The SAS System 1 15:54 Thursday, November 20, 2003 OBS X1 X2 X3 X4 Y YP X12 X13 X14 X23 X24 X34 1 6.7 62 81 2.59 200 2.3010 415.4 542.7 17.353 5022 160.58 209.79 2 5.1 59 66 1.70 101 2.0043 300.9 336.6 8.670 3894 100.30 112.20 3 7.4 57 83 2.16 204 2.3096 421.8 614.2 15.984 4731 123.12 179.28 4 6.5 73 41 2.01 101 2.0043 474.5 266.5 13.065 2993 146.73 82.41 5 7.8 65 115 4.30 509 2.7067 507.0 897.0 33.540 7475 279.50 494.50 6 5.8 38 72 1.42 80 1.9031 220.4 417.6 8.236 2736 53.96 102.24 7 5.7 46 63 1.91 80 1.9031 262.2 359.1 10.887 2898 87.86 120.33 8 3.7 68 81 2.57 127 2.1038 251.6 299.7 9.509 5508 174.76 208.17 9 6.0 67 93 2.50 202 2.3054 402.0 558.0 15.000 6231 167.50 232.50 10 3.7 76 94 2.40 203 2.3075 281.2 347.8 8.880 7144 182.40 225.60 11 6.3 84 83 4.13 329 2.5172 529.2 522.9 26.019 6972 346.92 342.79 12 6.7 51 43 1.86 65 1.8129 341.7 288.1 12.462 2193 94.86 79.98 13 5.8 96 114 3.95 830 2.9191 556.8 661.2 22.910 10944 379.20 450.30 14 5.8 83 88 3.95 330 2.5185 481.4 510.4 22.910 7304 327.85 347.60 15 7.7 62 67 3.40 168 2.2253 477.4 515.9 26.180 4154 210.80 227.80 16 7.4 74 68 2.40 217 2.3365 547.6 503.2 17.760 5032 177.60 163.20 17 6.0 85 28 2.98 87 1.9395 510.0 168.0 17.880 2380 253.30 83.44 18 3.7 51 41 1.55 34 1.5315 188.7 151.7 5.735 2091 79.05 63.55 19 7.3 68 74 3.56 215 2.3324 496.4 540.2 25.988 5032 242.08 263.44 20 5.6 57 87 3.02 172 2.2355 319.2 487.2 16.912 4959 172.14 262.74 21 5.2 52 76 2.85 109 2.0374 270.4 395.2 14.820 3952 148.20 216.60 22 3.4 83 53 1.12 136 2.1335 282.2 180.2 3.808 4399 92.96 59.36 23 6.7 26 68 2.10 70 1.8451 174.2 455.6 14.070 1768 54.60 142.80 24 5.8 67 86 3.40 220 2.3424 388.6 498.8 19.720 5762 227.80 292.40 25 6.3 59 100 2.95 276 2.4409 371.7 630.0 18.585 5900 174.05 295.00 26 5.8 61 73 3.50 144 2.1584 353.8 423.4 20.300 4453 213.50 255.50 27 5.2 52 86 2.45 181 2.2577 270.4 447.2 12.740 4472 127.40 210.70 28 11.2 76 90 5.59 574 2.7589 851.2 1008.0 62.608 6840 424.84 503.10 29 5.2 54 56 2.71 72 1.8573 280.8 291.2 14.092 3024 146.34 151.76 30 5.8 76 59 2.58 178 2.2504 440.8 342.2 14.964 4484 196.08 152.22 31 3.2 64 65 0.74 71 1.8513 204.8 208.0 2.368 4160 47.36 48.10 32 8.7 45 23 2.52 58 1.7634 391.5 200.1 21.924 1035 113.40 57.96 33 5.0 59 73 3.50 116 2.0645 295.0 365.0 17.500 4307 206.50 255.50 34 5.8 72 93 3.30 295 2.4698 417.6 539.4 19.140 6696 237.60 306.90 35 5.4 58 70 2.64 115 2.0607 313.2 378.0 14.256 4060 153.12 184.80 36 5.3 51 99 2.60 184 2.2648 270.3 524.7 13.780 5049 132.60 257.40 37 2.6 74 86 2.05 118 2.0719 192.4 223.6 5.330 6364 151.70 176.30 38 4.3 8 119 2.85 120 2.0792 34.4 511.7 12.255 952 22.80 339.15 39 4.8 61 76 2.45 151 2.1790 292.8 364.8 11.760 4636 149.45 186.20 40 5.4 52 88 1.81 148 2.1703 280.8 475.2 9.774 4576 94.12 159.28 41 5.2 49 72 1.84 95 1.9777 254.8 374.4 9.568 3528 90.16 132.48 42 3.6 28 99 1.30 75 1.8751 100.8 356.4 4.680 2772 36.40 128.70 43 8.8 86 88 6.40 483 2.6840 756.8 774.4 56.320 7568 550.40 563.20 44 6.5 56 77 2.85 153 2.1847 364.0 500.5 18.525 4312 159.60 219.45 45 3.4 77 93 1.48 191 2.2810 261.8 316.2 5.032 7161 113.96 137.64 46 6.5 40 84 3.00 123 2.0899 260.0 546.0 19.500 3360 120.00 252.00 47 4.5 73 106 3.05 311 2.4928 328.5 477.0 13.725 7738 222.65 323.30 48 4.8 86 101 4.10 398 2.5999 412.8 484.8 19.680 8686 352.60 414.10 49 5.1 67 77 2.86 158 2.1987 341.7 392.7 14.586 5159 191.62 220.22 50 3.9 82 103 4.55 310 2.4914 319.8 401.7 17.745 8446 373.10 468.65 51 6.6 77 46 1.95 124 2.0934 508.2 303.6 12.870 3542 150.15 89.70 52 6.4 85 40 1.21 125 2.0969 544.0 256.0 7.744 3400 102.85 48.40 53 6.4 59 85 2.33 198 2.2967 377.6 544.0 14.912 5015 137.47 198.05 54 8.8 78 72 3.20 313 2.4955 686.4 633.6 28.160 5616 249.60 230.40 The SAS System 2 15:54 Thursday, November 20, 2003 Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 4 936264.53767 234066.13442 62.788 0.0001 Error 49 182666.96233 3727.89719 C Total 53 1118931.5 Root MSE 61.05651 R-square 0.8367 Dep Mean 197.16667 Adj R-sq 0.8234 C.V. 30.96695 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 -621.597550 64.80042601 -9.592 0.0001 X1 1 33.163828 7.01727463 4.726 0.0001 X2 1 4.271860 0.56338454 7.582 0.0001 X3 1 4.125738 0.51116093 8.071 0.0001 X4 1 14.091563 12.52532754 1.125 0.2661 The SAS System 3 15:54 Thursday, November 20, 2003 Plot of Y*X1. Legend: A = 1 obs, B = 2 obs, etc. Y | | 900 + | | | A | 800 + | | | | 700 + | | | | 600 + | A | | | 500 + A | A | | | 400 + A | | | A | A A A A 300 + A | A | | | A AA 200 + A A A A A A | AA A A | A A A A | A A A | A A A A A AB 100 + C A | A A A AAA A | A A | A | 0 + | ---+-------------+-------------+-------------+-------------+-------------+-- 2 4 6 8 10 12 X1 The SAS System 4 15:54 Thursday, November 20, 2003 Plot of Y*X2. Legend: A = 1 obs, B = 2 obs, etc. Y | | 900 + | | | A | 800 + | | | | 700 + | | | | 600 + | A | | | 500 + A | A | | | 400 + A | | | A | A A A A 300 + A | A | | | AA A 200 + A A A A AA | AA A A | A AA A | A A A | A A AA A A A A 100 + A A A A | A A A A A A A | A A | A | 0 + | --+-------+-------+-------+-------+-------+-------+-------+-------+-------+- 8 18 28 38 48 58 68 78 88 98 X2 The SAS System 5 15:54 Thursday, November 20, 2003 Plot of Y*X3. Legend: A = 1 obs, B = 2 obs, etc. Y | | 900 + | | | A | 800 + | | | | 700 + | | | | 600 + | A | | | 500 + A | A | | | 400 + A | | | A | A A A A 300 + A | A | | | A A A 200 + AA A BA | A AA A | A AB | A A A | A A A A A AA A 100 + A A A A | A A A A A A A | A A | A | 0 + | ---+-------------+-------------+-------------+-------------+-------------+-- 20 40 60 80 100 120 X3 The SAS System 6 15:54 Thursday, November 20, 2003 Plot of Y*X4. Legend: A = 1 obs, B = 2 obs, etc. Y | | 900 + | | | A | 800 + | | | | 700 + | | | | 600 + | A | | | 500 + A | A | | | 400 + A | | | A | AA A A 300 + A | A | | | A A A 200 + A AAAAA | AB A | A B A | A A A | A AA B AA A 100 + AA A A | A AA A A A A | A A | A | 0 + | ---+---------+---------+---------+---------+---------+---------+---------+-- 0 1 2 3 4 5 6 7 X4 The SAS System 7 15:54 Thursday, November 20, 2003 Plot of X1*X2. Legend: A = 1 obs, B = 2 obs, etc. X1 | | 12 + | | | A 11 + | | | 10 + | | | 9 + | A A A | | 8 + | A A | A A | A 7 + | A A A | A A A A A A | A A 6 + A A | A A A A A A A A | A AA | AAB A 5 + B A | A A | A | A 4 + A | A A A | A A A | A 3 + | | A | 2 + | --+-------+-------+-------+-------+-------+-------+-------+-------+-------+-- 8 18 28 38 48 58 68 78 88 98 X2 The SAS System 8 15:54 Thursday, November 20, 2003 Plot of X1*X3. Legend: A = 1 obs, B = 2 obs, etc. X1 | | 12 + | | | A 11 + | | | 10 + | | | 9 + | A A A | | 8 + | A A | A A | A 7 + | A A A | AA A A AA | A A 6 + A A | A A AA AA A A | A AA | A A A A A 5 + A A A | A A | A | A 4 + A | A A A | A A A | A 3 + | | A | 2 + | ---+-----------+-----------+-----------+-----------+-----------+-- 20 40 60 80 100 120 X3 The SAS System 9 15:54 Thursday, November 20, 2003 Plot of X1*X4. Legend: A = 1 obs, B = 2 obs, etc. X1 | | 12 + | | | A 11 + | | | 10 + | | | 9 + | A A A | | 8 + | A A | A A | A 7 + | A A A | A B A AA | A A 6 + A A | A A A AAA B | A A A | A AAA A 5 + A A A | A A | A | A 4 + A | A A A | A A A | A 3 + | | A | 2 + | ---+---------+---------+---------+---------+---------+---------+---------+-- 0 1 2 3 4 5 6 7 X4 The SAS System 10 15:54 Thursday, November 20, 2003 Plot of X2*X3. Legend: A = 1 obs, B = 2 obs, etc. X2 | | 96 + A 94 + 92 + 90 + 88 + 86 + A A A A 84 + A A A 82 + A 80 + 78 + A A A 76 + A A A 74 + A A A A 72 + A 70 + 68 + A A A A A 66 + A 64 + A 62 + A A A A 60 + A A A A 58 + A A A 56 + A 54 + A 52 + AA A AA A 50 + A 48 + 46 + A A 44 + 42 + 40 + A 38 + A 36 + 34 + 32 + 30 + 28 + A 26 + A 24 + 22 + 20 + 18 + 16 + 14 + 12 + 10 + 8 + A | ---+-----------+-----------+-----------+-----------+-----------+-- 20 40 60 80 100 120 X3 The SAS System 11 15:54 Thursday, November 20, 2003 Plot of X2*X4. Legend: A = 1 obs, B = 2 obs, etc. X2 | | 96 + A 94 + 92 + 90 + 88 + 86 + A A A A 84 + A AA 82 + A 80 + 78 + A A A 76 + A A A 74 + AA A A 72 + A 70 + 68 + AA A A A 66 + A 64 + A 62 + AA AA 60 + A A A A 58 + A A A 56 + A 54 + A 52 + A AA AA A 50 + A 48 + 46 + A A 44 + 42 + 40 + A 38 + A 36 + 34 + 32 + 30 + 28 + A 26 + A 24 + 22 + 20 + 18 + 16 + 14 + 12 + 10 + 8 + A | ---+---------+---------+---------+---------+---------+---------+---------+-- 0 1 2 3 4 5 6 7 X4 The SAS System 12 15:54 Thursday, November 20, 2003 Plot of X3*X4. Legend: A = 1 obs, B = 2 obs, etc. X3 | | 120 + A | | A A | | | A | A 100 + A A A A | | A AA A | A | A A A | A A A A A | A A A 80 + B | A C | BA | A A A A | A A | A A A | A 60 + A | A | A | | | A | A 40 + A A A | | | | A | | A 20 + | ---+---------+---------+---------+---------+---------+---------+---------+-- 0 1 2 3 4 5 6 7 X4 The SAS System 13 15:54 Thursday, November 20, 2003 Plot of RESID*X1. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A A A AA | A B | B 0 + A A A | A BA A A | A B B A | A A AAA AA A | AA A B AA B -50 + A A A | | | A | -100 + | -+-------------+-------------+-------------+-------------+-------------+- 2 4 6 8 10 12 X1 The SAS System 14 15:54 Thursday, November 20, 2003 Plot of RESID*X2. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A A A A A | AA A | A A 0 + A A A | AA ABA | B AA A A | A A B AA AA | C AA A A A A -50 + A A A | | | A | -100 + | ---+------+------+------+------+------+------+------+------+------+-- 8 18 28 38 48 58 68 78 88 98 X2 The SAS System 15 15:54 Thursday, November 20, 2003 Plot of RESID*X3. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A A A A A | A A A | A A 0 + A A A | A A B A A | A A A A A A | AA A A AA A A | A A A AA AA A A -50 + A A A | | | A | -100 + | -+-------------+-------------+-------------+-------------+-------------+- 20 40 60 80 100 120 X3 The SAS System 16 15:54 Thursday, November 20, 2003 Plot of RESID*X4. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A AA A A | A A A | AA 0 + A AA | A AA A A A | A A A AA A | A A B AA A A | A B A AA AA A -50 + A A A | | | A | -100 + | -+---------+---------+---------+---------+---------+---------+---------+- 0 1 2 3 4 5 6 7 X4 The SAS System 17 15:54 Thursday, November 20, 2003 Plot of RESID*PRED. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | BB A | A A A | A A 0 + A A A | A A AA A A | BA A A A | BA A BA A | AA A BBA A -50 + A A A | | | A | -100 + | -+---------+---------+---------+---------+---------+---------+---------+- -100 0 100 200 300 400 500 600 Predicted Value of Y The SAS System 18 15:54 Thursday, November 20, 2003 Plot of RESID*X12. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A A AA A | AA A | A A 0 + A A A | A A A A A A | AA A A AA | CA A A A A | A B B A AA A -50 + A A A | | | A | -100 + | -+-------------+-------------+-------------+-------------+-------------+- 0 200 400 600 800 1000 X12 The SAS System 19 15:54 Thursday, November 20, 2003 Plot of RESID*X13. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A B A A | A A A | A A 0 + A AA | A A A A A A | A AA A A A | AA A A AB A | A AA BB A A -50 + A A A | | | A | -100 + | ---+----------+----------+----------+----------+----------+----------+-- 0 200 400 600 800 1000 1200 X13 The SAS System 20 15:54 Thursday, November 20, 2003 Plot of RESID*X14. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A A A AA | AA A | AA 0 + AA A | A A AA A A | A AAA A A | A A AB A A A | A ABBAB -50 + A B | | | A | -100 + | -+---------+---------+---------+---------+---------+---------+---------+- 0 10 20 30 40 50 60 70 X14 The SAS System 21 15:54 Thursday, November 20, 2003 Plot of RESID*X23. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A BA A | A A A | A A 0 + A B | A A A A AA | A B A A A | A A C AA A | B AAB A A A -50 + A A A | | | A | -100 + | ---+----------+----------+----------+----------+----------+----------+-- 0 2000 4000 6000 8000 10000 12000 X23 The SAS System 22 15:54 Thursday, November 20, 2003 Plot of RESID*X24. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | AAAA A | A A A | AA 0 + B A | A A A A A A | A AB A A | B B A A A A | A BAB A A A -50 + A A A | | | A | -100 + | ---+----------+----------+----------+----------+----------+----------+-- 0 100 200 300 400 500 600 X24 The SAS System 23 15:54 Thursday, November 20, 2003 Plot of RESID*X34. Legend: A = 1 obs, B = 2 obs, etc. | | 350 + | | | A | 300 + | | | | 250 + | | | | 200 + | | R | e | s 150 + i | d | u | A a | l 100 + | | | A | A A 50 + A A | A | A A AA A | A A A | A A 0 + A A A | A A A A A A | A A A A A A | A AAAA C | A A AAA AA A A -50 + A A A | | | A | -100 + | ---+----------+----------+----------+----------+----------+----------+-- 0 100 200 300 400 500 600 X34 The SAS System 24 15:54 Thursday, November 20, 2003 ------------------------------------------------------------------- 400 + | | | | | | | | | | | | | | + | | | 300 + | | | | | | | | | | | | | | | | | 200 + | R | | e | | s | | i | | d | | u | | a | + | l | | 100 + | | | | | | + | | + + | | + ++ | | +++++ | | +++ | | + | 0 + +++ | | +++++ | | ++++ | | + ++++++++++++ | | + ++ | | + + | | | | + | | | -100 + | +---------+----+-------+---------+---------+-------+----+---------+ 1 5 10 25 50 75 90 95 99 Normal Percentiles Observations: + (6 Hidden) The SAS System 25 15:54 Thursday, November 20, 2003 Model: MODEL1 Dependent Variable: YP Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 4 3.86300 0.96575 431.097 0.0001 Error 49 0.10977 0.00224 C Total 53 3.97277 Root MSE 0.04733 R-square 0.9724 Dep Mean 2.20614 Adj R-sq 0.9701 C.V. 2.14541 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 0.488756 0.05023319 9.730 0.0001 X1 1 0.068520 0.00543978 12.596 0.0001 X2 1 0.009254 0.00043673 21.189 0.0001 X3 1 0.009475 0.00039625 23.910 0.0001 X4 1 0.001925 0.00970961 0.198 0.8436 The SAS System 26 15:54 Thursday, November 20, 2003 Plot of YP*X1. Legend: A = 1 obs, B = 2 obs, etc. 3.0 + | | A | | | 2.8 + | A | | A A | | 2.6 + A | | A A YP | A A A | A | A 2.4 + | | A AA | A A A A A | A AA A | A A 2.2 + A A | A A A | A | A AB | A A A A | A 2.0 + A A | A | A | AA | A A A | A 1.8 + A | A | | | | 1.6 + | | A | | | 1.4 + ---+-------------+-------------+-------------+-------------+-------------+-- 2 4 6 8 10 12 X1 The SAS System 27 15:54 Thursday, November 20, 2003 Plot of YP*X2. Legend: A = 1 obs, B = 2 obs, etc. 3.0 + | | A | | | 2.8 + | A | | A A | | 2.6 + A | | AA YP | A A A | A | A 2.4 + | | AA A | A A A A A | AA AA | A A 2.2 + A A | A B | A | A A A A | A AA A | A 2.0 + A A | A | A | A A | A A A | A 1.8 + A | A | | | | 1.6 + | | A | | | 1.4 + --+-------+-------+-------+-------+-------+-------+-------+-------+-------+- 8 18 28 38 48 58 68 78 88 98 X2 The SAS System 28 15:54 Thursday, November 20, 2003 Plot of YP*X3. Legend: A = 1 obs, B = 2 obs, etc. 3.0 + | | A | | | 2.8 + | A | | A A | | 2.6 + A | | A A YP | A A A | A | A 2.4 + | | A A A | AA A AA | A A A A | A A 2.2 + B | A A A | A | A A A A | A A A A | A 2.0 + A A | A | A | A A | A A A | A 1.8 + A | A | | | | 1.6 + | | A | | | 1.4 + ---+-------------+-------------+-------------+-------------+-------------+-- 20 40 60 80 100 120 X3 The SAS System 29 15:54 Thursday, November 20, 2003 Plot of YP*X4. Legend: A = 1 obs, B = 2 obs, etc. 3.0 + | | A | | | 2.8 + | A | | A A | | 2.6 + A | | AA YP | AA A | A | A 2.4 + | | A A A | AAAAA | A AB | A A 2.2 + B | A A A | A | A A A A | A A A A | A 2.0 + A A | A | A | A A | A A A | A 1.8 + A | A | | | | 1.6 + | | A | | | 1.4 + ---+---------+---------+---------+---------+---------+---------+---------+-- 0 1 2 3 4 5 6 7 X4 The SAS System 30 15:54 Thursday, November 20, 2003 Plot of RESID*X1. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A A A a | A A l | A A A A B AA 0.00 + AA A AC | A B A A A A | AA A A | A AA A | | A A | A -0.05 + A | A | A A | A | | | -0.10 + A A | -+-------------+-------------+-------------+-------------+-------------+ 2 4 6 8 10 12 X1 The SAS System 31 15:54 Thursday, November 20, 2003 Plot of RESID*X2. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A A A a | A A l | A A AA AA B 0.00 + A A AA A A A | A A A A A A A | A A A A | A A A A | | B | A -0.05 + A | A | A A | A | | | -0.10 + A A | ---+------+------+------+------+------+------+------+------+------+-- 8 18 28 38 48 58 68 78 88 98 X2 The SAS System 32 15:54 Thursday, November 20, 2003 Plot of RESID*X3. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A AA a | B l | B AA A A A A 0.00 + AA A A A A A | AA B A A A | A A A A | A A A A | | AA | A -0.05 + A | A | A A | A | | | -0.10 + A A | -+-------------+-------------+-------------+-------------+-------------+ 20 40 60 80 100 120 X3 The SAS System 33 15:54 Thursday, November 20, 2003 Plot of RESID*X4. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A AA a | A A l | A A A AAA AA 0.00 + A AB B A | AB A A A A | AA A A | A A A A | | A A | A -0.05 + A | A | A A | A | | | -0.10 + A A | -+---------+---------+---------+---------+---------+---------+---------+ 0 1 2 3 4 5 6 7 X4 The SAS System 34 15:54 Thursday, November 20, 2003 Plot of RESID*PRED. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A A A a | A A l | A A A A AB A 0.00 + A A A B A A | A A A A A B | AAA A | A A A A | | AA | A -0.05 + A | A | A A |A | | | -0.10 + A A | -+---------+---------+---------+---------+---------+---------+---------+ 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Predicted Value of YP The SAS System 35 15:54 Thursday, November 20, 2003 Plot of RESID*X12. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A A A a | AA l | A AAAA A A A 0.00 + AA A A A A A | A AAA A A A | AA A A | A A A A | | A A | A -0.05 + A | A | A A | A | | | -0.10 + A A | -+-------------+-------------+-------------+-------------+-------------+ 0 200 400 600 800 1000 X12 The SAS System 36 15:54 Thursday, November 20, 2003 Plot of RESID*X13. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | AA u | AA A a | A A l | AA AAAA B 0.00 + AA A AA AA | A AA A A AA | A A A A | A B A | | A A | A -0.05 + A | A | A A | A | | | -0.10 + A A | ---+----------+----------+----------+----------+----------+----------+-- 0 200 400 600 800 1000 1200 X13 The SAS System 37 15:54 Thursday, November 20, 2003 Plot of RESID*X14. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | AA A a | A A l | BA BA A A 0.00 + A A BB A | AB A A A A | A A A A | A A A A | | A A | A -0.05 + A | A | A A | A | | | -0.10 + A A | -+---------+---------+---------+---------+---------+---------+---------+ 0 10 20 30 40 50 60 70 X14 The SAS System 38 15:54 Thursday, November 20, 2003 Plot of RESID*X23. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | AA u | A A A a | A A l | A A AD A 0.00 + B B A A A | A A A AA A A | A A A A | AA A A | | B | A -0.05 + A | A | A A | A | | | -0.10 + AA | ---+----------+----------+----------+----------+----------+----------+-- 0 2000 4000 6000 8000 10000 12000 X23 The SAS System 39 15:54 Thursday, November 20, 2003 Plot of RESID*X24. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A A A a | A A l | A AAAA AA A 0.00 + AA AABA | BA A A A A | A A A A | A A A A | | A A | A -0.05 + A | A | A A | A | | | -0.10 + AA | ---+----------+----------+----------+----------+----------+----------+-- 0 100 200 300 400 500 600 X24 The SAS System 40 15:54 Thursday, November 20, 2003 Plot of RESID*X34. Legend: A = 1 obs, B = 2 obs, etc. | | 0.15 + | A | | | | A | 0.10 + A | | A | | A | R | A e 0.05 + s | A i | d | A A u | A A A a | A A l | A A AA AB A 0.00 + A AA A A A A | A A A A B A | A B A | B A A | | A A | A -0.05 + A | A | A A | A | | | -0.10 + A A | ---+----------+----------+----------+----------+----------+----------+-- 0 100 200 300 400 500 600 X34 The SAS System 41 15:54 Thursday, November 20, 2003 ------------------------------------------------------------------ 0.15 + | | | | + | | | | | | | | + | | | 0.10 + + | | | | + | | | | + | | | | | | + | 0.05 + | | | | + | | + | R | ++ | e | + | s | +++ | i | +++++ | d 0 + ++++ | u | +++++ | a | ++ | l | +++++ | | + | | + | | + + | | | -0.05 + + | | | | + + | | + | | + | | | | | | | -0.10 + + + | | | | | | | | | | | | | | | -0.15 + | +---------+----+-------+---------+--------+-------+----+---------+ 1 5 10 25 50 75 90 95 99 Normal Percentiles Observations: + (8 Hidden) The SAS System 42 15:54 Thursday, November 20, 2003 Model: MODEL1 Dependent Variable: Y Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 2 737504.60446 368752.30223 49.305 0.0001 Error 51 381426.89554 7478.95874 C Total 53 1118931.5 Root MSE 86.48097 R-square 0.6591 Dep Mean 197.16667 Adj R-sq 0.6457 C.V. 43.86186 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 -424.564138 63.74961983 -6.660 0.0001 X2 1 4.882612 0.70299436 6.945 0.0001 X3 1 4.058440 0.55907160 7.259 0.0001 The SAS System 43 15:54 Thursday, November 20, 2003 Plot of RESID*X23. Legend: A = 1 obs, B = 2 obs, etc. | | 400 + | | | | | A | 300 + | | | A | | | 200 + | | A R | e | A s | A i | d 100 + u | A a | A A l | | A | A AA | A A A A 0 + AA A B A A | A B AA A A A A | A AB AA A A | A AA A | A A A | A | A A -100 + | A | A | A | | A | -200 + | ---+----------+----------+----------+----------+----------+----------+-- 0 2000 4000 6000 8000 10000 12000 X23 The SAS System 44 15:54 Thursday, November 20, 2003 Model: MODEL1 Dependent Variable: YP Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 2 3.22976 1.61488 110.845 0.0001 Error 51 0.74301 0.01457 C Total 53 3.97277 Root MSE 0.12070 R-square 0.8130 Dep Mean 2.20614 Adj R-sq 0.8056 C.V. 5.47115 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 0.907423 0.08897531 10.199 0.0001 X2 1 0.009863 0.00098117 10.053 0.0001 X3 1 0.008753 0.00078030 11.218 0.0001 The SAS System 45 15:54 Thursday, November 20, 2003 Plot of RESID*X23. Legend: A = 1 obs, B = 2 obs, etc. 0.4 + | | | | | A 0.3 + | | | | | A 0.2 + | A | | AA | | A A 0.1 + B | A B A R | B A e | A A A A s | A A i | A A A A A d 0.0 + A A A u | AA A A a | A A l | A A A A A | A A A A | A -0.1 + | | A | | A | A A -0.2 + A | | A | A | | -0.3 + | A | | | | -0.4 + ---+----------+----------+----------+----------+----------+----------+-- 0 2000 4000 6000 8000 10000 12000 X23 The SAS System 46 15:54 Thursday, November 20, 2003 Correlation Analysis 5 'VAR' Variables: YP X1 X2 X3 X4 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum YP 54 2.20614 0.27378 119.13180 1.53150 2.91910 X1 54 5.78333 1.60303 312.30000 2.60000 11.20000 X2 54 63.24074 16.90253 3415 8.00000 96.00000 X3 54 77.11111 21.25378 4164 23.00000 119.00000 X4 54 2.74426 1.07036 148.19000 0.74000 6.40000 Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 54 YP X1 X2 X3 X4 YP 1.00000 0.34640 0.59289 0.66512 0.72621 0.0 0.0103 0.0001 0.0001 0.0001 X1 0.34640 1.00000 0.09012 -0.14963 0.50242 0.0103 0.0 0.5169 0.2802 0.0001 X2 0.59289 0.09012 1.00000 -0.02361 0.36903 0.0001 0.5169 0.0 0.8655 0.0060 X3 0.66512 -0.14963 -0.02361 1.00000 0.41642 0.0001 0.2802 0.8655 0.0 0.0017 X4 0.72621 0.50242 0.36903 0.41642 1.00000 0.0001 0.0001 0.0060 0.0017 0.0 The SAS System 47 15:54 Thursday, November 20, 2003 N = 54 Regression Models for Dependent Variable: YP C(p) R-square Adjusted MSE SSE Variables in Model In R-square 3.03932 0.97234711 3 0.97068794 0.00219717 0.1098586 X1 X2 X3 5.00000 0.97236929 4 0.97011372 0.00224021 0.1097705 X1 X2 X3 X4 161.66249 0.88290076 3 0.87587480 0.00930417 0.4652086 X2 X3 X4 283.66945 0.81297421 2 0.80563986 0.01456884 0.7430109 X2 X3 451.98702 0.71918904 3 0.70234038 0.02231196 1.1155980 X1 X3 X4 507.89640 0.68653440 2 0.67424163 0.02441819 1.2453274 X3 X4 573.43719 0.64957646 2 0.63583436 0.02729712 1.3921529 X2 X4 574.70996 0.64998654 3 0.62898573 0.02781048 1.3905238 X1 X2 X4 580.14526 0.64579383 2 0.63190340 0.02759177 1.4071804 X1 X3 788.14814 0.52737486 1 0.51828592 0.03610831 1.8776320 X4 789.34038 0.52783035 2 0.50931390 0.03678083 1.8758225 X1 X4 938.86513 0.44238674 1 0.43166341 0.04260136 2.2152705 X3 948.55003 0.43805329 2 0.41601616 0.04377424 2.2324863 X1 X2 1100 0.35151718 1 0.33904635 0.04954374 2.5762746 X2 1511 0.11999586 1 0.10307271 0.06723185 3.4960560 X1 ------------------------------------------------------------- The SAS System 48 15:54 Thursday, November 20, 2003 N = 54 Regression Models for Dependent Variable: YP R-square Adjusted C(p) MSE SSE Variables in Model In R-square 1 0.5273749 0.5182859 788.1481 0.0361083 1.877632 X4 1 0.4423867 0.4316634 938.8651 0.0426014 2.215270 X3 1 0.3515172 0.3390464 1100 0.0495437 2.576275 X2 1 0.1199959 0.1030727 1511 0.0672318 3.496056 X1 ------------------------------------------------------------ 2 0.8129742 0.8056399 283.6695 0.0145688 0.743011 X2 X3 2 0.6865344 0.6742416 507.8964 0.0244182 1.245327 X3 X4 2 0.6495765 0.6358344 573.4372 0.0272971 1.392153 X2 X4 2 0.6457938 0.6319034 580.1453 0.0275918 1.407180 X1 X3 2 0.5278304 0.5093139 789.3404 0.0367808 1.875822 X1 X4 2 0.4380533 0.4160162 948.5500 0.0437742 2.232486 X1 X2 --------------------------------------------------------------- 3 0.9723471 0.9706879 3.0393 0.0021972 0.109859 X1 X2 X3 3 0.8829008 0.8758748 161.6625 0.0093042 0.465209 X2 X3 X4 3 0.7191890 0.7023404 451.9870 0.0223120 1.115598 X1 X3 X4 3 0.6499865 0.6289857 574.7100 0.0278105 1.390524 X1 X2 X4 ------------------------------------------------------------------ 4 0.9723693 0.9701137 5.0000 0.0022402 0.109771 X1 X2 X3 X4 --------------------------------------------------------------------- The SAS System 49 15:54 Thursday, November 20, 2003 Stepwise Procedure for Dependent Variable YP Step 1 Variable X4 Entered R-square = 0.52737486 C(p) =788.14813627 DF Sum of Squares Mean Square F Prob>F Regression 1 2.09514023 2.09514023 58.02 0.0001 Error 52 1.87763202 0.03610831 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.69638489 0.07174324 20.18803240 559.10 0.0001 X4 0.18575488 0.02438581 2.09514023 58.02 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- Step 2 Variable X3 Entered R-square = 0.68653440 C(p) =507.89639740 DF Sum of Squares Mean Square F Prob>F Regression 2 2.72744481 1.36372240 55.85 0.0001 Error 51 1.24532745 0.02441819 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.38877757 0.08446782 6.60079464 270.32 0.0001 X3 0.00565254 0.00111080 0.63230458 25.89 0.0001 X4 0.13901497 0.02205693 0.96994304 39.72 0.0001 Bounds on condition number: 1.209789, 4.839155 -------------------------------------------------------------------------------- Step 3 Variable X2 Entered R-square = 0.88290076 C(p) =161.66248928 DF Sum of Squares Mean Square F Prob>F Regression 3 3.50756363 1.16918788 125.66 0.0001 Error 50 0.46520862 0.00930417 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.94226338 0.07138961 1.62088545 174.21 0.0001 X2 0.00789866 0.00086260 0.78011882 83.85 0.0001 X3 0.00699974 0.00070128 0.92694429 99.63 0.0001 X4 0.08184608 0.01497852 0.27780226 29.86 0.0001 Bounds on condition number: 1.464174, 11.82183 -------------------------------------------------------------------------------- The SAS System 50 15:54 Thursday, November 20, 2003 Step 4 Variable X1 Entered R-square = 0.97236929 C(p) = 5.00000000 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86300172 0.96575043 431.10 0.0001 Error 49 0.10977053 0.00224021 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48875592 0.05023319 0.21207636 94.67 0.0001 X1 0.06852018 0.00543978 0.35543809 158.66 0.0001 X2 0.00925411 0.00043673 1.00582746 448.99 0.0001 X3 0.00947455 0.00039625 1.28075323 571.71 0.0001 X4 0.00192542 0.00970961 0.00008809 0.04 0.8436 Bounds on condition number: 2.555329, 29.28635 -------------------------------------------------------------------------------- Step 5 Variable X4 Removed R-square = 0.97234711 C(p) = 3.03932316 DF Sum of Squares Mean Square F Prob>F Regression 3 3.86291363 1.28763788 586.04 0.0001 Error 50 0.10985863 0.00219717 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48362086 0.04262871 0.28279376 128.71 0.0001 X1 0.06922508 0.00407795 0.63315225 288.17 0.0001 X2 0.00929454 0.00038250 1.29732180 590.45 0.0001 X3 0.00952364 0.00030641 2.12262768 966.07 0.0001 Bounds on condition number: 1.030813, 9.186356 -------------------------------------------------------------------------------- All variables left in the model are significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model. Summary of Stepwise Procedure for Dependent Variable YP Variable Number Partial Model Step Entered Removed In R**2 R**2 C(p) F Prob>F 1 X4 1 0.5274 0.5274 788.1481 58.0238 0.0001 2 X3 2 0.1592 0.6865 507.8964 25.8948 0.0001 3 X2 3 0.1964 0.8829 161.6625 83.8461 0.0001 4 X1 4 0.0895 0.9724 5.0000 158.6625 0.0001 5 X4 3 0.0000 0.9723 3.0393 0.0393 0.8436 The SAS System 51 15:54 Thursday, November 20, 2003 Stepwise Procedure for Dependent Variable YP Step 1 Variable X4 Entered R-square = 0.52737486 C(p) =788.14813627 DF Sum of Squares Mean Square F Prob>F Regression 1 2.09514023 2.09514023 58.02 0.0001 Error 52 1.87763202 0.03610831 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.69638489 0.07174324 20.18803240 559.10 0.0001 X4 0.18575488 0.02438581 2.09514023 58.02 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- Step 2 Variable X3 Entered R-square = 0.68653440 C(p) =507.89639740 DF Sum of Squares Mean Square F Prob>F Regression 2 2.72744481 1.36372240 55.85 0.0001 Error 51 1.24532745 0.02441819 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.38877757 0.08446782 6.60079464 270.32 0.0001 X3 0.00565254 0.00111080 0.63230458 25.89 0.0001 X4 0.13901497 0.02205693 0.96994304 39.72 0.0001 Bounds on condition number: 1.209789, 4.839155 -------------------------------------------------------------------------------- Step 3 Variable X2 Entered R-square = 0.88290076 C(p) =161.66248928 DF Sum of Squares Mean Square F Prob>F Regression 3 3.50756363 1.16918788 125.66 0.0001 Error 50 0.46520862 0.00930417 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.94226338 0.07138961 1.62088545 174.21 0.0001 X2 0.00789866 0.00086260 0.78011882 83.85 0.0001 X3 0.00699974 0.00070128 0.92694429 99.63 0.0001 X4 0.08184608 0.01497852 0.27780226 29.86 0.0001 Bounds on condition number: 1.464174, 11.82183 -------------------------------------------------------------------------------- The SAS System 52 15:54 Thursday, November 20, 2003 Step 4 Variable X1 Entered R-square = 0.97236929 C(p) = 5.00000000 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86300172 0.96575043 431.10 0.0001 Error 49 0.10977053 0.00224021 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48875592 0.05023319 0.21207636 94.67 0.0001 X1 0.06852018 0.00543978 0.35543809 158.66 0.0001 X2 0.00925411 0.00043673 1.00582746 448.99 0.0001 X3 0.00947455 0.00039625 1.28075323 571.71 0.0001 X4 0.00192542 0.00970961 0.00008809 0.04 0.8436 Bounds on condition number: 2.555329, 29.28635 -------------------------------------------------------------------------------- Step 5 Variable X4 Removed R-square = 0.97234711 C(p) = 3.03932316 DF Sum of Squares Mean Square F Prob>F Regression 3 3.86291363 1.28763788 586.04 0.0001 Error 50 0.10985863 0.00219717 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48362086 0.04262871 0.28279376 128.71 0.0001 X1 0.06922508 0.00407795 0.63315225 288.17 0.0001 X2 0.00929454 0.00038250 1.29732180 590.45 0.0001 X3 0.00952364 0.00030641 2.12262768 966.07 0.0001 Bounds on condition number: 1.030813, 9.186356 -------------------------------------------------------------------------------- All variables left in the model are significant at the 0.1000 level. No other variable met the 0.0500 significance level for entry into the model. Summary of Stepwise Procedure for Dependent Variable YP Variable Number Partial Model Step Entered Removed In R**2 R**2 C(p) F Prob>F 1 X4 1 0.5274 0.5274 788.1481 58.0238 0.0001 2 X3 2 0.1592 0.6865 507.8964 25.8948 0.0001 3 X2 3 0.1964 0.8829 161.6625 83.8461 0.0001 4 X1 4 0.0895 0.9724 5.0000 158.6625 0.0001 5 X4 3 0.0000 0.9723 3.0393 0.0393 0.8436 The SAS System 53 15:54 Thursday, November 20, 2003 Model: MODEL1 Dependent Variable: YP Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 4 3.86300 0.96575 431.097 0.0001 Error 49 0.10977 0.00224 C Total 53 3.97277 Root MSE 0.04733 R-square 0.9724 Dep Mean 2.20614 Adj R-sq 0.9701 C.V. 2.14541 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 0.488756 0.05023319 9.730 0.0001 X1 1 0.068520 0.00543978 12.596 0.0001 X2 1 0.009254 0.00043673 21.189 0.0001 X3 1 0.009475 0.00039625 23.910 0.0001 X4 1 0.001925 0.00970961 0.198 0.8436 Variance Variable DF Inflation INTERCEP 1 0.00000000 X1 1 1.79901252 X2 1 1.28921530 X3 1 1.67802997 X4 1 2.55532933 The SAS System 54 15:54 Thursday, November 20, 2003 Dep Var Predict Std Err Std Err Student Obs YP Value Predict Residual Residual Residual 1 2.3010 2.2940 0.009 0.00698 0.046 0.150 2 2.0043 2.0128 0.009 -0.00849 0.046 -0.183 3 2.3096 2.3138 0.015 -0.00424 0.045 -0.095 4 2.0043 2.0020 0.014 0.00229 0.045 0.050 5 2.7067 2.7226 0.017 -0.0159 0.044 -0.359 6 1.9031 1.9227 0.013 -0.0196 0.045 -0.433 7 1.9031 1.9056 0.010 -0.00248 0.046 -0.054 8 2.1038 2.1439 0.012 -0.0401 0.046 -0.875 9 2.3054 2.4058 0.011 -0.1004 0.046 -2.187 10 2.3075 2.3408 0.013 -0.0333 0.046 -0.732 11 2.5172 2.4921 0.012 0.0251 0.046 0.548 12 1.8129 1.8308 0.014 -0.0179 0.045 -0.394 13 2.9191 2.8623 0.019 0.0568 0.043 1.308 14 2.5185 2.4956 0.012 0.0229 0.046 0.499 15 2.2253 2.2315 0.011 -0.00616 0.046 -0.133 16 2.3365 2.3295 0.013 0.00700 0.045 0.154 17 1.9395 1.9575 0.021 -0.0180 0.043 -0.422 18 1.5315 1.6057 0.018 -0.0742 0.044 -1.700 19 2.3324 2.3262 0.009 0.00620 0.046 0.134 20 2.2355 2.2301 0.008 0.00545 0.047 0.117 21 2.0374 2.0518 0.010 -0.0144 0.046 -0.312 22 2.1335 1.9941 0.018 0.1394 0.044 3.176 23 1.8451 1.8368 0.017 0.00834 0.044 0.188 24 2.3424 2.3276 0.008 0.0148 0.047 0.318 25 2.4409 2.4196 0.011 0.0213 0.046 0.464 26 2.1584 2.1491 0.011 0.00935 0.046 0.203 27 2.2577 2.1458 0.008 0.1119 0.047 2.402 28 2.7589 2.8230 0.024 -0.0641 0.041 -1.579 29 1.8573 1.8806 0.014 -0.0233 0.045 -0.513 30 2.2504 2.1535 0.010 0.0969 0.046 2.094 31 1.8513 1.9176 0.015 -0.0663 0.045 -1.480 32 1.7634 1.7241 0.022 0.0393 0.042 0.941 33 2.0645 2.0757 0.014 -0.0112 0.045 -0.249 34 2.4698 2.4400 0.009 0.0298 0.047 0.642 35 2.0607 2.0638 0.008 -0.00310 0.047 -0.067 36 2.2648 2.2669 0.011 -0.00206 0.046 -0.045 37 2.0719 2.1705 0.015 -0.0986 0.045 -2.202 38 2.0792 1.9904 0.026 0.0888 0.039 2.264 39 2.1790 2.1069 0.008 0.0721 0.047 1.544 40 2.1703 2.1772 0.012 -0.00692 0.046 -0.151 41 1.9777 1.9842 0.009 -0.00652 0.046 -0.141 42 1.8751 1.9350 0.018 -0.0599 0.044 -1.372 43 2.6840 2.7337 0.024 -0.0497 0.041 -1.220 44 2.1847 2.1874 0.008 -0.00269 0.047 -0.058 45 2.2810 2.3183 0.017 -0.0373 0.044 -0.845 46 2.0899 2.1059 0.012 -0.0160 0.046 -0.351 47 2.4928 2.4828 0.013 0.00998 0.046 0.219 48 2.5999 2.5783 0.015 0.0216 0.045 0.481 49 2.1987 2.1933 0.008 0.00542 0.047 0.116 50 2.4914 2.4995 0.020 -0.00806 0.043 -0.188 51 2.0934 2.0931 0.014 0.000261 0.045 0.006 52 2.0969 2.0952 0.020 0.00170 0.043 0.040 53 2.2967 2.2831 0.011 0.0136 0.046 0.295 54 2.4955 2.5019 0.017 -0.00638 0.044 -0.144 The SAS System 55 15:54 Thursday, November 20, 2003 Cook's Hat Diag Cov Obs -2-1-0 1 2 D Rstudent H Ratio Dffits 1 | | | 0.000 0.1490 0.0397 1.1518 0.0303 2 | | | 0.000 -0.1811 0.0370 1.1472 -0.0355 3 | | | 0.000 -0.0937 0.1053 1.2380 -0.0321 4 | | | 0.000 0.0499 0.0822 1.2075 0.0149 5 | | | 0.004 -0.3555 0.1248 1.2501 -0.1342 6 | | | 0.003 -0.4291 0.0811 1.1836 -0.1275 7 | | | 0.000 -0.0532 0.0474 1.1635 -0.0119 8 | *| | 0.010 -0.8726 0.0598 1.0899 -0.2201 9 | ****| | 0.060 -2.2790 0.0586 0.7045 -0.5686 10 | *| | 0.009 -0.7286 0.0753 1.1347 -0.2079 11 | |* | 0.004 0.5443 0.0657 1.1506 0.1444 12 | | | 0.003 -0.3909 0.0815 1.1880 -0.1165 13 | |** | 0.064 1.3177 0.1572 1.1013 0.5691 14 | | | 0.003 0.4947 0.0606 1.1505 0.1257 15 | | | 0.000 -0.1321 0.0502 1.1651 -0.0304 16 | | | 0.000 0.1528 0.0812 1.2036 0.0454 17 | | | 0.008 -0.4185 0.1880 1.3407 -0.2014 18 | ***| | 0.102 -1.7350 0.1505 0.9628 -0.7302 19 | | | 0.000 0.1322 0.0386 1.1510 0.0265 20 | | | 0.000 0.1155 0.0271 1.1379 0.0193 21 | | | 0.001 -0.3087 0.0432 1.1472 -0.0656 22 | |******| 0.329 3.5270 0.1402 0.4073 1.4241 23 | | | 0.001 0.1864 0.1240 1.2610 0.0701 24 | | | 0.001 0.3152 0.0279 1.1287 0.0534 25 | | | 0.003 0.4603 0.0559 1.1487 0.1120 26 | | | 0.000 0.2010 0.0538 1.1667 0.0479 27 | |**** | 0.037 2.5311 0.0313 0.6117 0.4550 28 | ***| | 0.180 -1.6038 0.2649 1.1616 -0.9627 29 | *| | 0.005 -0.5095 0.0824 1.1760 -0.1527 30 | |**** | 0.039 2.1719 0.0431 0.7250 0.4608 31 | **| | 0.052 -1.4988 0.1055 0.9860 -0.5147 32 | |* | 0.050 0.9398 0.2206 1.2984 0.5000 33 | | | 0.001 -0.2463 0.0896 1.2100 -0.0772 34 | |* | 0.003 0.6379 0.0347 1.1009 0.1209 35 | | | 0.000 -0.0659 0.0284 1.1405 -0.0113 36 | | | 0.000 -0.0442 0.0510 1.1679 -0.0102 37 | ****| | 0.115 -2.2965 0.1059 0.7362 -0.7904 38 | |**** | 0.468 2.3685 0.3132 0.9289 1.5995 39 | |*** | 0.013 1.5662 0.0270 0.8880 0.2608 40 | | | 0.000 -0.1495 0.0611 1.1780 -0.0381 41 | | | 0.000 -0.1391 0.0381 1.1502 -0.0277 42 | **| | 0.066 -1.3847 0.1483 1.0701 -0.5779 43 | **| | 0.105 -1.2261 0.2599 1.2839 -0.7267 44 | | | 0.000 -0.0571 0.0265 1.1384 -0.0094 45 | *| | 0.022 -0.8430 0.1325 1.1873 -0.3294 46 | | | 0.002 -0.3477 0.0671 1.1734 -0.0932 47 | | | 0.001 0.2165 0.0698 1.1859 0.0593 48 | | | 0.005 0.4768 0.1008 1.2041 0.1596 49 | | | 0.000 0.1149 0.0269 1.1376 0.0191 50 | | | 0.002 -0.1864 0.1816 1.3496 -0.0878 51 | | | 0.000 0.0057 0.0860 1.2129 0.0017 52 | | | 0.000 0.0392 0.1733 1.3408 0.0179 53 | | | 0.001 0.2921 0.0502 1.1568 0.0671 54 | | | 0.001 -0.1426 0.1237 1.2624 -0.0536 The SAS System 56 15:54 Thursday, November 20, 2003 INTERCEP X1 X2 X3 X4 Obs Dfbetas Dfbetas Dfbetas Dfbetas Dfbetas 1 -0.0139 0.0212 0.0059 0.0154 -0.0176 2 -0.0107 -0.0010 -0.0025 0.0018 0.0160 3 0.0176 -0.0272 -0.0058 -0.0197 0.0243 4 0.0026 0.0028 0.0047 -0.0073 -0.0030 5 0.0885 -0.0701 -0.0073 -0.0903 0.0145 6 -0.0254 -0.0451 0.0530 -0.0261 0.0615 7 -0.0069 -0.0002 0.0064 0.0035 0.0009 8 -0.1063 0.1702 -0.0102 0.0456 -0.0719 9 0.3485 -0.3104 -0.2442 -0.4393 0.3892 10 0.0218 0.0714 -0.1015 -0.0773 0.0435 11 -0.0213 -0.0308 0.0497 -0.0234 0.0705 12 -0.0551 -0.0222 0.0357 0.0627 0.0078 13 -0.4040 0.0974 0.4012 0.3524 -0.1262 14 -0.0211 -0.0355 0.0483 -0.0041 0.0531 15 0.0000 -0.0119 0.0061 0.0085 -0.0066 16 -0.0252 0.0348 0.0247 0.0143 -0.0304 17 -0.0954 0.0748 -0.0286 0.1714 -0.0907 18 -0.6816 0.4839 0.2784 0.5679 -0.2882 19 -0.0040 0.0085 0.0001 -0.0042 0.0066 20 0.0042 -0.0036 -0.0075 0.0023 0.0053 21 -0.0473 0.0352 0.0420 0.0275 -0.0378 22 0.2943 -0.4235 0.7990 -0.2854 -0.4306 23 0.0300 0.0138 -0.0555 -0.0088 0.0014 24 0.0023 -0.0130 -0.0017 0.0005 0.0226 25 -0.0580 0.0555 0.0062 0.0867 -0.0464 26 0.0279 -0.0251 -0.0213 -0.0282 0.0382 27 0.1148 -0.0418 -0.1796 0.1232 -0.0376 28 0.5313 -0.6053 -0.0577 -0.1628 -0.1021 29 -0.1325 0.0910 0.0805 0.1229 -0.0995 30 0.0833 -0.0494 0.1968 -0.2097 0.0107 31 -0.1427 0.1217 -0.1513 -0.0164 0.2489 32 0.2144 0.1056 -0.2125 -0.3282 0.1028 33 -0.0549 0.0563 0.0372 0.0484 -0.0655 34 -0.0498 0.0086 0.0440 0.0564 -0.0052 35 -0.0076 0.0048 0.0045 0.0055 -0.0045 36 0.0011 -0.0012 0.0026 -0.0064 0.0025 37 -0.2112 0.5135 -0.2376 -0.0283 -0.0093 38 0.6075 -0.3897 -1.3063 0.2868 0.4342 39 0.1390 -0.1322 -0.0367 -0.0537 0.0460 40 0.0080 -0.0156 -0.0003 -0.0244 0.0264 41 -0.0122 -0.0001 0.0105 -0.0001 0.0076 42 -0.1716 0.0699 0.2910 -0.2203 0.1426 43 0.0670 0.0661 0.0391 0.2035 -0.5251 44 -0.0007 -0.0030 0.0033 -0.0004 0.0000 45 0.0914 0.0065 -0.1994 -0.1785 0.2016 46 -0.0284 -0.0086 0.0725 -0.0006 -0.0226 47 -0.0188 -0.0104 0.0217 0.0351 -0.0076 48 -0.0214 -0.0723 0.0564 0.0166 0.0649 49 0.0075 -0.0100 0.0005 -0.0052 0.0069 50 -0.0186 0.0635 -0.0024 0.0145 -0.0609 51 -0.0001 0.0006 0.0009 -0.0004 -0.0007 52 -0.0039 0.0074 0.0117 -0.0008 -0.0112 53 -0.0305 0.0448 0.0113 0.0427 -0.0462 54 0.0362 -0.0454 -0.0252 -0.0170 0.0259 The SAS System 57 15:54 Thursday, November 20, 2003 Sum of Residuals 0 Sum of Squared Residuals 0.1098 Predicted Resid SS (Press) 0.1456 The SAS System 58 15:54 Thursday, November 20, 2003 Partial Regression Residual Plot -+---------+---------+---------+---------+---------+---------+---------+-- YP | | 0.20 + + | | | 1 | | 1 | | | | | 0.15 + + | | | 1 1 | | | | 1 | | 1 | 0.10 + + | 1 1 | | 1 | | 11 1 | | | | 1 1 | 0.05 + 1 + | 1 | | 1 2 | | 1 1 | | 1 1 1 1 | | 1 1 | 0.00 + 2 1 + | 1 11 1 1 | | 1 | | 1 1 | | 1 11 1 | | 1 | -0.05 + 1 + | 1 | | 1 | | 1 1 | | 1 1 | | | -0.10 + + | | | 1 | | 1 | | | | | -0.15 + + | | | 1 | | | | | | 1 | -0.20 + + -+---------+---------+---------+---------+---------+---------+---------+-- -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 INTERCEP The SAS System 59 15:54 Thursday, November 20, 2003 Partial Regression Residual Plot ------+----+----+----+----+----+----+----+----+----+----+----+----+------- YP | | | | 0.20 + + | | | | | 1 | | 1 | 0.15 + + | 1 | | 1 | | | | | 0.10 + 1 1 1 1 1 + | 1 1 1 | | 1 | | 1 | | 1 | 0.05 + 1 11 + | 1 1 1 | | 11 | | 1 | | 1 1 1 | 0.00 + 1 1 + | 111 2 | | 1 1 1 | | | | 1 | -0.05 + 11 + | 1 1 | | | | 1 1 | | 1 1 | -0.10 + + | 1 1 | | | | 1 | | 1 | -0.15 + 1 + | | | | | | | 1 | -0.20 + + | | | 1 | | 1 | | | -0.25 + + | | | | ------+----+----+----+----+----+----+----+----+----+----+----+----+------- -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 X1 The SAS System 60 15:54 Thursday, November 20, 2003 Partial Regression Residual Plot -----+-------+-------+-------+-------+-------+-------+-------+-------+----- YP | | 0.4 + + | | | | | 1 | | 1 | | | 0.3 + + | | | 1 | | | | | | | 0.2 + + | 1 1 | | 11 | | 1 | | 1 | | 2 | 0.1 + 1 2 1 + | | | | | 1 1 2 2 | | 1 1 | | 2 | 0.0 + 221 11 + | | | 1 1 | | 1 | | 22 | | 1 1 | -0.1 + 11 + | 1 | | 1 | | 2 | | 1 | | 1 | -0.2 + + | 1 1 | | | | 1 | | 1 | | | -0.3 + + | | | | | | | 1 | | | -0.4 + + -----+-------+-------+-------+-------+-------+-------+-------+-------+----- -50 -40 -30 -20 -10 0 10 20 30 X2 The SAS System 61 15:54 Thursday, November 20, 2003 Partial Regression Residual Plot -----+-------+-------+-------+-------+-------+-------+-------+-------+----- YP | | | | 0.4 + + | | | | | 1 | | | 0.3 + + | | | 1 | | | | 1 1 | 0.2 + 1 + | 12 1 | | 1 1 | | | | 1 11 1 | 0.1 + 1 1 + | 1 | | 1 1 | | 1 1 1 | | 11 1 | 0.0 + 1 11 + | 11111 | | 2 | | 1 | | 22 1 | -0.1 + 1 1 + | 1 | | 1 | | 1 | | | -0.2 + 1 + | 1 1 | | | | | | 1 | -0.3 + 1 + | | | | | | | | -0.4 + + | 1 | | 1 | | | | | -0.5 + + | | | | -----+-------+-------+-------+-------+-------+-------+-------+-------+----- -50 -40 -30 -20 -10 0 10 20 30 X3 The SAS System 62 15:54 Thursday, November 20, 2003 Partial Regression Residual Plot -+---------+---------+---------+---------+---------+---------+---------+-- YP | | | | | | | | | | 0.15 + + | | | 1 | | | | | | | | 1 | | | 0.10 + 1 + | | | 1 | | | | 1 | | | | | | 1 | 0.05 + + | | | 1 | | 1 | | 1 11 | | 1 | | 1 1 1 1 | | 1 1 1 111 | 0.00 + 1 1 11 1 1 1 + | 1 2 1 1 1 1 1 | | 1 1 | | 1 1 1 11 | | | | 1 | | 1 1 | | 1 | -0.05 + + | | | 1 1 | | 1 | | 1 | | | | | | | -0.10 + 1 1 + | | | | | | | | -+---------+---------+---------+---------+---------+---------+---------+-- -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 X4 The SAS System 63 15:54 Thursday, November 20, 2003 Forward Selection Procedure for Dependent Variable YP Step 1 Variable X4 Entered R-square = 0.52737486 C(p) =788.14813627 DF Sum of Squares Mean Square F Prob>F Regression 1 2.09514023 2.09514023 58.02 0.0001 Error 52 1.87763202 0.03610831 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.69638489 0.07174324 20.18803240 559.10 0.0001 X4 0.18575488 0.02438581 2.09514023 58.02 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- Step 2 Variable X3 Entered R-square = 0.68653440 C(p) =507.89639740 DF Sum of Squares Mean Square F Prob>F Regression 2 2.72744481 1.36372240 55.85 0.0001 Error 51 1.24532745 0.02441819 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.38877757 0.08446782 6.60079464 270.32 0.0001 X3 0.00565254 0.00111080 0.63230458 25.89 0.0001 X4 0.13901497 0.02205693 0.96994304 39.72 0.0001 Bounds on condition number: 1.209789, 4.839155 -------------------------------------------------------------------------------- Step 3 Variable X2 Entered R-square = 0.88290076 C(p) =161.66248928 DF Sum of Squares Mean Square F Prob>F Regression 3 3.50756363 1.16918788 125.66 0.0001 Error 50 0.46520862 0.00930417 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.94226338 0.07138961 1.62088545 174.21 0.0001 X2 0.00789866 0.00086260 0.78011882 83.85 0.0001 X3 0.00699974 0.00070128 0.92694429 99.63 0.0001 X4 0.08184608 0.01497852 0.27780226 29.86 0.0001 Bounds on condition number: 1.464174, 11.82183 -------------------------------------------------------------------------------- The SAS System 64 15:54 Thursday, November 20, 2003 Step 4 Variable X1 Entered R-square = 0.97236929 C(p) = 5.00000000 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86300172 0.96575043 431.10 0.0001 Error 49 0.10977053 0.00224021 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48875592 0.05023319 0.21207636 94.67 0.0001 X1 0.06852018 0.00543978 0.35543809 158.66 0.0001 X2 0.00925411 0.00043673 1.00582746 448.99 0.0001 X3 0.00947455 0.00039625 1.28075323 571.71 0.0001 X4 0.00192542 0.00970961 0.00008809 0.04 0.8436 Bounds on condition number: 2.555329, 29.28635 -------------------------------------------------------------------------------- All variables have been entered into the model. Summary of Forward Selection Procedure for Dependent Variable YP Variable Number Partial Model Step Entered In R**2 R**2 C(p) F Prob>F 1 X4 1 0.5274 0.5274 788.1481 58.0238 0.0001 2 X3 2 0.1592 0.6865 507.8964 25.8948 0.0001 3 X2 3 0.1964 0.8829 161.6625 83.8461 0.0001 4 X1 4 0.0895 0.9724 5.0000 158.6625 0.0001 The SAS System 65 15:54 Thursday, November 20, 2003 Backward Elimination Procedure for Dependent Variable YP Step 0 All Variables Entered R-square = 0.97236929 C(p) = 5.00000000 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86300172 0.96575043 431.10 0.0001 Error 49 0.10977053 0.00224021 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48875592 0.05023319 0.21207636 94.67 0.0001 X1 0.06852018 0.00543978 0.35543809 158.66 0.0001 X2 0.00925411 0.00043673 1.00582746 448.99 0.0001 X3 0.00947455 0.00039625 1.28075323 571.71 0.0001 X4 0.00192542 0.00970961 0.00008809 0.04 0.8436 Bounds on condition number: 2.555329, 29.28635 -------------------------------------------------------------------------------- Step 1 Variable X4 Removed R-square = 0.97234711 C(p) = 3.03932316 DF Sum of Squares Mean Square F Prob>F Regression 3 3.86291363 1.28763788 586.04 0.0001 Error 50 0.10985863 0.00219717 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48362086 0.04262871 0.28279376 128.71 0.0001 X1 0.06922508 0.00407795 0.63315225 288.17 0.0001 X2 0.00929454 0.00038250 1.29732180 590.45 0.0001 X3 0.00952364 0.00030641 2.12262768 966.07 0.0001 Bounds on condition number: 1.030813, 9.186356 -------------------------------------------------------------------------------- All variables left in the model are significant at the 0.1000 level. Summary of Backward Elimination Procedure for Dependent Variable YP Variable Number Partial Model Step Removed In R**2 R**2 C(p) F Prob>F 1 X4 3 0.0000 0.9723 3.0393 0.0393 0.8436 The SAS System 66 15:54 Thursday, November 20, 2003 Maximum R-square Improvement for Dependent Variable YP Step 1 Variable X4 Entered R-square = 0.52737486 C(p) =788.14813627 DF Sum of Squares Mean Square F Prob>F Regression 1 2.09514023 2.09514023 58.02 0.0001 Error 52 1.87763202 0.03610831 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.69638489 0.07174324 20.18803240 559.10 0.0001 X4 0.18575488 0.02438581 2.09514023 58.02 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- The above model is the best 1-variable model found. Step 2 Variable X3 Entered R-square = 0.68653440 C(p) =507.89639740 DF Sum of Squares Mean Square F Prob>F Regression 2 2.72744481 1.36372240 55.85 0.0001 Error 51 1.24532745 0.02441819 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.38877757 0.08446782 6.60079464 270.32 0.0001 X3 0.00565254 0.00111080 0.63230458 25.89 0.0001 X4 0.13901497 0.02205693 0.96994304 39.72 0.0001 Bounds on condition number: 1.209789, 4.839155 -------------------------------------------------------------------------------- Step 3 Variable X4 Removed R-square = 0.81297421 C(p) =283.66945272 Variable X2 Entered DF Sum of Squares Mean Square F Prob>F Regression 2 3.22976137 1.61488069 110.84 0.0001 Error 51 0.74301088 0.01456884 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.90742299 0.08897531 1.51532399 104.01 0.0001 X2 0.00986333 0.00098117 1.47225960 101.06 0.0001 X3 0.00875305 0.00078030 1.83326369 125.83 0.0001 Bounds on condition number: 1.000558, 4.00223 -------------------------------------------------------------------------------- The SAS System 67 15:54 Thursday, November 20, 2003 The above model is the best 2-variable model found. Step 4 Variable X1 Entered R-square = 0.97234711 C(p) = 3.03932316 DF Sum of Squares Mean Square F Prob>F Regression 3 3.86291363 1.28763788 586.04 0.0001 Error 50 0.10985863 0.00219717 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48362086 0.04262871 0.28279376 128.71 0.0001 X1 0.06922508 0.00407795 0.63315225 288.17 0.0001 X2 0.00929454 0.00038250 1.29732180 590.45 0.0001 X3 0.00952364 0.00030641 2.12262768 966.07 0.0001 Bounds on condition number: 1.030813, 9.186356 -------------------------------------------------------------------------------- The above model is the best 3-variable model found. Step 5 Variable X4 Entered R-square = 0.97236929 C(p) = 5.00000000 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86300172 0.96575043 431.10 0.0001 Error 49 0.10977053 0.00224021 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48875592 0.05023319 0.21207636 94.67 0.0001 X1 0.06852018 0.00543978 0.35543809 158.66 0.0001 X2 0.00925411 0.00043673 1.00582746 448.99 0.0001 X3 0.00947455 0.00039625 1.28075323 571.71 0.0001 X4 0.00192542 0.00970961 0.00008809 0.04 0.8436 Bounds on condition number: 2.555329, 29.28635 -------------------------------------------------------------------------------- The above model is the best 4-variable model found. No further improvement in R-square is possible. The SAS System 68 15:54 Thursday, November 20, 2003 Minimum R-square Improvement for Dependent Variable YP Step 1 Variable X1 Entered R-square = 0.11999586 C(p) =1510.5895060 DF Sum of Squares Mean Square F Prob>F Regression 1 0.47671624 0.47671624 7.09 0.0103 Error 52 3.49605601 0.06723185 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.86398572 0.13325133 13.15579413 195.68 0.0001 X1 0.05916289 0.02221810 0.47671624 7.09 0.0103 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- Step 2 Variable X1 Removed R-square = 0.35151718 C(p) =1100.0121983 Variable X2 Entered DF Sum of Squares Mean Square F Prob>F Regression 1 1.39649768 1.39649768 28.19 0.0001 Error 52 2.57627457 0.04954374 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.59881086 0.11833581 9.04379284 182.54 0.0001 X2 0.00960352 0.00180886 1.39649768 28.19 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- Step 3 Variable X2 Removed R-square = 0.44238674 C(p) =938.86512552 Variable X3 Entered DF Sum of Squares Mean Square F Prob>F Regression 1 1.75750177 1.75750177 41.25 0.0001 Error 52 2.21527048 0.04260136 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.54546518 0.10662778 8.94954929 210.08 0.0001 X3 0.00856789 0.00133394 1.75750177 41.25 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- The SAS System 69 15:54 Thursday, November 20, 2003 Step 4 Variable X3 Removed R-square = 0.52737486 C(p) =788.14813627 Variable X4 Entered DF Sum of Squares Mean Square F Prob>F Regression 1 2.09514023 2.09514023 58.02 0.0001 Error 52 1.87763202 0.03610831 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.69638489 0.07174324 20.18803240 559.10 0.0001 X4 0.18575488 0.02438581 2.09514023 58.02 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- The above model is the best 1-variable model found. Step 5 Variable X1 Entered R-square = 0.52783035 C(p) =789.34038021 DF Sum of Squares Mean Square F Prob>F Regression 2 2.09694978 1.04847489 28.51 0.0001 Error 51 1.87582248 0.03678083 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.71206085 0.10118189 10.53062992 286.31 0.0001 X1 -0.00421576 0.01900648 0.00180955 0.05 0.8254 X4 0.18892703 0.02846532 1.62023354 44.05 0.0001 Bounds on condition number: 1.337652, 5.350609 -------------------------------------------------------------------------------- Step 6 Variable X4 Removed R-square = 0.64579383 C(p) =580.14525882 Variable X3 Entered DF Sum of Squares Mean Square F Prob>F Regression 2 2.56559182 1.28279591 46.49 0.0001 Error 51 1.40718043 0.02759177 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.02711474 0.12859970 1.76010108 63.79 0.0001 X1 0.07790522 0.01439549 0.80809005 29.29 0.0001 X3 0.00944712 0.00108576 2.08887559 75.71 0.0001 Bounds on condition number: 1.022903, 4.091613 -------------------------------------------------------------------------------- The SAS System 70 15:54 Thursday, November 20, 2003 Step 7 Variable X1 Removed R-square = 0.68653440 C(p) =507.89639740 Variable X4 Entered DF Sum of Squares Mean Square F Prob>F Regression 2 2.72744481 1.36372240 55.85 0.0001 Error 51 1.24532745 0.02441819 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.38877757 0.08446782 6.60079464 270.32 0.0001 X3 0.00565254 0.00111080 0.63230458 25.89 0.0001 X4 0.13901497 0.02205693 0.96994304 39.72 0.0001 Bounds on condition number: 1.209789, 4.839155 -------------------------------------------------------------------------------- Step 8 Variable X4 Removed R-square = 0.81297421 C(p) =283.66945272 Variable X2 Entered DF Sum of Squares Mean Square F Prob>F Regression 2 3.22976137 1.61488069 110.84 0.0001 Error 51 0.74301088 0.01456884 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.90742299 0.08897531 1.51532399 104.01 0.0001 X2 0.00986333 0.00098117 1.47225960 101.06 0.0001 X3 0.00875305 0.00078030 1.83326369 125.83 0.0001 Bounds on condition number: 1.000558, 4.00223 -------------------------------------------------------------------------------- The above model is the best 2-variable model found. Step 9 Variable X4 Entered R-square = 0.88290076 C(p) =161.66248928 DF Sum of Squares Mean Square F Prob>F Regression 3 3.50756363 1.16918788 125.66 0.0001 Error 50 0.46520862 0.00930417 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.94226338 0.07138961 1.62088545 174.21 0.0001 X2 0.00789866 0.00086260 0.78011882 83.85 0.0001 X3 0.00699974 0.00070128 0.92694429 99.63 0.0001 X4 0.08184608 0.01497852 0.27780226 29.86 0.0001 Bounds on condition number: 1.464174, 11.82183 The SAS System 71 15:54 Thursday, November 20, 2003 -------------------------------------------------------------------------------- Step10 Variable X4 Removed R-square = 0.97234711 C(p) = 3.03932316 Variable X1 Entered DF Sum of Squares Mean Square F Prob>F Regression 3 3.86291363 1.28763788 586.04 0.0001 Error 50 0.10985863 0.00219717 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48362086 0.04262871 0.28279376 128.71 0.0001 X1 0.06922508 0.00407795 0.63315225 288.17 0.0001 X2 0.00929454 0.00038250 1.29732180 590.45 0.0001 X3 0.00952364 0.00030641 2.12262768 966.07 0.0001 Bounds on condition number: 1.030813, 9.186356 -------------------------------------------------------------------------------- The above model is the best 3-variable model found. Step11 Variable X4 Entered R-square = 0.97236929 C(p) = 5.00000000 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86300172 0.96575043 431.10 0.0001 Error 49 0.10977053 0.00224021 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48875592 0.05023319 0.21207636 94.67 0.0001 X1 0.06852018 0.00543978 0.35543809 158.66 0.0001 X2 0.00925411 0.00043673 1.00582746 448.99 0.0001 X3 0.00947455 0.00039625 1.28075323 571.71 0.0001 X4 0.00192542 0.00970961 0.00008809 0.04 0.8436 Bounds on condition number: 2.555329, 29.28635 -------------------------------------------------------------------------------- The above model is the best 4-variable model found. No further improvement in R-square is possible. The SAS System 72 15:54 Thursday, November 20, 2003 Stepwise Procedure for Dependent Variable YP Step 1 Variable X23 Entered R-square = 0.77052213 C(p) =412.50972677 DF Sum of Squares Mean Square F Prob>F Regression 1 3.06110896 3.06110896 174.60 0.0001 Error 52 0.91166330 0.01753199 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.62545432 0.04749662 20.53313828 1171.18 0.0001 X23 0.00011928 0.00000903 3.06110896 174.60 0.0001 Bounds on condition number: 1, 1 -------------------------------------------------------------------------------- Step 2 Variable X13 Entered R-square = 0.91681880 C(p) =119.65065485 DF Sum of Squares Mean Square F Prob>F Regression 2 3.64231229 1.82115614 281.06 0.0001 Error 51 0.33045997 0.00647961 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.45887964 0.03380984 12.06427882 1861.88 0.0001 X13 0.00071762 0.00007577 0.58120333 89.70 0.0001 X23 0.00008850 0.00000638 1.24738010 192.51 0.0001 Bounds on condition number: 1.350804, 5.403216 -------------------------------------------------------------------------------- Step 3 Variable X2 Entered R-square = 0.93918699 C(p) = 76.56784377 DF Sum of Squares Mean Square F Prob>F Regression 3 3.73117603 1.24372534 257.40 0.0001 Error 50 0.24159623 0.00483192 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 1.29433154 0.04821491 3.48215880 720.66 0.0001 X2 0.00383131 0.00089340 0.08886374 18.39 0.0001 X13 0.00085884 0.00007325 0.66422510 137.47 0.0001 X23 0.00005974 0.00000868 0.22892632 47.38 0.0001 Bounds on condition number: 3.353557, 22.64306 -------------------------------------------------------------------------------- The SAS System 73 15:54 Thursday, November 20, 2003 Step 4 Variable X3 Entered R-square = 0.95762279 C(p) = 41.41072549 DF Sum of Squares Mean Square F Prob>F Regression 4 3.80441726 0.95110431 276.82 0.0001 Error 49 0.16835500 0.00343582 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.84444334 0.10558290 0.21977780 63.97 0.0001 X2 0.01026640 0.00158434 0.14426722 41.99 0.0001 X3 0.00550797 0.00119297 0.07324123 21.32 0.0001 X13 0.00080979 0.00006268 0.57354703 166.93 0.0001 X23 -0.00001425 0.00001762 0.00224740 0.65 0.4226 Bounds on condition number: 19.4319, 168.6167 -------------------------------------------------------------------------------- Step 5 Variable X23 Removed R-square = 0.95705709 C(p) = 40.55088729 DF Sum of Squares Mean Square F Prob>F Regression 3 3.80216986 1.26738995 371.45 0.0001 Error 50 0.17060240 0.00341205 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.92235192 0.04307449 1.56447336 458.51 0.0001 X2 0.00904543 0.00047901 1.21669486 356.59 0.0001 X3 0.00463033 0.00049387 0.29992015 87.90 0.0001 X13 0.00080440 0.00006210 0.57240849 167.76 0.0001 Bounds on condition number: 1.723303, 13.35905 -------------------------------------------------------------------------------- Step 6 Variable X1 Entered R-square = 0.97284040 C(p) = 10.73982505 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86487336 0.96621834 438.79 0.0001 Error 49 0.10789890 0.00220202 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.39306435 0.10505022 0.03082864 14.00 0.0005 X1 0.08347014 0.01564212 0.06270350 28.48 0.0001 X2 0.00936086 0.00038933 1.27299385 578.10 0.0001 X3 0.01060649 0.00118812 0.17548606 79.69 0.0001 X13 -0.00018034 0.00019116 0.00195973 0.89 0.3501 Bounds on condition number: 25.29958, 227.292 The SAS System 74 15:54 Thursday, November 20, 2003 -------------------------------------------------------------------------------- Step 7 Variable X13 Removed R-square = 0.97234711 C(p) = 9.73404556 DF Sum of Squares Mean Square F Prob>F Regression 3 3.86291363 1.28763788 586.04 0.0001 Error 50 0.10985863 0.00219717 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48362086 0.04262871 0.28279376 128.71 0.0001 X1 0.06922508 0.00407795 0.63315225 288.17 0.0001 X2 0.00929454 0.00038250 1.29732180 590.45 0.0001 X3 0.00952364 0.00030641 2.12262768 966.07 0.0001 Bounds on condition number: 1.030813, 9.186356 -------------------------------------------------------------------------------- All variables left in the model are significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model. Summary of Stepwise Procedure for Dependent Variable YP Variable Number Partial Model Step Entered Removed In R**2 R**2 C(p) F Prob>F 1 X23 1 0.7705 0.7705 412.5097 174.6014 0.0001 2 X13 2 0.1463 0.9168 119.6507 89.6973 0.0001 3 X2 3 0.0224 0.9392 76.5678 18.3910 0.0001 4 X3 4 0.0184 0.9576 41.4107 21.3170 0.0001 5 X23 3 0.0006 0.9571 40.5509 0.6541 0.4226 6 X1 4 0.0158 0.9728 10.7398 28.4755 0.0001 7 X13 3 0.0005 0.9723 9.7340 0.8900 0.3501 The SAS System 75 15:54 Thursday, November 20, 2003 Stepwise Procedure for Dependent Variable YP The first 4 variables are forced into the model because of the INCLUDE= option. Step 0 The First 4 Vars Entered R-square = 0.97236929 C(p) = 11.68935411 DF Sum of Squares Mean Square F Prob>F Regression 4 3.86300172 0.96575043 431.10 0.0001 Error 49 0.10977053 0.00224021 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.48875592 0.05023319 0.21207636 94.67 0.0001 X1 0.06852018 0.00543978 0.35543809 158.66 0.0001 X2 0.00925411 0.00043673 1.00582746 448.99 0.0001 X3 0.00947455 0.00039625 1.28075323 571.71 0.0001 X4 0.00192542 0.00970961 0.00008809 0.04 0.8436 Bounds on condition number: 2.555329, 29.28635 -------------------------------------------------------------------------------- Step 1 Variable X14 Entered R-square = 0.97555005 C(p) = 7.27856453 DF Sum of Squares Mean Square F Prob>F Regression 5 3.87563817 0.77512763 383.04 0.0001 Error 48 0.09713408 0.00202363 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.36717657 0.06816564 0.05871504 29.01 0.0001 X1 0.08755159 0.00920505 0.18306554 90.46 0.0001 X2 0.00933242 0.00041627 1.01712481 502.62 0.0001 X3 0.00953177 0.00037730 1.29149611 638.21 0.0001 X4 0.03894132 0.01745235 0.01007497 4.98 0.0304 X14 -0.00594793 0.00238023 0.01263645 6.24 0.0159 Bounds on condition number: 16.90966, 173.6621 -------------------------------------------------------------------------------- Step 2 Variable X23 Entered R-square = 0.97694021 C(p) = 6.47671461 DF Sum of Squares Mean Square F Prob>F Regression 6 3.88116096 0.64686016 331.86 0.0001 Error 47 0.09161129 0.00194918 Total 53 3.97277225 Parameter Standard Type II Variable Estimate Error Sum of Squares F Prob>F INTERCEP 0.23504811 0.10313627 0.01012376 5.19 0.0273 The SAS System 76 15:54 Thursday, November 20, 2003 X1 0.08901696 0.00907598 0.18750374 96.20 0.0001 X2 0.01124431 0.00120706 0.16914505 86.78 0.0001 X3 0.01094406 0.00091710 0.27757228 142.40 0.0001 X4 0.04238745 0.01725022 0.01176891 6.04 0.0177 X14 -0.00630152 0.00234546 0.01406975 7.22 0.0099 X23 -0.00002253 0.00001339 0.00552279 2.83 0.0990 Bounds on condition number: 19.78272, 441.0223 -------------------------------------------------------------------------------- All variables left in the model are required or significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model. Summary of Stepwise Procedure for Dependent Variable YP Variable Number Partial Model Step Entered Removed In R**2 R**2 C(p) F Prob>F 1 X14 5 0.0032 0.9756 7.2786 6.2445 0.0159 2 X23 6 0.0014 0.9769 6.4767 2.8334 0.0990