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Regression Results for ConsGOODS



  Fitted Stnd. Error Lower 95, 0% Upper 95, 0% Lower 95, 0% Upper 95, 0%
Row Value CL for Forecast CL for Forecast CL for Forecast CL for Mean CL for Mean
1116, 57 144, 057 831, 417 1401, 72 1087, 73 1145, 4
1117, 98 144, 059 832, 825 1403, 14 1089, 11 1146, 85
1119, 38 144, 06 834, 217 1404, 54 1090, 47 1148, 28
1120, 76 144, 062 835, 595 1405, 92 1091, 82 1149, 7
1122, 13 144, 064 836, 959 1407, 29 1093, 15 1151, 1
1123, 48 144, 066 838, 308 1408, 65 1094, 47 1152, 49

 

6) Первая функция Торнквиста: , где

Multiple Regression - (ConsGOODS) (num< 125)

Dependent variable: (ConsGOODS)

Independent variables:

num/(0.85+num)

Selection variable: num< 125

 

    Standard T  
Parameter Estimate Error Statistic P-Value
num/(0.85+num) 1012, 93 15, 2086 66, 6023 0, 0000

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 19883E8 1, 19883E8 4435, 87 0, 0000
Residual 3, 32417E6 27025, 7    
Total 1, 23207E8      

 

R-squared = 97, 302 percent

R-squared (adjusted for d.f.) = 97, 302 percent

Standard Error of Est. = 164, 395

Mean absolute error = 142, 836

Durbin-Watson statistic = 0, 0900128

Lag 1 residual autocorrelation = 0, 940484

 

Stepwise regression

Method: backward selection

F-to-enter: 4, 0

F-to-remove: 4, 0

 

Step 0:

1 variables in the model. 123 d.f. for error.

R-squared = 97, 30% Adjusted R-squared = 97, 28% MSE = 27025, 7

 

Final model selected.

 

The StatAdvisor

The output shows the results of fitting a multiple linear regression model to describe the relationship between (ConsGOODS) and 1 independent variables. The equation of the fitted model is

 

(ConsGOODS) = 1012, 93*num/(0.85+num)

 

Regression Results for (ConsGOODS)

  Fitted Stnd. Error Lower 95, 0% Upper 95, 0% Lower 95, 0% Upper 95, 0%
Row Value CL for Forecast CL for Forecast CL for Forecast CL for Mean CL for Mean
1006, 09 165, 088 679, 307 1332, 87 976, 187 1035, 99
1006, 14 165, 088 679, 361 1332, 92 976, 24 1036, 05
1006, 2 165, 088 679, 414 1332, 98 976, 291 1036, 1
1006, 25 165, 088 679, 466 1333, 03 976, 342 1036, 15
1006, 3 165, 088 679, 517 1333, 08 976, 392 1036, 21
1006, 35 165, 088 679, 568 1333, 13 976, 441 1036, 26

 

 

7) Кривая Гомперца: , где

Multiple Regression - (ConsGOODS) (num< 125)

Dependent variable: (ConsGOODS)

Independent variables:

1.09^(0.03*num)

Selection variable: num< 125

 

    Standard T  
Parameter Estimate Error Statistic P-Value
1.09^(0.03*num) 832, 081 10, 9289 76, 1357 0, 0000

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 20647E8 1, 20647E8 5796, 65 0, 0000
Residual 2, 56002E6 20813, 2    
Total 1, 23207E8      

 

R-squared = 97, 9222 percent

R-squared (adjusted for d.f.) = 97, 9222 percent

Standard Error of Est. = 144, 268

Mean absolute error = 111, 305

Durbin-Watson statistic =

Lag 1 residual autocorrelation = 0, 945027

 

Stepwise regression

Method: backward selection

F-to-enter: 4, 0

F-to-remove: 4, 0

 

Step 0:

1 variables in the model. 123 d.f. for error.

R-squared = 97, 92% Adjusted R-squared = 97, 91% MSE = 20813, 2

 

Final model selected.

 

(ConsGOODS) = 832, 081*1.09^(0.03*num)

 

Regression Results for (ConsGOODS)

  Fitted Stnd. Error Lower 95, 0% Upper 95, 0% Lower 95, 0% Upper 95, 0%
Row Value CL for Forecast CL for Forecast CL for Forecast CL for Mean CL for Mean
1149, 52 145, 056 862, 387 1436, 65 1119, 63 1179, 4
1152, 49 145, 06 865, 355 1439, 63 1122, 53 1182, 46
1155, 48 145, 064 868, 33 1442, 62 1125, 43 1185, 52
1158, 47 145, 068 871, 313 1445, 62 1128, 35 1188, 59
1161, 47 145, 072 874, 304 1448, 63 1131, 27 1191, 66
1164, 47 145, 076 877, 302 1451, 64 1134, 2 1194, 75

 


Приложение 9

Остатки по моделям тренда

период Остатки для модели тренда
линейного тренда Линейно-логарифмическая функция 2-го порядка Парабола третьего порядка Логистическая функция Первая функция Торнквиста Кривая Гомперца
вид модели Y = a + b* t Y = a + b* log(t)+c*log^2(t) Y = a + b* t^2+c*t^3 Y = a/(1+b*e^(-c*t)) Y = a*t/(b+t) Y = a*b^(c*t)
Y = 824, 41 + 2, 52608*t Y= 951, 229 - 136, 183*log(t) + 17, 7058*2*log(t)^2 Y = 829, 366 + 0, 0739677*t^2 - 0, 000476454*t^3 Y= 1237, 5*1/(1+0.55*exp(-0.013*t)) Y = 1012, 93*t/(0.85+t) Y= 832, 081*1.09^(0.03*t)
-13, 7665 -138, 059 -16, 2691 11, 1099 265, 64 -21, 0652
47, 5575 3, 17168 47, 3623 71, 2982 166, 192 40, 6252
12, 3714 0, 00269228 14, 3416 34, 9908 55, 064 5, 80008
22, 1753 26, 1956 26, 1714 43, 6879 21, 2839 15, 9593
87, 9292 101, 192 93, 8148 108, 35 59, 2179 82, 0629
113, 613 132, 272 121, 254 132, 957 65, 9421 108, 091
50, 647 72, 4217 59, 9134 68, 9291 -10, 5096 45, 4633
29, 841 53, 2923 40, 6044 47, 0768 -41, 1829 24, 9899
-75, 7451 -51, 5651 -63, 6096 -59, 54 -154, 12 -80, 2691
-63, 9512 -39, 6856 -50, 5659 -48, 7609 -147, 856 -68, 1538
-22, 8373 1, 06951 -8, 32152 -8, 64581 -110, 913 -26, 7242
10, 3566 33, 594 25, 8864 23, 5655 -80, 8468 6, 77971
34, 9006 57, 2509 51, 3306 47, 1432 -58, 6145 31, 6279
87, 5045 108, 816 104, 724 98, 7974 -7, 67077 84, 5302
86, 2984 106, 468 104, 2 96, 6584 -10, 0088 83, 6169
127, 962 146, 922 146, 44 137, 406 30, 9574 125, 568
150, 006 167, 713 168, 959 158, 551 52, 6648 147, 893
127, 61 144, 042 146, 938 135, 273 30, 236 125, 772
39, 5641 54, 7139 59, 1701 46, 363 -57, 5851 37, 9954
-37, 722 -23, 8504 -17, 931 -31, 7699 -134, 425 -39, 0271
-20, 0381 -7, 43201 -0, 152903 -14, 9151 -116, 105 -21, 0854
-81, 9742 -70, 6142 -62, 0827 -77, 6625 -177, 24 -82, 7695
-23, 1802 -13, 0419 -3, 36748 -19, 6619 -117, 5 -23, 7296
-35, 7663 -26, 8212 -16, 1145 -33, 0232 -129, 012 -36, 0755
-48, 9124 -41, 1291 -29, 5008 -46, 9263 -140, 973 -48, 9874
-65, 7785 -59, 1236 -46, 6836 -64, 531 -156, 553 -65, 6252
-72, 0546 -66, 493 -53, 35 -71, 5273 -161, 455 -71, 679
-73, 8606 -69, 3562 -55, 6171 -74, 035 -161, 806 -73, 2687
-85, 2267 -81, 7424 -67, 5122 -86, 0839 -171, 646 -84, 4244
-113, 643 -111, 141 -96, 5223 -115, 164 -198, 471 -112, 636
-97, 8789 -96, 3224 -81, 4145 -100, 045 -181, 057 -96, 6738
-70, 295 -69, 646 -54, 5461 -73, 0876 -151, 77 -68, 8975
-44, 161 -44, 382 -29, 1841 -47, 5607 -123, 884 -42, 5773
-93, 4171 -94, 4707 -79, 2657 -97, 4047 -171, 344 -91, 6531
-50, 4332 -52, 2824 -37, 158 -54, 9893 -126, 523 -48, 495
-75, 6793 -78, 2876 -63, 3283 -80, 7846 -149, 895 -73, 573
-105, 655 -108, 987 -94, 2735 -111, 291 -177, 962 -103, 387
-98, 3614 -102, 38 -87, 9909 -104, 507 -168, 728 -95, 9373
-99, 6675 -104, 339 -90, 3477 -106, 304 -168, 064 -97, 0936
-82, 0636 -87, 3525 -73, 8308 -89, 1709 -148, 463 -79, 3461
-62, 5597 -68, 4325 -55, 4476 -70, 1184 -126, 937 -59, 7048
-104, 846 -111, 269 -98, 8851 -112, 836 -167, 177 -101, 86
-82, 7718 -89, 7132 -77, 9904 -91, 174 -143, 035 -79, 6607
-107, 218 -114, 645 -103, 641 -116, 012 -165, 393 -103, 988
-155, 064 -162, 946 -152, 713 -164, 23 -211, 132 -151, 721
-132, 9 -141, 205 -131, 795 -142, 418 -186, 842 -129, 451
-151, 406 -160, 104 -151, 563 -161, 257 -203, 206 -147, 857
-116, 342 -125, 404 -117, 775 -126, 505 -165, 985 -112, 699
-84, 5383 -93, 9338 -87, 2576 -94, 9933 -132, 008 -80, 808
-72, 5244 -82, 2255 -76, 538 -83, 2515 -117, 808 -68, 7129
-58, 5605 -68, 5392 -63, 8734 -69, 5396 -101, 645 -54, 6742
-82, 3366 -92, 5654 -88, 9509 -93, 5476 -123, 209 -78, 3817
-116, 873 -127, 325 -124, 788 -128, 296 -155, 521 -112, 856
-36, 8787 -47, 5275 -46, 091 -48, 4933 -73, 2927 -32, 806
-44, 3348 -55, 1544 -54, 8378 -56, 121 -78, 5038 -40, 2127
-46, 6809 -57, 646 -58, 4653 -58, 6186 -78, 595 -42, 5158
-87, 217 -98, 3026 -100, 271 -99, 286 -116, 867 -83, 0153
-59, 863 -71, 0449 -74, 1709 -72, 0433 -87, 2397 -55, 6313
-51, 8491 -63, 1032 -67, 3934 -64, 1205 -76, 9441 -47, 5938
40, 4148 29, 112 23, 6549 28, 0724 17, 6095 44, 6873
76, 8687 65, 5403 58, 9167 64, 4754 56, 3607 81, 1519
122, 483 111, 151 103, 365 110, 058 104, 279 126, 77
128, 917 117, 604 108, 663 116, 482 113, 025 133, 201
132, 95 121, 679 111, 592 120, 525 119, 377 137, 226
124, 434 113, 225 102, 007 112, 038 113, 185 128, 695
37, 0683 25, 9424 13, 6099 24, 7209 28, 1495 41, 3067
45, 1222 34, 1002 20, 6733 32, 844 38, 5397 49, 332
90, 2462 79, 3482 64, 8503 78, 0569 86, 0054 94, 4206
107, 25 96, 4961 80, 9538 95, 1697 105, 356 111, 383
124, 564 113, 973 97, 4166 112, 612 125, 022 128, 648
121, 118 110, 71 93, 1715 109, 315 123, 933 125, 147
156, 392 146, 185 127, 702 144, 757 161, 569 160, 359
196, 106 186, 119 166, 729 184, 659 203, 649 200, 004
220, 9 211, 151 190, 898 209, 66 230, 813 224, 723
124, 824 115, 331 94, 2603 113, 811 137, 111 128, 564
214, 398 205, 179 183, 339 203, 632 229, 064 218, 05
252, 801 243, 873 221, 317 242, 302 269, 85 256, 358
286, 335 277, 715 254, 497 276, 122 305, 769 289, 79
304, 209 295, 913 272, 093 294, 301 326, 033 307, 554
283, 973 276, 018 251, 656 274, 389 308, 189 287, 202
297, 127 289, 529 264, 69 287, 886 323, 739 300, 233
313, 011 305, 786 280, 537 304, 133 342, 022 315, 988
314, 755 307, 918 282, 331 306, 258 346, 168 317, 595
288, 139 281, 706 255, 855 280, 043 321, 957 290, 835
308, 593 302, 579 276, 54 300, 916 344, 819 311, 139
171, 837 166, 257 140, 111 164, 599 210, 474 174, 226
101, 441 96, 3097 70, 1396 94, 6601 142, 491 103, 665
134, 275 129, 607 103, 499 127, 97 177, 74 136, 328
131, 838 127, 648 101, 692 126, 029 177, 723 133, 714
93, 5124 89, 8131 64, 1013 88, 2156 141, 817 95, 2024
-58, 7637 -61, 9579 -87, 3298 -63, 5289 -8, 03605 -57, 2659
-99, 0798 -101, 755 -126, 689 -103, 295 -45, 927 -97, 7812
-28, 8658 -31, 0094 -55, 4027 -32, 5129 26, 7142 -27, 7736
-74, 1619 -75, 7602 -99, 5087 -77, 2225 -16, 1525 -73, 283
-190, 178 -191, 218 -214, 214 -192, 634 -129, 737 -189, 52
-317, 134 -317, 603 -339, 735 -318, 968 -254, 26 -316, 703
-254, 19 -254, 076 -275, 231 -255, 383 -188, 881 -253, 994
-283, 076 -282, 366 -302, 426 -283, 611 -215, 33 -283, 122
-386, 342 -385, 023 -403, 87 -386, 201 -316, 157 -386, 637
-387, 168 -385, 229 -402, 738 -386, 334 -314, 543 -387, 719
-320, 714 -318, 143 -334, 189 -319, 169 -245, 646 -321, 529
-268, 441 -265, 225 -279, 678 -266, 166 -190, 929 -269, 525
-264, 107 -260, 235 -272, 964 -261, 086 -184, 149 -265, 469
-180, 513 -175, 974 -186, 844 -176, 729 -98, 1083 -182, 161
-187, 609 -182, 392 -191, 264 -183, 045 -102, 756 -189, 549
-150, 605 -144, 699 -151, 432 -145, 244 -63, 302 -152, 845
-106, 331 -99, 7244 -104, 175 -100, 156 -16, 5767 -108, 878
-72, 9371 -65, 6192 -67, 6394 -65, 931 19, 27 -75, 7984
17, 9269 25, 9667 26, 5265 25, 7807 112, 588 14, 7439
22, 8308 31, 6031 34, 8961 31, 5489 119, 947 19, 3187
37, 7947 47, 3099 53, 4923 47, 3936 137, 368 33, 9462
89, 1186 99, 387 108, 618 99, 6147 191, 15 84, 9262
83, 9825 95, 0142 107, 456 95, 3921 188, 473 79, 4389
50, 8765 62, 6815 78, 4984 63, 2157 157, 827 45, 974
26, 1104 38, 6986 58, 0593 39, 3953 135, 522 20, 8418
53, 2843 66, 6654 89, 7409 67, 5308 165, 158 47, 642
12, 3582 26, 5419 53, 5062 27, 5823 126, 696 6, 33469
21, 4221 36, 418 67, 4481 37, 6394 138, 224 15, 0099
-4, 93394 10, 8834 46, 1593 12, 2922 114, 334 -11, 7425
0, 719984 17, 3681 57, 0728 18, 9704 122, 455 -6, 4924
77, 2839 94, 772 139, 091 96, 5741 201, 486 69, 6601
15, 9478 34, 2849 83, 408 36, 2931 142, 619 7, 90498
28, 7717 47, 9668 102, 085 50, 1872 157, 912 20, 3022
29, 3157 49, 3775 108, 687 51, 8164 160, 926 20, 4119
16, 49 37, 43 102, 12 40, 09 150, 57 7, 14
12, 96392 34, 79 105, 07 37, 68 149, 52 3, 17
-10, 94216 11, 77 87, 85 14, 9 128, 08 -21, 2
-42, 87824 -19, 26 62, 82 -15, 89 98, 62 -53, 6
-94, 72432 -70, 2 18, 09 -66, 58 49, 25 -105, 92
           

 


Приложение 10

Построение логистической модели в зависимости продолжительности ретроспективного периода.

1) N=110

 

Multiple Regression - (ConsGOODS) (num> 14)

Dependent variable: (ConsGOODS)

Independent variables:

1.09^(0.03*num)

Selection variable: num> 14

 

    Standard T  
Parameter Estimate Error Statistic P-Value
1.09^(0.03*num) 830, 49 12, 0228 69, 0765 0, 0000

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 10146E8 1, 10146E8 4771, 56 0, 0000
Residual 2, 51613E6 23083, 8    
Total 1, 12662E8      

 

R-squared = 97, 7667 percent

R-squared (adjusted for d.f.) = 97, 7667 percent

Standard Error of Est. = 151, 933

Mean absolute error = 119, 51

Durbin-Watson statistic = 0, 0988071

Lag 1 residual autocorrelation = 0, 94905

 

 

(ConsGOODS) = 830, 49*1.09^(0.03*num)

 

Regression Results for (ConsGOODS)

  Fitted Stnd. Error Lower 95, 0% Upper 95, 0%
Row Value CL for Forecast CL for Forecast CL for Forecast
1147, 32 152, 839 844, 396 1450, 24
1150, 29 152, 843 847, 357 1453, 22
1153, 27 152, 848 850, 325 1456, 21
1156, 25 152, 853 853, 301 1459, 2
1159, 24 152, 857 856, 285 1462, 2
1162, 24 152, 862 859, 276 1465, 21

 

2) N=100

 

Multiple Regression - (ConsGOODS) (num> 24)

Dependent variable: (ConsGOODS)

Independent variables:

1.09^(0.03*num)

Selection variable: num> 24

 

    Standard T  
Parameter Estimate Error Statistic P-Value
1.09^(0.03*num) 828, 155 12, 8814 64, 2906 0, 0000

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 0194E8 1, 0194E8 4133, 28 0, 0000
Residual 2, 44167E6 24663, 3    
Total 1, 04382E8      

 

R-squared = 97, 6608 percent

R-squared (adjusted for d.f.) = 97, 6608 percent

Standard Error of Est. = 157, 046

Mean absolute error = 124, 028

Durbin-Watson statistic = 0, 0918624

Lag 1 residual autocorrelation = 0, 953521

 

(ConsGOODS) = 828, 155*1.09^(0.03*num)

 

 

Regression Results for (ConsGOODS)

  Fitted Stnd. Error Lower 95, 0% Upper 95, 0%
Row Value CL for Forecast CL for Forecast CL for Forecast
1144, 09 158, 051 830, 484 1457, 7
1147, 05 158, 056 833, 436 1460, 67
1150, 02 158, 061 836, 395 1463, 65
1153, 0 158, 066 839, 361 1466, 64
1155, 98 158, 072 842, 336 1469, 63
1158, 98 158, 077 845, 318 1472, 64

 

3) N=90

 

Multiple Regression - (ConsGOODS) (num> 34)

Dependent variable: (ConsGOODS)

Independent variables:

1.09^(0.03*num)

Selection variable: num> 34

 

    Standard T  
Parameter Estimate Error Statistic P-Value
1.09^(0.03*num) 833, 784 13, 9784 59, 648 0, 0000

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 9, 52324E7 9, 52324E7 3557, 88 0, 0000
Residual 2, 38223E6 26766, 6    
Total 9, 76146E7      

 

R-squared = 97, 5596 percent

R-squared (adjusted for d.f.) = 97, 5596 percent

Standard Error of Est. = 163, 605

Mean absolute error = 129, 731

Durbin-Watson statistic = 0, 0911199

Lag 1 residual autocorrelation = 0, 953839

 

(ConsGOODS) = 833, 784*1.09^(0.03*num)

 


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