENT 1 31454.041246 31454.041246 5.07 0.0342 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 6321.588775 6321.588775 1.02 0.3234 POTENT 1 31454.041246 31454.041246 5.07 0.0342 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 48.79477924 0.80 0.4320 61.00084351 PROMO 8.70202008 1.01 0.3234 8.62244495 POTENT 7.52230240 2.25 0.0342 3.34145820 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 2 176503.75630 88251.87815 918.27 0.0001 Error 23 2210.44216 96.10618 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.987631 5.759655 9.8033760 170.20769 Source DF Type I SS Mean Square F Value Pr > F ACTIVE 1 109524.08874 109524.08874 1139.62 0.0001 COMPET 1 66979.66755 66979.66755 696.93 0.0001 Source DF Type III SS Mean Square F Value Pr > F ACTIVE 1 52501.717952 52501.717952 546.29 0.0001 COMPET 1 66979.667554 66979.667554 696.93 0.0001 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 186.6940191 15.23 0.0001 12.25868869 ACTIVE 3.4080772 23.37 0.0001 0.14581370 COMPET -21.1929644 -26.40 0.0001 0.80277876 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 2 109903.84080 54951.92040 18.37 0.0001 Error 23 68810.35766 2991.75468 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.614970 32.13541 54.696935 170.20769 Source DF Type I SS Mean Square F Value Pr > F ACTIVE 1 109524.08874 109524.08874 36.61 0.0001 POTENT 1 379.75206 379.75206 0.13 0.7249 Source DF Type III SS Mean Square F Value Pr > F ACTIVE 1 80260.790290 80260.790290 26.83 0.0001 POTENT 1 379.752055 379.752055 0.13 0.7249 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT -72.89888526 -1.75 0.0929 41.58849196 ACTIVE 4.51110643 5.18 0.0001 0.87095225 POTENT 0.93307219 0.36 0.7249 2.61895580 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 2 134641.08945 67320.54473 35.13 0.0001 Error 23 44073.10901 1916.22213 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.753388 25.71839 43.774675 170.20769 Source DF Type I SS Mean Square F Value Pr > F COMPET 1 124002.03835 124002.03835 64.71 0.0001 POTENT 1 10639.05111 10639.05111 5.55 0.0274 Source DF Type III SS Mean Square F Value Pr > F COMPET 1 104998.03894 104998.03894 54.79 0.0001 POTENT 1 10639.05111 10639.05111 5.55 0.0274 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 359.7830558 8.84 0.0001 40.71321792 COMPET -25.6291831 -7.40 0.0001 3.46231914 POTENT 4.4558636 2.36 0.0274 1.89105156 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 1 4510.5980388 4510.5980388 0.62 0.4382 Error 24 174203.6004228 7258.4833509 Corrected Total 25 178714.1984615 R-Square C.V. Root MSE SALES Mean 0.025239 50.05457 85.196733 170.20769 Source DF Type I SS Mean Square F Value Pr > F PROMO 1 4510.5980388 4510.5980388 0.62 0.4382 Source DF Type III SS Mean Square F Value Pr > F PROMO 1 4510.5980388 4510.5980388 0.62 0.4382 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 130.5568847 2.46 0.0213 53.00136911 PROMO 7.3322973 0.79 0.4382 9.30134908 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 1 109524.08874 109524.08874 37.99 0.0001 Error 24 69190.10972 2882.92124 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.612845 31.54548 53.692842 170.20769 Source DF Type I SS Mean Square F Value Pr > F ACTIVE 1 109524.08874 109524.08874 37.99 0.0001 Source DF Type III SS Mean Square F Value Pr > F ACTIVE 1 109524.08874 109524.08874 37.99 0.0001 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT -71.20836328 -1.76 0.0919 40.55844917 ACTIVE 4.65639276 6.16 0.0001 0.75545947 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 1 124002.03835 124002.03835 54.39 0.0001 Error 24 54712.16012 2279.67334 Corrected Total 25 178714.19846 R-Square C.V. Root MSE SALES Mean 0.693857 28.05157 47.745925 170.20769 Source DF Type I SS Mean Square F Value Pr > F COMPET 1 124002.03835 124002.03835 54.39 0.0001 Source DF Type III SS Mean Square F Value Pr > F COMPET 1 124002.03835 124002.03835 54.39 0.0001 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 418.8538426 11.97 0.0001 34.98969502 COMPET -27.2776367 -7.38 0.0001 3.69852569 Dependent Variable: SALES Sum of Mean Source DF Squares Square F Value Pr > F Model 1 29643.050510 29643.050510 4.77 0.0389 Error 24 149071.147952 6211.297831 Corrected Total 25 178714.198462 R-Square C.V. Root MSE SALES Mean 0.165868 46.30331 78.811787 170.20769 Source DF Type I SS Mean Square F Value Pr > F POTENT 1 29643.050510 29643.050510 4.77 0.0389 Source DF Type III SS Mean Square F Value Pr > F POTENT 1 29643.050510 29643.050510 4.77 0.0389 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 98.20481928 2.70 0.0126 36.40356320 POTENT 7.28433735 2.18 0.0389 3.33441599