options nodate nonumber ps=2000; proc reg data=ncaa; model y=x1-x19/selection=forward slentry=.99; run; Output follows. Summary with full sequence is at the bottom. The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Number of Observations Read 97 Number of Observations Used 94 Number of Observations with Missing Values 3 Forward Selection: Step 1 Statistics for Entry DF = 1,92 Model Variable Tolerance R-Square F Value Pr > F x1 1.000000 0.2845 36.59 <.0001 x2 1.000000 0.7069 221.89 <.0001 x3 1.000000 0.6042 140.43 <.0001 x4 1.000000 0.2528 31.13 <.0001 x5 1.000000 0.0031 0.28 0.5957 x6 1.000000 0.0297 2.82 0.0966 x7 1.000000 0.0278 2.63 0.1083 x8 1.000000 0.2975 38.96 <.0001 x9 1.000000 0.1747 19.48 <.0001 x10 1.000000 0.0000 0.00 0.9765 x11 1.000000 0.4880 87.68 <.0001 x12 1.000000 0.2803 35.83 <.0001 x13 1.000000 0.0100 0.93 0.3385 x14 1.000000 0.4147 65.18 <.0001 x15 1.000000 0.0007 0.06 0.8018 x16 1.000000 0.1390 14.85 0.0002 x17 1.000000 0.3843 57.42 <.0001 x18 1.000000 0.0003 0.03 0.8660 x19 1.000000 0.3279 44.88 <.0001 Variable x2 Entered: R-Square = 0.7069 and C(p) = 60.9413 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 17071 17071 221.89 <.0001 Error 92 7077.86139 76.93328 Corrected Total 93 24149 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 1 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -45.22664 7.06068 3156.53210 41.03 <.0001 x2 4.84442 0.32521 17071 221.89 <.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------------------------- Forward Selection: Step 2 Statistics for Entry DF = 1,91 Model Variable Tolerance R-Square F Value Pr > F x1 0.651854 0.7090 0.67 0.4156 x3 0.429135 0.7539 17.39 <.0001 x4 0.871574 0.7535 17.20 <.0001 x5 0.997687 0.7071 0.07 0.7920 x6 0.979371 0.7096 0.85 0.3582 x7 0.878143 0.7252 6.06 0.0157 x8 0.625259 0.7084 0.47 0.4939 x9 0.819857 0.7115 1.44 0.2336 x10 0.984320 0.7188 3.86 0.0525 x11 0.444554 0.7185 3.76 0.0555 x12 0.672153 0.7103 1.08 0.3020 x13 0.997506 0.7103 1.05 0.3076 x14 0.492046 0.7110 1.28 0.2608 x15 0.974208 0.7191 3.94 0.0503 x16 0.789164 0.7071 0.07 0.7928 x17 0.530102 0.7105 1.13 0.2915 x18 0.992816 0.7098 0.91 0.3431 x19 0.580062 0.7082 0.41 0.5216 Variable x3 Entered: R-Square = 0.7539 and C(p) = 38.7296 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 2 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 18206 9103.16701 139.40 <.0001 Error 91 5942.53875 65.30262 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -23.32838 8.36055 508.42916 7.79 0.0064 x2 3.40349 0.45738 3615.92871 55.37 <.0001 x3 0.28122 0.06744 1135.32264 17.39 <.0001 Bounds on condition number: 2.3303, 9.3211 -------------------------------------------------------------------------------------------------- Forward Selection: Step 3 Statistics for Entry DF = 1,90 Model Variable Tolerance R-Square F Value Pr > F x1 0.649578 0.7574 1.30 0.2576 x4 0.657181 0.7695 6.08 0.0156 x5 0.784223 0.7708 6.64 0.0116 x6 0.930835 0.7645 4.06 0.0470 x7 0.849824 0.7635 3.65 0.0592 x8 0.471029 0.7602 2.36 0.1281 x9 0.804747 0.7554 0.54 0.4628 x10 0.945600 0.7585 1.70 0.1955 x11 0.439512 0.7612 2.74 0.1013 x12 0.583277 0.7544 0.17 0.6779 x13 0.971972 0.7545 0.20 0.6537 x14 0.490874 0.7595 2.07 0.1534 x15 0.944526 0.7593 2.02 0.1586 x16 0.755278 0.7549 0.34 0.5585 x17 0.526221 0.7556 0.63 0.4284 x18 0.884440 0.7543 0.13 0.7187 x19 0.514208 0.7554 0.56 0.4574 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 3 Variable x5 Entered: R-Square = 0.7708 and C(p) = 32.0193 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 18615 6204.92387 100.91 <.0001 Error 90 5534.10115 61.49001 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -20.74450 8.17453 395.99067 6.44 0.0129 x2 2.91189 0.48308 2234.14335 36.33 <.0001 x3 0.36922 0.07382 1538.32110 25.02 <.0001 x5 0.21404 0.08305 408.43760 6.64 0.0116 Bounds on condition number: 2.9646, 21.001 -------------------------------------------------------------------------------------------------- Forward Selection: Step 4 Statistics for Entry DF = 1,89 Model Variable Tolerance R-Square F Value Pr > F x1 0.619481 0.7788 3.20 0.0769 x4 0.650272 0.7901 8.17 0.0053 x6 0.906844 0.7778 2.77 0.0993 x7 0.830297 0.7850 5.87 0.0174 x8 0.415013 0.7722 0.53 0.4704 x9 0.791154 0.7739 1.23 0.2710 x10 0.889468 0.7813 4.26 0.0419 x11 0.414486 0.7740 1.23 0.2707 x12 0.546529 0.7710 0.05 0.8253 x13 0.961155 0.7709 0.04 0.8466 x14 0.470875 0.7733 0.95 0.3323 x15 0.944196 0.7759 2.01 0.1601 x16 0.750597 0.7713 0.16 0.6873 x17 0.526207 0.7726 0.69 0.4068 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 4 Statistics for Entry DF = 1,89 Model Variable Tolerance R-Square F Value Pr > F x18 0.829767 0.7736 1.10 0.2973 x19 0.438874 0.7710 0.05 0.8170 Variable x4 Entered: R-Square = 0.7901 and C(p) = 24.0946 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 19080 4770.03929 83.76 <.0001 Error 89 5068.71560 56.95186 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -31.02143 8.64962 732.55032 12.86 0.0005 x2 3.03206 0.46681 2402.70047 42.19 <.0001 x3 0.27552 0.07824 706.25278 12.40 0.0007 x4 0.57525 0.20123 465.38554 8.17 0.0053 x5 0.23759 0.08035 497.96867 8.74 0.0040 Bounds on condition number: 3.5957, 36.822 -------------------------------------------------------------------------------------------------- Forward Selection: Step 5 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 5 Statistics for Entry DF = 1,88 Model Variable Tolerance R-Square F Value Pr > F x1 0.614075 0.8006 4.65 0.0337 x6 0.888626 0.7942 1.76 0.1878 x7 0.806953 0.8110 9.70 0.0025 x8 0.413970 0.7920 0.81 0.3713 x9 0.765435 0.7969 2.93 0.0907 x10 0.882602 0.8033 5.91 0.0170 x11 0.413050 0.7942 1.76 0.1881 x12 0.530739 0.7914 0.53 0.4699 x13 0.906581 0.7907 0.24 0.6250 x14 0.462186 0.7948 2.02 0.1584 x15 0.938582 0.7938 1.57 0.2142 x16 0.745094 0.7912 0.44 0.5067 x17 0.490003 0.7967 2.87 0.0939 x18 0.810434 0.7957 2.42 0.1234 x19 0.431583 0.7901 0.02 0.8997 Variable x7 Entered: R-Square = 0.8110 and C(p) = 15.3596 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 19584 3916.70766 75.50 <.0001 Error 88 4565.33448 51.87880 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -42.10691 8.98980 1138.14217 21.94 <.0001 x2 3.47142 0.46733 2862.58274 55.18 <.0001 x3 0.23906 0.07558 518.96951 10.00 0.0021 x4 0.67700 0.19482 626.46769 12.08 0.0008 x5 0.27872 0.07781 665.56781 12.83 0.0006 x7 -2.59134 0.83190 503.38113 9.70 0.0025 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 5 Bounds on condition number: 3.684, 54.473 -------------------------------------------------------------------------------------------------- Forward Selection: Step 6 Statistics for Entry DF = 1,87 Model Variable Tolerance R-Square F Value Pr > F x1 0.610071 0.8193 4.01 0.0483 x6 0.876135 0.8177 3.20 0.0771 x8 0.408948 0.8145 1.69 0.1975 x9 0.763657 0.8166 2.69 0.1045 x10 0.501020 0.8117 0.33 0.5690 x11 0.413043 0.8150 1.90 0.1718 x12 0.529607 0.8118 0.38 0.5388 x13 0.906581 0.8115 0.26 0.6099 x14 0.450631 0.8131 1.00 0.3191 x15 0.923663 0.8173 3.00 0.0867 x16 0.734363 0.8135 1.17 0.2816 x17 0.486804 0.8197 4.20 0.0433 x18 0.803203 0.8189 3.80 0.0544 x19 0.428909 0.8110 0.01 0.9113 Variable x17 Entered: R-Square = 0.8197 and C(p) = 12.8709 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 19794 3299.00336 65.91 <.0001 Error 87 4354.85259 50.05578 Corrected Total 93 24149 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 6 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -25.32221 12.04057 221.39283 4.42 0.0383 x2 3.04148 0.50466 1818.13210 36.32 <.0001 x3 0.20950 0.07563 384.05908 7.67 0.0069 x4 0.78783 0.19885 785.70373 15.70 0.0002 x5 0.28602 0.07652 699.39484 13.97 0.0003 x7 -2.72718 0.81983 553.89893 11.07 0.0013 x17 -0.12016 0.05860 210.48188 4.20 0.0433 Bounds on condition number: 3.8229, 83.183 -------------------------------------------------------------------------------------------------- Forward Selection: Step 7 Statistics for Entry DF = 1,86 Model Variable Tolerance R-Square F Value Pr > F x1 0.352629 0.8213 0.78 0.3790 x6 0.873753 0.8272 3.76 0.0559 x8 0.398312 0.8254 2.85 0.0952 x9 0.662751 0.8216 0.95 0.3321 x10 0.501015 0.8204 0.35 0.5578 x11 0.318556 0.8201 0.22 0.6393 x12 0.509234 0.8198 0.05 0.8174 x13 0.630583 0.8208 0.53 0.4693 x14 0.393685 0.8199 0.10 0.7573 x15 0.916451 0.8274 3.86 0.0527 x16 0.732301 0.8217 0.99 0.3227 x18 0.791904 0.8258 3.04 0.0848 x19 0.427227 0.8198 0.06 0.8094 Variable x15 Entered: R-Square = 0.8274 and C(p) = 10.8834 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 7 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 7 19981 2854.42868 58.90 <.0001 Error 86 4167.87202 48.46363 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -27.16279 11.88453 253.16330 5.22 0.0247 x2 3.23035 0.50579 1976.82304 40.79 <.0001 x3 0.18717 0.07528 299.56989 6.18 0.0148 x4 0.77648 0.19575 762.54484 15.73 0.0002 x5 0.28591 0.07529 698.86274 14.42 0.0003 x7 -2.94004 0.81394 632.32897 13.05 0.0005 x15 -9.17444E-7 4.670777E-7 186.98057 3.86 0.0527 x17 -0.13021 0.05789 245.21884 5.06 0.0270 Bounds on condition number: 3.9121, 106.56 -------------------------------------------------------------------------------------------------- Forward Selection: Step 8 Statistics for Entry DF = 1,85 Model Variable Tolerance R-Square F Value Pr > F x1 0.351478 0.8287 0.62 0.4334 x6 0.846871 0.8327 2.68 0.1056 x8 0.347029 0.8297 1.13 0.2906 x9 0.640427 0.8312 1.91 0.1704 x10 0.497729 0.8286 0.58 0.4494 x11 0.304346 0.8291 0.84 0.3629 x12 0.494253 0.8281 0.34 0.5635 x13 0.581249 0.8275 0.04 0.8434 x14 0.365954 0.8289 0.75 0.3879 x16 0.729900 0.8290 0.81 0.3713 x18 0.773537 0.8317 2.19 0.1427 x19 0.426841 0.8276 0.09 0.7613 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 8 Variable x6 Entered: R-Square = 0.8327 and C(p) = 10.1715 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 8 20108 2513.52069 52.87 <.0001 Error 85 4040.70727 47.53773 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -24.35518 11.89497 199.29393 4.19 0.0437 x2 3.06795 0.51069 1715.64709 36.09 <.0001 x3 0.20846 0.07569 360.59907 7.59 0.0072 x4 0.74482 0.19484 694.71460 14.61 0.0003 x5 0.26683 0.07548 594.16263 12.50 0.0007 x6 0.14766 0.09028 127.16475 2.68 0.1056 x7 -3.07254 0.81018 683.70366 14.38 0.0003 x15 -7.82643E-7 4.698792E-7 131.88447 2.77 0.0995 x17 -0.13369 0.05737 258.13383 5.43 0.0222 Bounds on condition number: 4.0313, 134.19 -------------------------------------------------------------------------------------------------- Forward Selection: Step 9 Statistics for Entry DF = 1,84 Model Variable Tolerance R-Square F Value Pr > F x1 0.339074 0.8352 1.27 0.2635 x8 0.327710 0.8337 0.50 0.4828 x9 0.616781 0.8386 3.09 0.0826 x10 0.496281 0.8336 0.46 0.4985 x11 0.297891 0.8354 1.39 0.2422 x12 0.491894 0.8336 0.49 0.4856 x13 0.574960 0.8327 0.00 0.9753 x14 0.365937 0.8342 0.75 0.3894 x16 0.724526 0.8338 0.59 0.4439 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 9 Statistics for Entry DF = 1,84 Model Variable Tolerance R-Square F Value Pr > F x18 0.771513 0.8365 1.99 0.1622 x19 0.423765 0.8331 0.20 0.6556 Variable x9 Entered: R-Square = 0.8386 and C(p) = 9.1181 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 9 20251 2250.14889 48.50 <.0001 Error 84 3897.53275 46.39920 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -33.68169 12.89538 316.54078 6.82 0.0107 x2 3.00722 0.50572 1640.69674 35.36 <.0001 x3 0.20156 0.07488 336.20653 7.25 0.0086 x4 0.76162 0.19273 724.61572 15.62 0.0002 x5 0.28072 0.07498 650.29174 14.02 0.0003 x6 0.17834 0.09089 178.64443 3.85 0.0531 x7 -3.01598 0.80107 657.69766 14.17 0.0003 x9 1.48237 0.84388 143.17452 3.09 0.0826 x15 -9.0737E-7 4.696171E-7 173.21755 3.73 0.0567 x17 -0.09599 0.06060 116.41462 2.51 0.1170 Bounds on condition number: 4.0425, 169.34 -------------------------------------------------------------------------------------------------- Forward Selection: Step 10 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 10 Statistics for Entry DF = 1,83 Model Variable Tolerance R-Square F Value Pr > F x1 0.336110 0.8404 0.96 0.3313 x8 0.237282 0.8457 3.83 0.0536 x10 0.495313 0.8393 0.37 0.5429 x11 0.245589 0.8391 0.25 0.6203 x12 0.486189 0.8391 0.27 0.6026 x13 0.511789 0.8394 0.42 0.5185 x14 0.327034 0.8388 0.10 0.7497 x16 0.706423 0.8391 0.26 0.6135 x18 0.771313 0.8426 2.12 0.1489 x19 0.372621 0.8387 0.03 0.8699 Variable x8 Entered: R-Square = 0.8457 and C(p) = 7.4498 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 10 20423 2042.33536 45.50 <.0001 Error 83 3725.51916 44.88577 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -42.57529 13.47244 448.26175 9.99 0.0022 x2 3.20967 0.50804 1791.59263 39.91 <.0001 x3 0.24775 0.07733 460.67217 10.26 0.0019 x4 0.84161 0.19391 845.52642 18.84 <.0001 x5 0.23485 0.07738 413.40817 9.21 0.0032 x6 0.15009 0.09055 123.32703 2.75 0.1012 x7 -3.08519 0.78869 686.84527 15.30 0.0002 x8 -0.49165 0.25115 172.01359 3.83 0.0536 x9 2.48543 0.97542 291.42603 6.49 0.0127 x15 -6.27414E-7 4.83527E-7 75.57450 1.68 0.1980 x17 -0.08786 0.05975 97.04027 2.16 0.1452 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 10 Bounds on condition number: 4.4574, 246.12 -------------------------------------------------------------------------------------------------- Forward Selection: Step 11 Statistics for Entry DF = 1,82 Model Variable Tolerance R-Square F Value Pr > F x1 0.324132 0.8465 0.40 0.5282 x10 0.495081 0.8466 0.44 0.5087 x11 0.243399 0.8466 0.48 0.4899 x12 0.440231 0.8484 1.43 0.2350 x13 0.510063 0.8463 0.30 0.5862 x14 0.326811 0.8459 0.08 0.7842 x16 0.704954 0.8464 0.37 0.5466 x18 0.743703 0.8481 1.26 0.2646 x19 0.321422 0.8464 0.36 0.5515 Variable x12 Entered: R-Square = 0.8484 and C(p) = 8.0866 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 11 20487 1862.47980 41.71 <.0001 Error 82 3661.59499 44.65360 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -36.94434 14.23786 300.65100 6.73 0.0112 x2 3.15919 0.50848 1723.72430 38.60 <.0001 x3 0.23373 0.07802 400.77212 8.98 0.0036 x4 0.87862 0.19587 898.54080 20.12 <.0001 x5 0.24826 0.07799 452.43953 10.13 0.0021 x6 0.14986 0.09031 122.94622 2.75 0.1009 x7 -3.07002 0.78675 679.93426 15.23 0.0002 x8 -0.58849 0.26325 223.15269 5.00 0.0281 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 11 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F x9 2.57024 0.97547 310.00967 6.94 0.0101 x12 -0.34801 0.29086 63.92417 1.43 0.2350 x15 -6.54741E-7 4.828153E-7 82.11702 1.84 0.1788 x17 -0.07614 0.06040 70.96486 1.59 0.2110 Bounds on condition number: 4.6544, 303.74 -------------------------------------------------------------------------------------------------- Forward Selection: Step 12 Statistics for Entry DF = 1,81 Model Variable Tolerance R-Square F Value Pr > F x1 0.323973 0.8491 0.37 0.5444 x10 0.451299 0.8505 1.15 0.2864 x11 0.234274 0.8488 0.22 0.6377 x13 0.485950 0.8496 0.69 0.4098 x14 0.312796 0.8484 0.00 0.9764 x16 0.635518 0.8485 0.06 0.8073 x18 0.731515 0.8501 0.96 0.3305 x19 0.320480 0.8489 0.29 0.5937 Variable x10 Entered: R-Square = 0.8505 and C(p) = 8.9921 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 12 20539 1711.54985 38.40 <.0001 Error 81 3610.27459 44.57129 Corrected Total 93 24149 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 12 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -32.68504 14.76817 218.32319 4.90 0.0297 x2 3.11660 0.50955 1667.38793 37.41 <.0001 x3 0.22913 0.07807 383.96460 8.61 0.0043 x4 0.88397 0.19575 908.92561 20.39 <.0001 x5 0.26739 0.07993 498.74576 11.19 0.0012 x6 0.14328 0.09044 111.87143 2.51 0.1170 x7 -2.31236 1.05660 213.47634 4.79 0.0315 x8 -0.62160 0.26481 245.59100 5.51 0.0213 x9 2.56522 0.97458 308.79177 6.93 0.0102 x10 -0.00022804 0.00021252 51.32040 1.15 0.2864 x12 -0.44513 0.30436 95.33393 2.14 0.1475 x15 -7.01302E-7 4.843179E-7 93.45546 2.10 0.1515 x17 -0.07433 0.06036 67.58004 1.52 0.2218 Bounds on condition number: 4.7184, 375.51 -------------------------------------------------------------------------------------------------- Forward Selection: Step 13 Statistics for Entry DF = 1,80 Model Variable Tolerance R-Square F Value Pr > F x1 0.320739 0.8510 0.25 0.6152 x11 0.226404 0.8506 0.08 0.7788 x13 0.474424 0.8524 1.02 0.3163 x14 0.311090 0.8505 0.00 0.9609 x16 0.635501 0.8506 0.06 0.8113 x18 0.730633 0.8521 0.89 0.3486 x19 0.318999 0.8512 0.37 0.5434 Variable x13 Entered: R-Square = 0.8524 and C(p) = 10.0258 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 13 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 13 20584 1583.37763 35.53 <.0001 Error 80 3564.96353 44.56204 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -31.15116 14.84478 196.23020 4.40 0.0390 x2 2.97188 0.52933 1404.66931 31.52 <.0001 x3 0.20701 0.08108 290.49196 6.52 0.0126 x4 0.87509 0.19593 888.97795 19.95 <.0001 x5 0.26768 0.07993 499.80441 11.22 0.0012 x6 0.13930 0.09052 105.53557 2.37 0.1278 x7 -2.19058 1.06337 189.11240 4.24 0.0426 x8 -0.62961 0.26490 251.73413 5.65 0.0199 x9 2.85383 1.01565 351.83318 7.90 0.0062 x10 -0.00026144 0.00021506 65.85386 1.48 0.2277 x12 -0.52540 0.31457 124.31400 2.79 0.0988 x13 0.06412 0.06359 45.31105 1.02 0.3163 x15 -6.11206E-7 4.924412E-7 68.64849 1.54 0.2182 x17 -0.10505 0.06761 107.57524 2.41 0.1242 Bounds on condition number: 4.9351, 457.91 -------------------------------------------------------------------------------------------------- Forward Selection: Step 14 Statistics for Entry DF = 1,79 Model Variable Tolerance R-Square F Value Pr > F x1 0.313495 0.8532 0.44 0.5088 x11 0.201077 0.8532 0.43 0.5135 x14 0.284164 0.8525 0.07 0.7978 x16 0.632766 0.8526 0.09 0.7604 x18 0.713735 0.8546 1.24 0.2697 x19 0.295212 0.8526 0.12 0.7281 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 14 Variable x18 Entered: R-Square = 0.8546 and C(p) = 10.8552 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 14 20639 1474.20004 33.18 <.0001 Error 79 3510.07220 44.43129 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -26.90197 15.30803 137.22024 3.09 0.0827 x2 2.76929 0.55910 1090.07021 24.53 <.0001 x3 0.22954 0.08346 336.09282 7.56 0.0074 x4 0.89107 0.19617 916.78887 20.63 <.0001 x5 0.29527 0.08358 554.50675 12.48 0.0007 x6 0.13718 0.09040 102.30606 2.30 0.1332 x7 -2.24533 1.06295 198.25569 4.46 0.0378 x8 -0.56341 0.27113 191.85444 4.32 0.0410 x9 2.79654 1.01546 336.97854 7.58 0.0073 x10 -0.00025881 0.00021476 64.52691 1.45 0.2318 x12 -0.49333 0.31543 108.68171 2.45 0.1218 x13 0.07498 0.06424 60.52505 1.36 0.2467 x15 -5.48318E-7 4.949627E-7 54.52670 1.23 0.2713 x17 -0.10353 0.06752 104.45117 2.35 0.1292 x18 -0.07397 0.06655 54.89134 1.24 0.2697 Bounds on condition number: 5.2444, 531.84 -------------------------------------------------------------------------------------------------- Forward Selection: Step 15 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 15 Statistics for Entry DF = 1,78 Model Variable Tolerance R-Square F Value Pr > F x1 0.306402 0.8551 0.25 0.6162 x11 0.200954 0.8555 0.47 0.4953 x14 0.282962 0.8547 0.03 0.8530 x16 0.630920 0.8549 0.13 0.7147 x19 0.282688 0.8547 0.02 0.9014 Variable x11 Entered: R-Square = 0.8555 and C(p) = 12.4075 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 15 20660 1377.31964 30.79 <.0001 Error 78 3489.07824 44.73177 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -31.78995 16.93600 157.60649 3.52 0.0642 x2 2.64968 0.58753 909.80381 20.34 <.0001 x3 0.22110 0.08464 305.20202 6.82 0.0108 x4 0.86650 0.20007 839.05373 18.76 <.0001 x5 0.26758 0.09309 369.57546 8.26 0.0052 x6 0.14078 0.09086 107.37949 2.40 0.1253 x7 -2.32411 1.07272 209.97066 4.69 0.0333 x8 -0.56625 0.27208 193.74404 4.33 0.0407 x9 2.60267 1.05746 270.97292 6.06 0.0161 x10 -0.00023797 0.00021762 53.49190 1.20 0.2775 x11 0.09651 0.14087 20.99396 0.47 0.4953 x12 -0.45745 0.32080 90.95545 2.03 0.1579 x13 0.09064 0.06839 78.56767 1.76 0.1889 x15 -5.5371E-7 4.966959E-7 55.59040 1.24 0.2684 x17 -0.09478 0.06894 84.54146 1.89 0.1731 x18 -0.07510 0.06679 56.55065 1.26 0.2643 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 15 Bounds on condition number: 5.6132, 671.61 -------------------------------------------------------------------------------------------------- Forward Selection: Step 16 Statistics for Entry DF = 1,77 Model Variable Tolerance R-Square F Value Pr > F x1 0.306089 0.8559 0.23 0.6326 x14 0.186731 0.8556 0.07 0.7950 x16 0.565500 0.8556 0.02 0.8778 x19 0.281233 0.8556 0.03 0.8630 Variable x1 Entered: R-Square = 0.8559 and C(p) = 14.1856 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 16 20670 1291.88748 28.60 <.0001 Error 77 3478.67305 45.17757 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -32.74485 17.13609 164.96251 3.65 0.0597 x1 0.02882 0.06006 10.40519 0.23 0.6326 x2 2.55602 0.62186 763.24738 16.89 <.0001 x3 0.22948 0.08684 315.48101 6.98 0.0100 x4 0.84591 0.20559 764.85240 16.93 <.0001 x5 0.27517 0.09488 379.98013 8.41 0.0049 x6 0.14991 0.09328 116.69656 2.58 0.1121 x7 -2.27731 1.08245 199.96398 4.43 0.0387 x8 -0.54482 0.27706 174.69920 3.87 0.0528 x9 2.54343 1.06986 255.33358 5.65 0.0199 x10 -0.00023053 0.00021925 49.94373 1.11 0.2964 x11 0.09433 0.14165 20.03834 0.44 0.5074 x12 -0.45860 0.32240 91.41137 2.02 0.1589 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 16 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F x13 0.09430 0.06915 83.99962 1.86 0.1767 x15 -5.37984E-7 5.002393E-7 52.25231 1.16 0.2855 x17 -0.07448 0.08118 38.03571 0.84 0.3617 x18 -0.07017 0.06791 48.24363 1.07 0.3047 Bounds on condition number: 6.2264, 808.72 -------------------------------------------------------------------------------------------------- Forward Selection: Step 17 Statistics for Entry DF = 1,76 Model Variable Tolerance R-Square F Value Pr > F x14 0.176901 0.8562 0.14 0.7056 x16 0.561210 0.8560 0.01 0.9108 x19 0.280940 0.8560 0.02 0.8757 Variable x14 Entered: R-Square = 0.8562 and C(p) = 16.0456 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 17 20677 1216.28040 26.62 <.0001 Error 76 3472.10600 45.68561 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -31.10460 17.76695 140.02409 3.06 0.0840 x1 0.03422 0.06205 13.89518 0.30 0.5829 x2 2.59528 0.63386 765.87581 16.76 0.0001 x3 0.23185 0.08755 320.38897 7.01 0.0098 x4 0.83917 0.20751 747.17294 16.35 0.0001 x5 0.27928 0.09603 386.42668 8.46 0.0048 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 17 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F x6 0.15660 0.09544 122.99111 2.69 0.1050 x7 -2.36126 1.11081 206.43630 4.52 0.0368 x8 -0.55220 0.27929 178.59469 3.91 0.0516 x9 2.57117 1.07834 259.73241 5.69 0.0196 x10 -0.00022351 0.00022125 46.62327 1.02 0.3156 x11 0.13374 0.17632 26.28239 0.58 0.4505 x12 -0.46599 0.32480 94.03956 2.06 0.1555 x13 0.09223 0.06976 79.86162 1.75 0.1901 x14 -0.13123 0.34613 6.56705 0.14 0.7056 x15 -4.95163E-7 5.15567E-7 42.14106 0.92 0.3399 x17 -0.06881 0.08299 31.40697 0.69 0.4096 x18 -0.07183 0.06843 50.33886 1.10 0.2972 Bounds on condition number: 7.6333, 1015.2 -------------------------------------------------------------------------------------------------- Forward Selection: Step 18 Statistics for Entry DF = 1,75 Model Variable Tolerance R-Square F Value Pr > F x16 0.561026 0.8562 0.01 0.9059 x19 0.280149 0.8563 0.03 0.8605 Variable x19 Entered: R-Square = 0.8563 and C(p) = 18.0149 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 18 20678 1148.78916 24.82 <.0001 Error 75 3470.66781 46.27557 Corrected Total 93 24149 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 18 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -30.54141 18.16443 130.82375 2.83 0.0968 x1 0.03401 0.06246 13.71783 0.30 0.5877 x2 2.57257 0.65081 723.06010 15.63 0.0002 x3 0.23267 0.08824 321.76439 6.95 0.0102 x4 0.83654 0.20937 738.74115 15.96 0.0001 x5 0.28196 0.09783 384.36160 8.31 0.0052 x6 0.15615 0.09609 122.20492 2.64 0.1083 x7 -2.38246 1.12441 207.75616 4.49 0.0374 x8 -0.57333 0.30556 162.91566 3.52 0.0645 x9 2.53083 1.10915 240.93103 5.21 0.0253 x10 -0.00022417 0.00022271 46.88335 1.01 0.3174 x11 0.13656 0.17818 27.18315 0.59 0.4458 x12 -0.46057 0.32833 91.05688 1.97 0.1648 x13 0.08873 0.07296 68.43977 1.48 0.2278 x14 -0.13449 0.34884 6.87826 0.15 0.7009 x15 -4.86747E-7 5.210768E-7 40.37890 0.87 0.3532 x17 -0.06942 0.08360 31.91328 0.69 0.4089 x18 -0.06942 0.07021 45.23601 0.98 0.3260 x19 0.01210 0.06863 1.43819 0.03 0.8605 Bounds on condition number: 7.6956, 1171.7 -------------------------------------------------------------------------------------------------- Forward Selection: Step 19 Statistics for Entry DF = 1,74 Model Variable Tolerance R-Square F Value Pr > F x16 0.560712 0.8563 0.01 0.9032 Variable x16 Entered: R-Square = 0.8563 and C(p) = 20.0000 The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Forward Selection: Step 19 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 19 20679 1088.36333 23.21 <.0001 Error 74 3469.96942 46.89148 Corrected Total 93 24149 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept -31.42637 19.67027 119.69101 2.55 0.1144 x1 0.03338 0.06308 13.13142 0.28 0.5983 x2 2.56147 0.66142 703.25895 15.00 0.0002 x3 0.23462 0.09024 316.95185 6.76 0.0113 x4 0.83979 0.21243 732.81433 15.63 0.0002 x5 0.28254 0.09860 385.04781 8.21 0.0054 x6 0.15417 0.09808 115.85286 2.47 0.1203 x7 -2.39179 1.13445 208.43562 4.45 0.0384 x8 -0.57169 0.30788 161.67933 3.45 0.0673 x9 2.52743 1.11686 240.13565 5.12 0.0266 x10 -0.00022573 0.00022455 47.38536 1.01 0.3181 x11 0.13088 0.18531 23.39074 0.50 0.4822 x12 -0.45036 0.34093 81.82271 1.74 0.1906 x13 0.08823 0.07356 67.45552 1.44 0.2342 x14 -0.13532 0.35122 6.96082 0.15 0.7011 x15 -4.78982E-7 5.283772E-7 38.53408 0.82 0.3676 x16 0.01673 0.13710 0.69839 0.01 0.9032 x17 -0.07105 0.08521 32.60796 0.70 0.4070 x18 -0.06991 0.07079 45.72924 0.98 0.3266 x19 0.01230 0.06910 1.48517 0.03 0.8592 Bounds on condition number: 8.2144, 1295.2 -------------------------------------------------------------------------------------------------- All variables have been entered into the model. The REG Procedure Model: MODEL1 Dependent Variable: y avg_grad Summary of Forward Selection Variable Number Partial Model Step Entered Label Vars In R-Square R-Square C(p) F Value Pr > F 1 x2 act25 1 0.7069 0.7069 60.9413 221.89 <.0001 2 x3 oncampus 2 0.0470 0.7539 38.7296 17.39 <.0001 3 x5 size 3 0.0169 0.7708 32.0193 6.64 0.0116 4 x4 ft_grad 4 0.0193 0.7901 24.0946 8.17 0.0053 5 x7 bbindex 5 0.0208 0.8110 15.3596 9.70 0.0025 6 x17 accept 6 0.0087 0.8197 12.8709 4.20 0.0433 7 x15 pop 7 0.0077 0.8274 10.8834 3.86 0.0527 8 x6 tateach 8 0.0053 0.8327 10.1715 2.68 0.1056 9 x9 board 9 0.0059 0.8386 9.1181 3.09 0.0826 10 x8 tuition 10 0.0071 0.8457 7.4498 3.83 0.0536 11 x12 sf_ratio 11 0.0026 0.8484 8.0866 1.43 0.2350 12 x10 attend 12 0.0021 0.8505 8.9921 1.15 0.2864 13 x13 white 13 0.0019 0.8524 10.0258 1.02 0.3163 14 x18 l_pct 14 0.0023 0.8546 10.8552 1.24 0.2697 15 x11 full_sal 15 0.0009 0.8555 12.4075 0.47 0.4953 16 x1 top10 16 0.0004 0.8559 14.1856 0.23 0.6326 17 x14 ast_sal 17 0.0003 0.8562 16.0456 0.14 0.7056 18 x19 outstate 18 0.0001 0.8563 18.0149 0.03 0.8605 19 x16 phd 19 0.0000 0.8563 20.0000 0.01 0.9032