Thursday, January 20, 2022 05:35:01 PM 85 Obs id y x1 x2 x3 x4 x5 x6 1 Phoenix 10 70.3 213 582 6.0 7.05 36 2 Little_R 13 61.0 91 132 8.2 48.52 100 3 San_Fran 12 56.7 453 716 8.7 20.66 67 4 Denver 17 51.9 454 515 9.0 12.95 86 5 Hartford 56 49.1 412 158 9.0 43.37 127 6 Wilmingt 36 54.0 80 80 9.0 40.25 114 7 Washingt 29 57.3 434 757 9.3 38.89 111 8 Jacksonv 14 68.4 136 529 8.8 54.47 116 9 Miami 10 75.5 207 335 9.0 59.80 128 10 Atlanta 24 61.5 368 497 9.1 48.34 115 Thursday, January 20, 2022 05:35:01 PM 86 The CORR Procedure 7 Variables: y x1 x2 x3 x4 x5 x6 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum y 41 30.04878 23.47227 1232 8.00000 110.00000 x1 41 55.76341 7.22772 2286 43.50000 75.50000 x2 41 463.09756 563.47395 18987 35.00000 3344 x3 41 608.60976 579.11302 24953 71.00000 3369 x4 41 9.44390 1.42864 387.20000 6.00000 12.70000 x5 41 36.76902 11.77155 1508 7.05000 59.80000 x6 41 113.90244 26.50642 4670 36.00000 166.00000 Thursday, January 20, 2022 05:35:02 PM 87 The CORR Procedure Pearson Correlation Coefficients, N = 41 Prob > |r| under H0: Rho=0 y x1 x2 x3 x4 x5 x6 y 1.00000 -0.43360 0.64477 0.49378 0.09469 0.05429 0.36956 0.0046 <.0001 0.0010 0.5559 0.7360 0.0174 x1 -0.43360 1.00000 -0.19004 -0.06268 -0.34974 0.38625 -0.43024 0.0046 0.2340 0.6970 0.0250 0.0126 0.0050 x2 0.64477 -0.19004 1.00000 0.95527 0.23795 -0.03242 0.13183 <.0001 0.2340 <.0001 0.1341 0.8405 0.4113 x3 0.49378 -0.06268 0.95527 1.00000 0.21264 -0.02612 0.04208 0.0010 0.6970 <.0001 0.1819 0.8712 0.7939 x4 0.09469 -0.34974 0.23795 0.21264 1.00000 -0.01299 0.16411 0.5559 0.0250 0.1341 0.1819 0.9357 0.3052 x5 0.05429 0.38625 -0.03242 -0.02612 -0.01299 1.00000 0.49610 0.7360 0.0126 0.8405 0.8712 0.9357 0.0010 x6 0.36956 -0.43024 0.13183 0.04208 0.16411 0.49610 1.00000 0.0174 0.0050 0.4113 0.7939 0.3052 0.0010 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 88 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 41 Number of Observations Used 41 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 14755 2459.10601 11.48 <.0001 Error 34 7283.26641 214.21372 Corrected Total 40 22038 Root MSE 14.63604 R-Square 0.6695 Dependent Mean 30.04878 Adj R-Sq 0.6112 Coeff Var 48.70761 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 89 The REG Procedure Model: MODEL1 Dependent Variable: y Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 111.72848 47.31810 2.36 0.0241 x1 1 -1.26794 0.62118 -2.04 0.0491 x2 1 0.06492 0.01575 4.12 0.0002 x3 1 -0.03928 0.01513 -2.60 0.0138 x4 1 -3.18137 1.81502 -1.75 0.0887 x5 1 0.51236 0.36276 1.41 0.1669 x6 1 -0.05205 0.16201 -0.32 0.7500 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 90 Plot of resid1*pred1. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d | A A u | A A A A a | AA AAA A A l 0 +--------------A-A-------A---A---------A--------------------------A----- | A A BA | A A A | AA B | AB A A | -25 + A -+---------+---------+---------+---------+---------+---------+---------+ -20 0 20 40 60 80 100 120 Predicted Value of y *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 91 Plot of resid1*x1. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d | A A u | A A A A a | A A A A A A A l 0 +-----------------AAAA--------A-----------------------------A--------- | B A A A | A A A | A A A A | A A A A A | -25 + A ---+-------+-------+-------+-------+-------+-------+-------+-------+-- 40 45 50 55 60 65 70 75 80 x1 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 92 Plot of resid1*x2. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d | A A u | A A A A a | AAA AA A A l 0 +---AAA--A------------A---------------------------------------------A--- | A B AA | A A A | A AA A | A B A A | -25 + A -+---------+---------+---------+---------+---------+---------+---------+ 0 500 1000 1500 2000 2500 3000 3500 x2 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 93 Plot of resid1*x3. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d | A A u | AA A A a | A AA A B A l 0 +---A--AA---A------------------A------------------------------------A--- | A AA AA | A A A | A AA A | A AA AA | -25 + A -+---------+---------+---------+---------+---------+---------+---------+ 0 500 1000 1500 2000 2500 3000 3500 x3 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 94 Plot of resid1*x4. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d |A A u | A A AA a | A A AA A AA l 0 +--------------------------A---B----------A--A----------------------A--- | A A A A A | A A A | A A A A | A A A A A | -25 + A -+---------+---------+---------+---------+---------+---------+---------+ 6 7 8 9 10 11 12 13 x4 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 95 Plot of resid1*x5. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d | A A u | A AA A a | A A A AA A A l 0 +------------------------------------B---A--A------A-----------------A-- | A A A A A | A A A | A A A A | A A AA A | -25 + A ---+----------+----------+----------+----------+----------+----------+-- 0 10 20 30 40 50 60 x5 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 96 Plot of resid1*x6. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d | A A u | A A B a | A A A A AA A l 0 +---------------------------A---------------A-BA-A-------------------- | A B A A | A A A | A A A A | B A A A | -25 + A ---+-------+-------+-------+-------+-------+-------+-------+-------+-- 20 40 60 80 100 120 140 160 180 x6 *** フルモデル *** Thursday, January 20, 2022 05:35:02 PM 97 Plot of resid1*y. Legend: A = 1 obs, B = 2 obs, etc. | 50 + A | | | | R | A e 25 + s | i | A A d | A A u | A A A A a | AA BA A A l 0 +------AA-------A----A---------A--------------------------A------- | A AA AA | AA A | B B | ABA A | -25 + A ---+---------+---------+---------+---------+---------+---------+-- 0 20 40 60 80 100 120 y *** 逐次増減法 *** Thursday, January 20, 2022 05:35:02 PM 98 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 41 Number of Observations Used 41 Stepwise Selection: Step 1 Variable x2 Entered: R-Square = 0.4157 and C(p) = 23.1089 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 9161.74469 9161.74469 27.75 <.0001 Error 39 12876 330.15789 Corrected Total 40 22038 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:02 PM 99 The REG Procedure Model: MODEL1 Dependent Variable: y Stepwise Selection: Step 1 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 17.61057 3.69159 7513.50474 22.76 <.0001 x2 0.02686 0.00510 9161.74469 27.75 <.0001 Bounds on condition number: 1, 1 ------------------------------------------------------------------------------ Stepwise Selection: Step 2 Variable x3 Entered: R-Square = 0.5863 and C(p) = 7.5586 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:02 PM 100 The REG Procedure Model: MODEL1 Dependent Variable: y Stepwise Selection: Step 2 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 12921 6460.63359 26.93 <.0001 Error 38 9116.63526 239.91145 Corrected Total 40 22038 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 26.32508 3.84044 11273 46.99 <.0001 x2 0.08243 0.01470 7548.02378 31.46 <.0001 x3 -0.05661 0.01430 3759.52248 15.67 0.0003 Bounds on condition number: 11.434, 45.735 ------------------------------------------------------------------------------ Stepwise Selection: Step 3 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:02 PM 101 The REG Procedure Model: MODEL1 Dependent Variable: y Stepwise Selection: Step 3 Variable x6 Entered: R-Square = 0.6174 and C(p) = 6.3610 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 13606 4535.41173 19.90 <.0001 Error 37 8431.66725 227.88290 Corrected Total 40 22038 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 6.96585 11.77691 79.72552 0.35 0.5578 x2 0.07433 0.01507 5547.32154 24.34 <.0001 x3 -0.04939 0.01454 2628.36952 11.53 0.0016 x6 0.16436 0.09480 684.96801 3.01 0.0913 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:02 PM 102 The REG Procedure Model: MODEL1 Dependent Variable: y Stepwise Selection: Step 3 Bounds on condition number: 12.65, 78.633 ------------------------------------------------------------------------------ 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 Selection Variable Variable Number Partial Model Step Entered Removed Vars In R-Square R-Square C(p) F Value Pr > F 1 x2 1 0.4157 0.4157 23.1089 27.75 <.0001 2 x3 2 0.1706 0.5863 7.5586 15.67 0.0003 3 x6 3 0.0311 0.6174 6.3610 3.01 0.0913 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 103 Obs id y x1 x2 x3 x4 x5 x6 pred2 resid2 1 Phoenix 10 70.3 213 582 6.0 7.05 36 -0.032 10.0316 2 Little_R 13 61.0 91 132 8.2 48.52 100 23.646 -10.6461 3 San_Fran 12 56.7 453 716 8.7 20.66 67 16.285 -4.2849 4 Denver 17 51.9 454 515 9.0 12.95 86 29.410 -12.4103 5 Hartford 56 49.1 412 158 9.0 43.37 127 50.661 5.3392 6 Wilmingt 36 54.0 80 80 9.0 40.25 114 27.698 8.3020 7 Washingt 29 57.3 434 757 9.3 38.89 111 20.079 8.9208 8 Jacksonv 14 68.4 136 529 8.8 54.47 116 10.011 3.9887 9 Miami 10 75.5 207 335 9.0 59.80 128 26.844 -16.8439 10 Atlanta 24 61.5 368 497 9.1 48.34 115 28.673 -4.6731 11 Chicago 110 50.6 3344 3369 10.4 34.44 122 109.181 0.8191 12 Indianap 28 52.3 361 746 9.7 38.74 121 16.840 11.1603 13 Des_Moin 17 49.0 104 201 11.2 30.85 103 21.697 -4.6973 14 Wichita 8 56.6 125 277 12.7 30.58 82 16.053 -8.0528 15 Louisvil 30 55.6 291 593 8.3 43.11 123 19.522 10.4776 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 104 Plot of resid2*pred2. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | B s | A AAA A i | A A AAA A B d 0 +----------------A--AA-----------------------------------------A-------- u | CAAA A A A A a | B AA l | AA A A A -25 + | A | | -50 + | ---+----------+----------+----------+----------+----------+----------+-- 0 20 40 60 80 100 120 Predicted Value of y *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 105 Plot of resid2*x1. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A A A A A i | A B A A AA A d 0 +------------------AA------A---A-------------------------------------- u | A A B B A AA A a | A A A A l | A A A A A -25 + | A | | -50 + | ---+-------+-------+-------+-------+-------+-------+-------+-------+-- 40 45 50 55 60 65 70 75 80 x1 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 106 Plot of resid2*x2. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A A AA A i | AAB A AA A d 0 +-A--A----------------A---------------------------------------------A--- u | AAA ABAA A A a | A A AA l | A A A AA -25 + | A | | -50 + | -+---------+---------+---------+---------+---------+---------+---------+ 0 500 1000 1500 2000 2500 3000 3500 x2 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 107 Plot of resid2*x3. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A B A A i | AAAA BA A d 0 +-A----A-----------------------A------------------------------------A--- u | A AA AAAA AA A a | A A B l | A A AA A -25 + | A | | -50 + | -+---------+---------+---------+---------+---------+---------+---------+ 0 500 1000 1500 2000 2500 3000 3500 x3 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 108 Plot of resid2*x4. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s |A A AA A i | AAAAB A A d 0 +-----A----------A------------------------A--A-------------------------- u | A A AA A AB A A a | A A A A l | A A A A A -25 + | A | | -50 + | -+---------+---------+---------+---------+---------+---------+---------+ 6 7 8 9 10 11 12 13 x4 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 109 Plot of resid2*x5. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A AA A A i | A A A A AA A A d 0 +------------------------------------A---A------A-A--------------------- u | A AB A A A BA a | A A A A l | A A A A A -25 + | A | | -50 + | ---+----------+----------+----------+----------+----------+----------+-- 0 10 20 30 40 50 60 x5 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 110 Plot of resid2*x6. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A B AA i | A A A A B A A d 0 +----------------------------------------A--A--A------A--------------- u | A A A BA A A A A a | A B A l | A A A A A -25 + | A | | -50 + | ---+-------+-------+-------+-------+-------+-------+-------+-------+-- 20 40 60 80 100 120 140 160 180 x6 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 111 Plot of resid2*x1. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A A A A A i | A B A A AA A d 0 +------------------AA------A---A-------------------------------------- u | A A B B A AA A a | A A A A l | A A A A A -25 + | A | | -50 + | ---+-------+-------+-------+-------+-------+-------+-------+-------+-- 40 45 50 55 60 65 70 75 80 x1 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 112 Plot of resid2*x2. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A A AA A i | AAB A AA A d 0 +-A--A----------------A---------------------------------------------A--- u | AAA ABAA A A a | A A AA l | A A A AA -25 + | A | | -50 + | -+---------+---------+---------+---------+---------+---------+---------+ 0 500 1000 1500 2000 2500 3000 3500 x2 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 113 Plot of resid2*x3. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A B A A i | AAAA BA A d 0 +-A----A-----------------------A------------------------------------A--- u | A AA AAAA AA A a | A A B l | A A AA A -25 + | A | | -50 + | -+---------+---------+---------+---------+---------+---------+---------+ 0 500 1000 1500 2000 2500 3000 3500 x3 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 114 Plot of resid2*x4. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s |A A AA A i | AAAAB A A d 0 +-----A----------A------------------------A--A-------------------------- u | A A AA A AB A A a | A A A A l | A A A A A -25 + | A | | -50 + | -+---------+---------+---------+---------+---------+---------+---------+ 6 7 8 9 10 11 12 13 x4 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 115 Plot of resid2*x5. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A AA A A i | A A A A AA A A d 0 +------------------------------------A---A------A-A--------------------- u | A AB A A A BA a | A A A A l | A A A A A -25 + | A | | -50 + | ---+----------+----------+----------+----------+----------+----------+-- 0 10 20 30 40 50 60 x5 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 116 Plot of resid2*x6. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | A A s | A B AA i | A A A A B A A d 0 +----------------------------------------A--A--A------A--------------- u | A A A BA A A A A a | A B A l | A A A A A -25 + | A | | -50 + | ---+-------+-------+-------+-------+-------+-------+-------+-------+-- 20 40 60 80 100 120 140 160 180 x6 *** 逐次増減法 *** Thursday, January 20, 2022 05:35:03 PM 117 Plot of resid2*y. Legend: A = 1 obs, B = 2 obs, etc. | | 50 + A | | | A R 25 + e | AA s | A AAA A i | AA AAA A B d 0 +---------------A--A-A------------------------------------A------- u | ABAA B A A A a | A B A l | B A A A -25 + | A | | -50 + | ---+---------+---------+---------+---------+---------+---------+-- 0 20 40 60 80 100 120 y *** 総当たり法 *** Thursday, January 20, 2022 05:35:03 PM 118 The REG Procedure Model: MODEL1 Dependent Variable: y R-Square Selection Method Number of Observations Read 41 Number of Observations Used 41 Number in Model R-Square Variables in Model 1 0.4157 x2 1 0.2438 x3 1 0.1880 x1 1 0.1366 x6 1 0.0090 x4 1 0.0029 x5 ------------------------------------------- 2 0.5863 x2 x3 2 0.5161 x1 x2 2 0.4981 x2 x6 2 0.4214 x2 x5 2 0.4194 x2 x4 2 0.4066 x1 x3 2 0.3657 x3 x6 *** 総当たり法 *** Thursday, January 20, 2022 05:35:03 PM 119 The REG Procedure Model: MODEL1 Dependent Variable: y R-Square Selection Method Number in Model R-Square Variables in Model 2 0.2483 x3 x5 2 0.2458 x1 x5 2 0.2439 x3 x4 2 0.2291 x1 x6 2 0.1917 x1 x4 2 0.1587 x5 x6 2 0.1378 x4 x6 2 0.0120 x4 x5 ------------------------------------------- 3 0.6174 x2 x3 x6 3 0.6125 x1 x2 x3 3 0.5930 x2 x3 x5 3 0.5930 x2 x3 x4 3 0.5622 x1 x2 x5 3 0.5452 x1 x2 x6 3 0.5452 x1 x2 x4 3 0.5083 x2 x4 x6 3 0.5047 x2 x5 x6 3 0.4649 x1 x3 x5 *** 総当たり法 *** Thursday, January 20, 2022 05:35:03 PM 120 The REG Procedure Model: MODEL1 Dependent Variable: y R-Square Selection Method Number in Model R-Square Variables in Model 3 0.4446 x1 x3 x6 3 0.4320 x1 x3 x4 3 0.4250 x2 x4 x5 3 0.3808 x3 x5 x6 3 0.3702 x3 x4 x6 3 0.2550 x1 x4 x5 3 0.2484 x3 x4 x5 3 0.2462 x1 x5 x6 3 0.2332 x1 x4 x6 3 0.1590 x4 x5 x6 ------------------------------------------- 4 0.6396 x1 x2 x3 x5 4 0.6329 x1 x2 x3 x4 4 0.6291 x1 x2 x3 x6 4 0.6285 x2 x3 x4 x6 4 0.6176 x2 x3 x5 x6 4 0.6028 x1 x2 x4 x5 4 0.5997 x2 x3 x4 x5 4 0.5747 x1 x2 x4 x6 *** 総当たり法 *** Thursday, January 20, 2022 05:35:03 PM 121 The REG Procedure Model: MODEL1 Dependent Variable: y R-Square Selection Method Number in Model R-Square Variables in Model 4 0.5622 x1 x2 x5 x6 4 0.5164 x2 x4 x5 x6 4 0.5035 x1 x3 x4 x5 4 0.4708 x1 x3 x4 x6 4 0.4649 x1 x3 x5 x6 4 0.3871 x3 x4 x5 x6 4 0.2550 x1 x4 x5 x6 ------------------------------------------- 5 0.6685 x1 x2 x3 x4 x5 5 0.6501 x1 x2 x3 x4 x6 5 0.6396 x1 x2 x3 x5 x6 5 0.6290 x2 x3 x4 x5 x6 5 0.6040 x1 x2 x4 x5 x6 5 0.5043 x1 x3 x4 x5 x6 ------------------------------------------- 6 0.6695 x1 x2 x3 x4 x5 x6