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Bảng tra thống kê Durbin-Watson

Kiểm định thống kê Durbin-Watson là một loại kiểm định được sử dụng phổ biến để phát hiện vấn đề tự tương quan trong mô hình tự hồi quy bậc 1. Sau khi chạy hồi quy, có thể sử dụng câu lệnh dwstat để có được giá trị thống kê Durbin-Watson tính toán (dw). Kết quả của dw sẽ được so sánh với các giá trị dL, dU tra bảng (ở mức ý nghĩa alpha và số biến giải thích trong mô hình). Các giá trị này được tổng hợp ở bảng bên dưới, cụ thể như sau:

Chúng tôi đã tổng hợp ra 2 bộ bảng tra theo Savin & White (1977) và Farebrother (1980). Bảng A.1 và A.2 được trình bày theo Savin & White (1977) cho phép tra với cở mẫu từ 6 đến 200 cùng với hệ số cắt và 1 đến 20 biến giải thích trong mô hình. Bảng A.3; A.4 tra theo Farebrother (1980) cho phép tra với cở mẫu từ 2 đến 200 và 0 đến 21 biến giải thích trong mô hình (không có hằng số cắt) với sự tự tương quan dương và Bảng A.5; A.6 cho phép tra với sự tự tương quan âm.

Hướng dẫn cách tra dL, dU, d ở mức ý nghĩa anpha và số biến giải thích k’

Bước 1: Chọn một mức ý nghĩa cho kiểm định và tra bảng các giá trị tới hạn dL và dU tại các bảng từ A.1 đến A.6 trong Ramanathan, với n là số quan sát, k’ là số biến bên vế phải của phương trình hồi quy (không bao gồm hằng số). Trong ví dụ trên, giả sử mức ý nghĩa 5%, với n = 37, k’ = 2 thì các giá trị tới hạn tra bảng là: dL = 1.36, dU = 1.59.

Bước 2: So sánh giá trị tính toán của kiểm định thống kê Durbin-Watson với giá trị tra bảng.

  • Nếu d < dL thì bác bỏ giả thuyết không và kết luận rằng có sự tự tương quan bậc 1. Nếu d > dU thì chấp nhận giả thuyết không và kết luận rằng không có sự tự tương quan bậc 1.
  • Nếu dL < d < dU chưa thể kết luận.

Sự tự tương quan theo Durbin - Watson

  • Intercept 1%
  • Intercept 5%
  • No intercept 1%
  • No intercept 5%
  • No intercept 95%
  • No intercept 99%

Bảng A.1: Mô hình với hệ số cắt theo Savin và White (1977)

  • Thống kê DW ở mức ý nghĩa 1% của các giá trị dL và dU
  • *k’ là số biến giải thích (không bao gồm hệ số cắt)
k’*=1 k’=2 k’=3 k’=4 k’=5 k’=6 k’=7 k’=8 k’=9 k’=10
n dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU
6 0.390 1.142 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
7 0.435 1.036 0.294 1.676 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
8 0.497 1.003 0.345 1.489 0.229 2.102 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
9 0.554 0.998 0.408 1.389 0.279 1.875 0.183 2.433 —– —– —– —– —– —– —– —– —– —– —– —–
10 0.604 1.001 0.466 1.333 0.340 1.733 0.230 2.193 0.150 2.690 —– —– —– —– —– —– —– —– —– —–
11 0.653 1.010 0.519 1.297 0.396 1.640 0.286 2.030 0.193 2.453 0.124 2.892 —– —– —– —– —– —– —– —–
12 0.697 1.023 0.569 1.274 0.449 1.575 0.339 1.913 0.244 2.280 0.164 2.665 0.105 3.053 —– —– —– —– —– —–
13 0.738 1.038 0.616 1.261 0.499 1.526 0.391 1.826 0.294 2.150 0.211 2.490 0.140 2.838 0.090 3.182 —– —– —– —–
14 0.776 1.054 0.660 1.254 0.547 1.490 0.441 1.757 0.343 2.049 0.257 2.354 0.183 2.667 0.122 2.981 0.078 3.287 —– —–
15 0.811 1.070 0.700 1.252 0.591 1.465 0.487 1.705 0.390 1.967 0.303 2.244 0.226 2.530 0.161 2.817 0.107 3.101 0.068 3.374
16 0.844 1.086 0.738 1.253 0.633 1.447 0.532 1.664 0.437 1.901 0.349 2.153 0.269 2.416 0.200 2.681 0.142 2.944 0.094 3.201
17 0.873 1.102 0.773 1.255 0.672 1.432 0.574 1.631 0.481 1.847 0.393 2.078 0.313 2.319 0.241 2.566 0.179 2.811 0.127 3.053
18 0.902 1.118 0.805 1.259 0.708 1.422 0.614 1.604 0.522 1.803 0.435 2.015 0.355 2.238 0.282 2.467 0.216 2.697 0.160 2.925
19 0.928 1.133 0.835 1.264 0.742 1.416 0.650 1.583 0.561 1.767 0.476 1.963 0.396 2.169 0.322 2.381 0.255 2.597 0.196 2.813
20 0.952 1.147 0.862 1.270 0.774 1.410 0.684 1.567 0.598 1.736 0.515 1.918 0.436 2.110 0.362 2.308 0.294 2.510 0.232 2.174
21 0.975 1.161 0.889 1.276 0.803 1.408 0.718 1.554 0.634 1.712 0.552 1.881 0.474 2.059 0.400 2.244 0.331 2.434 0.268 2.625
22 0.997 1.174 0.915 1.284 0.832 1.407 0.748 1.543 0.666 1.691 0.587 1.849 0.510 2.015 0.437 2.188 0.368 2.367 0.304 2.548
23 1.017 1.186 0.938 1.290 0.858 1.407 0.777 1.535 0.699 1.674 0.620 1.821 0.545 1.977 0.473 2.140 0.404 2.308 0.340 2.479
24 1.037 1.199 0.959 1.298 0.881 1.407 0.805 1.527 0.728 1.659 0.652 1.797 0.578 1.944 0.507 2.097 0.439 2.255 0.375 2.417
25 1.055 1.210 0.981 1.305 0.906 1.408 0.832 1.521 0.756 1.645 0.682 1.776 0.610 1.915 0.540 2.059 0.473 2.209 0.409 2.362
26 1.072 1.222 1.000 1.311 0.928 1.410 0.855 1.517 0.782 1.635 0.711 1.759 0.640 1.889 0.572 2.026 0.505 2.168 0.441 2.313
27 1.088 1.232 1.019 1.318 0.948 1.413 0.878 1.514 0.808 1.625 0.738 1.743 0.669 1.867 0.602 1.997 0.536 2.131 0.473 2.269
28 1.104 1.244 1.036 1.325 0.969 1.414 0.901 1.512 0.832 1.618 0.764 1.729 0.696 1.847 0.630 1.970 0.566 2.098 0.504 2.229
29 1.119 1.254 1.053 1.332 0.988 1.418 0.921 1.511 0.855 1.611 0.788 1.718 0.723 1.830 0.658 1.947 0.595 2.068 0.533 2.193
30 1.134 1.264 1.070 1.339 1.006 1.421 0.941 1.510 0.877 1.606 0.812 1.707 0.748 1.814 0.684 1.925 0.622 2.041 0.562 2.160
31 1.147 1.274 1.085 1.345 1.022 1.425 0.960 1.509 0.897 1.601 0.834 1.698 0.772 1.800 0.710 1.906 0.649 2.017 0.589 2.131
32 1.160 1.283 1.100 1.351 1.039 1.428 0.978 1.509 0.917 1.597 0.856 1.690 0.794 1.788 0.734 1.889 0.674 1.995 0.615 2.104
33 1.171 1.291 1.114 1.358 1.055 1.432 0.995 1.510 0.935 1.594 0.876 1.683 0.816 1.776 0.757 1.874 0.698 1.975 0.641 2.080
34 1.184 1.298 1.128 1.364 1.070 1.436 1.012 1.511 0.954 1.591 0.896 1.677 0.837 1.766 0.779 1.860 0.722 1.957 0.665 2.057
35 1.195 1.307 1.141 1.370 1.085 1.439 1.028 1.512 0.971 1.589 0.914 1.671 0.857 1.757 0.800 1.847 0.744 1.940 0.689 2.037
36 1.205 1.315 1.153 1.376 1.098 1.442 1.043 1.513 0.987 1.587 0.932 1.666 0.877 1.749 0.821 1.836 0.766 1.925 0.711 2.018
37 1.217 1.322 1.164 1.383 1.112 1.446 1.058 1.514 1.004 1.585 0.950 1.662 0.895 1.742 0.841 1.825 0.787 1.911 0.733 2.001
38 1.227 1.330 1.176 1.388 1.124 1.449 1.072 1.515 1.019 1.584 0.966 1.658 0.913 1.735 0.860 1.816 0.807 1.899 0.754 1.985
39 1.237 1.337 1.187 1.392 1.137 1.452 1.085 1.517 1.033 1.583 0.982 1.655 0.930 1.729 0.878 1.807 0.826 1.887 0.774 1.970
40 1.246 1.344 1.197 1.398 1.149 1.456 1.098 1.518 1.047 1.583 0.997 1.652 0.946 1.724 0.895 1.799 0.844 1.876 0.749 1.956
45 1.288 1.376 1.245 1.424 1.201 1.474 1.156 1.528 1.111 1.583 1.065 1.643 1.019 1.704 0.974 1.768 0.927 1.834 0.881 1.902
50 1.324 1.403 1.285 1.445 1.245 1.491 1.206 1.537 1.164 1.587 1.123 1.639 1.081 1.692 1.039 1.748 0.997 1.805 0.955 1.864
55 1.356 1.428 1.320 1.466 1.284 1.505 1.246 1.548 1.209 1.592 1.172 1.638 1.134 1.685 1.095 1.734 1.057 1.785 1.018 1.837
60 1.382 1.449 1.351 1.484 1.317 1.520 1.283 1.559 1.248 1.598 1.214 1.639 1.179 1.682 1.144 1.726 1.108 1.771 1.072 1.817
65 1.407 1.467 1.377 1.500 1.346 1.534 1.314 1.568 1.283 1.604 1.251 1.642 1.218 1.680 1.186 1.720 1.153 1.761 1.120 1.802
70 1.429 1.485 1.400 1.514 1.372 1.546 1.343 1.577 1.313 1.611 1.283 1.645 1.253 1.680 1.223 1.716 1.192 1.754 1.162 1.792
75 1.448 1.501 1.422 1.529 1.395 1.557 1.368 1.586 1.340 1.617 1.313 1.649 1.284 1.682 1.256 1.714 1.227 1.748 1.199 1.783
80 1.465 1.514 1.440 1.541 1.416 1.568 1.390 1.595 1.364 1.624 1.338 1.653 1.312 1.683 1.285 1.714 1.259 1.745 1.232 1.777
85 1.481 1.529 1.458 1.553 1.434 1.577 1.411 1.603 1.386 1.630 1.362 1.657 1.337 1.685 1.312 1.714 1.287 1.743 1.262 1.773
90 1.496 1.541 1.474 1.563 1.452 1.587 1.429 1.611 1.406 1.636 1.383 1.661 1.360 1.687 1.336 1.714 1.312 1.741 1.288 1.769
95 1.510 1.552 1.489 1.573 1.468 1.596 1.446 1.618 1.425 1.641 1.403 1.666 1.381 1.690 1.358 1.715 1.336 1.741 1.313 1.767
100 1.522 1.562 1.502 1.582 1.482 1.604 1.461 1.625 1.441 1.647 1.421 1.670 1.400 1.693 1.378 1.717 1.357 1.741 1.335 1.765
150 1.611 1.637 1.598 1.651 1.584 1.665 1.571 1.679 1.557 1.693 1.543 1.708 1.530 1.722 1.515 1.737 1.501 1.752 1.486 1.767
200 1.664 1.684 1.653 1.693 1.643 1.704 1.633 1.715 1.623 1.725 1.613 1.735 1.603 1.746 1.592 1.757 1.582 1.768 1.571 1.779
16 0.060 3.446 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
17 0.084 3.286 0.053 3.506 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
18 0.113 3.146 0.075 3.358 0.047 3.557 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
19 0.145 3.023 0.102 3.227 0.067 3.420 0.043 3.601 —– —– —– —– —– —– —– —– —– —– —– —–
20 0.178 2.914 0.131 3.109 0.092 3.297 0.061 3.474 0.038 3.639 —– —– —– —– —– —– —– —– —– —–
21 0.212 2.817 0.162 3.004 0.119 3.185 0.084 3.358 0.055 3.521 0.035 3.671 —– —– —– —– —– —– —– —–
22 0.246 2.729 0.194 2.909 0.148 3.084 0.109 3.252 0.077 3.412 0.050 3.562 0.032 3.700 —– —– —– —– —– —–
23 0.281 2.651 0.227 2.822 0.178 2.991 0.136 3.155 0.100 3.311 0.070 3.459 0.046 3.597 0.029 3.725 —– —– —– —–
24 0.315 2.580 0.260 2.744 0.209 2.906 0.165 3.065 0.125 3.218 0.092 3.363 0.065 3.501 0.043 3.629 0.027 3.747 —– —–
25 0.348 2.517 0.292 2.674 0.240 2.829 0.194 2.982 0.152 3.131 0.116 3.274 0.085 3.410 0.060 3.538 0.039 3.657 0.025 3.766
26 0.381 2.460 0.324 2.610 0.272 2.758 0.224 2.906 0.180 3.050 0.141 3.191 0.107 3.325 0.079 3.452 0.055 3.572 0.036 3.682
27 0.413 2.409 0.356 2.552 0.303 2.694 0.253 2.836 0.208 2.976 0.167 3.113 0.131 3.245 0.100 3.371 0.073 3.490 0.051 3.602
28 0.444 2.363 0.387 2.499 0.333 2.635 0.283 2.772 0.237 2.907 0.194 3.040 0.156 3.169 0.122 3.294 0.093 3.412 0.068 3.524
29 0.474 2.321 0.417 2.451 0.363 2.582 0.313 2.713 0.266 2.843 0.222 2.972 0.182 3.098 0.146 3.220 0.114 3.338 0.087 3.450
30 0.503 2.283 0.447 2.407 0.393 2.533 0.342 2.659 0.294 2.785 0.249 2.909 0.208 3.032 0.171 3.152 0.137 3.267 0.107 3.379
31 0.531 2.248 0.475 2.367 0.422 2.487 0.371 2.609 0.322 2.730 0.277 2.851 0.234 2.970 0.193 3.087 0.160 3.201 0.128 3.311
32 0.558 2.216 0.503 2.330 0.450 2.446 0.399 2.563 0.350 2.680 0.304 2.797 0.261 2.912 0.221 3.026 0.184 3.137 0.151 3.246
33 0.585 2.187 0.530 2.296 0.477 2.408 0.426 2.520 0.377 2.633 0.331 2.746 0.287 2.858 0.246 2.969 0.209 3.078 0.174 3.184
34 0.610 2.160 0.556 2.266 0.503 2.373 0.452 2.481 0.404 2.590 0.357 2.699 0.313 2.808 0.272 2.915 0.233 3.022 0.197 3.126
35 0.634 2.136 0.581 2.237 0.529 2.340 0.478 2.444 0.430 2.550 0.383 2.655 0.339 2.761 0.297 2.865 0.257 2.969 0.221 3.071
36 0.658 2.113 0.605 2.210 0.554 2.310 0.504 2.410 0.455 2.512 0.409 2.614 0.364 2.717 0.322 2.818 0.282 2.919 0.244 3.019
37 0.680 2.092 0.628 2.186 0.578 2.282 0.528 2.379 0.480 2.477 0.434 2.576 0.389 2.675 0.347 2.774 0.306 2.872 0.268 2.969
38 0.702 2.073 0.651 2.164 0.601 2.256 0.552 2.350 0.504 2.445 0.458 2.540 0.414 2.637 0.371 2.733 0.330 2.828 0.291 2.923
39 0.723 2.055 0.673 2.143 0.623 2.232 0.575 2.323 0.528 2.414 0.482 2.507 0.438 2.600 0.395 2.694 0.354 2.787 0.315 2.879
40 0.744 2.039 0.694 2.123 0.645 2.210 0.597 2.297 0.551 2.386 0.505 2.476 0.461 2.566 0.418 2.657 0.377 2.748 0.338 2.838
45 0.835 1.972 0.790 2.044 0.744 2.118 0.700 2.193 0.655 2.269 0.612 2.346 0.570 2.424 0.528 2.503 0.488 2.582 0.448 2.661
50 0.913 1.925 0.871 1.987 0.829 2.051 0.787 2.116 0.746 2.182 0.705 2.250 0.665 2.318 0.625 2.387 0.586 2.456 0.548 2.526
55 0.979 1.891 0.940 1.945 0.902 2.002 0.863 2.059 0.825 2.117 0.786 2.176 0.748 2.237 0.711 2.298 0.674 2.359 0.637 2.421
60 1.037 1.865 1.001 1.914 0.965 1.964 0.929 2.015 0.893 2.067 0.857 2.120 0.822 2.173 0.786 2.227 0.751 2.283 0.716 2.338
65 1.087 1.845 1.053 1.889 1.020 1.934 0.986 1.980 0.953 2.027 0.919 2.075 0.886 2.123 0.852 2.172 0.819 2.221 0.789 2.272
70 1.131 1.831 1.099 1.870 1.068 1.911 1.037 1.953 1.005 1.995 0.974 2.038 0.943 2.082 0.911 2.127 0.880 2.172 0.849 2.217
75 1.170 1.819 1.141 1.856 1.111 1.893 1.082 1.931 1.052 1.970 1.023 2.009 0.993 2.049 0.964 2.090 0.934 2.131 0.905 2.172
80 1.205 1.810 1.177 1.844 1.150 1.878 1.122 1.913 1.094 1.949 1.066 1.984 1.039 2.022 1.011 2.059 0.983 2.097 0.955 2.135
85 1.236 1.803 1.210 1.834 1.184 1.866 1.158 1.898 1.132 1.931 1.106 1.965 1.080 1.999 1.053 2.033 1.027 2.068 1.000 2.104
90 1.264 1.798 1.240 1.827 1.215 1.856 1.191 1.886 1.166 1.917 1.141 1.948 1.116 1.979 1.091 2.012 1.066 2.044 1.041 2.077
95 1.290 1.793 1.267 1.821 1.244 1.848 1.221 1.876 1.197 1.905 1.174 1.943 1.150 1.963 1.126 1.993 1.102 2.023 1.079 2.054
100 1.314 1.790 1.292 1.816 1.270 1.841 1.248 1.868 1.225 1.895 1.203 1.922 1.181 1.949 1.158 1.977 1.136 2.006 1.113 2.034
150 1.473 1.783 1.458 1.799 1.444 1.814 1.429 1.830 1.414 1.847 1.400 1.863 1.385 1.880 1.370 1.897 1.355 1.913 1.340 1.931
200 1.561 1.791 1.550 1.801 1.539 1.813 1.528 1.824 1.518 1.836 1.507 1.847 1.495 1.860 1.484 1.871 1.474 1.883 1.462 1.896

Bảng A.2: Mô hình với hệ số cắt theo Savin và White (1977)

  • Thống kê DW ở mức ý nghĩa 5% của các giá trị dL và dU
  • *k’ là số biến giải thích (không bao gồm hệ số cắt)
k’*=1 k’=2 k’=3 k’=4 k’=5 k’=6 k’=7 k’=8 k’=9 k’=10
n dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU dL dU
6 0.610 1.400 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
7 0.700 1.356 0.467 1.896 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
8 0.763 1.332 0.559 1.777 0.367 2.287 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
9 0.824 1.320 0.629 1.699 0.455 2.128 0.296 2.588 —– —– —– —– —– —– —– —– —– —– —– —–
10 0.879 1.320 0.697 1.641 0.525 2.016 0.376 2.414 0.243 2.822 —– —– —– —– —– —– —– —– —– —–
11 0.927 1.324 0.758 1.604 0.595 1.928 0.444 2.283 0.315 2.645 0.203 3.004 —– —– —– —– —– —– —– —–
12 0.971 1.331 0.812 1.579 0.658 1.864 0.512 2.177 0.380 2.506 0.268 2.832 0.171 3.149 —– —– —– —– —– —–
13 1.010 1.340 0.861 1.562 0.715 1.816 0.574 2.094 0.444 2.390 0.328 2.692 0.230 2.985 0.147 3.266 —– —– —– —–
14 1.045 1.350 0.905 1.551 0.767 1.779 0.632 2.030 0.505 2.296 0.389 2.572 0.286 2.848 0.200 3.111 0.127 3.360 —– —–
15 1.077 1.361 0.946 1.543 0.814 1.750 0.685 1.977 0.562 2.220 0.447 2.471 0.343 2.727 0.251 2.979 0.175 3.216 0.111 3.438
16 1.106 1.371 0.982 1.539 0.857 1.728 0.734 1.935 0.615 2.157 0.502 2.388 0.398 2.624 0.304 2.860 0.222 3.090 0.155 3.304
17 1.133 1.381 1.015 1.536 0.897 1.710 0.779 1.900 0.664 2.104 0.554 2.318 0.451 2.537 0.356 2.757 0.272 2.975 0.198 3.184
18 1.158 1.391 1.046 1.535 0.933 1.696 0.820 1.872 0.710 2.060 0.603 2.258 0.502 2.461 0.407 2.668 0.321 2.873 0.244 3.073
19 1.180 1.401 1.074 1.536 0.967 1.685 0.859 1.848 0.752 2.023 0.649 2.206 0.549 2.396 0.456 2.589 0.369 2.783 0.290 2.974
20 1.201 1.411 1.100 1.537 0.998 1.676 0.894 1.828 0.792 1.991 0.691 2.162 0.595 2.339 0.502 2.521 0.416 2.704 0.336 2.885
21 1.221 1.420 1.125 1.538 1.026 1.669 0.927 1.812 0.829 1.964 0.731 2.124 0.637 2.290 0.546 2.461 0.461 2.633 0.380 2.806
22 1.239 1.429 1.147 1.541 1.053 1.664 0.958 1.797 0.863 1.940 0.769 2.090 0.677 2.246 0.588 2.407 0.504 2.571 0.424 2.735
23 1.257 1.437 1.168 1.543 1.078 1.660 0.986 1.785 0.895 1.920 0.804 2.061 0.715 2.208 0.628 2.360 0.545 2.514 0.465 2.670
24 1.273 1.446 1.188 1.546 1.101 1.656 1.013 1.775 0.925 1.902 0.837 2.035 0.750 2.174 0.666 2.318 0.584 2.464 0.506 2.613
25 1.288 1.454 1.206 1.550 1.123 1.654 1.038 1.767 0.953 1.886 0.868 2.013 0.784 2.144 0.702 2.280 0.621 2.419 0.544 2.560
26 1.302 1.461 1.224 1.553 1.143 1.652 1.062 1.759 0.979 1.873 0.897 1.992 0.816 2.117 0.735 2.246 0.657 2.379 0.581 2.513
27 1.316 1.469 1.240 1.556 1.162 1.651 1.084 1.753 1.004 1.861 0.925 1.974 0.845 2.093 0.767 2.216 0.691 2.342 0.616 2.470
28 1.328 1.476 1.255 1.560 1.181 1.650 1.104 1.747 1.028 1.850 0.951 1.959 0.874 2.071 0.798 2.188 0.723 2.309 0.649 2.431
29 1.341 1.483 1.270 1.563 1.198 1.650 1.124 1.743 1.050 1.841 0.975 1.944 0.900 2.052 0.826 2.164 0.753 2.278 0.681 2.396
30 1.352 1.489 1.284 1.567 1.214 1.650 1.143 1.739 1.071 1.833 0.998 1.931 0.926 2.034 0.854 2.141 0.782 2.251 0.712 2.363
31 1.363 1.496 1.297 1.570 1.229 1.650 1.160 1.735 1.090 1.825 1.020 1.920 0.950 2.018 0.879 2.120 0.810 2.226 0.741 2.333
32 1.373 1.502 1.309 1.574 1.244 1.650 1.177 1.732 1.109 1.819 1.041 1.909 0.972 2.004 0.904 2.102 0.836 2.203 0.769 2.306
33 1.383 1.508 1.321 1.577 1.258 1.651 1.193 1.730 1.127 1.813 1.061 1.900 0.994 1.991 0.927 2.085 0.861 2.181 0.796 2.281
34 1.393 1.514 1.333 1.580 1.271 1.652 1.208 1.728 1.144 1.808 1.079 1.891 1.015 1.978 0.950 2.069 0.885 2.162 0.821 2.257
35 1.402 1.519 1.343 1.584 1.283 1.653 1.222 1.726 1.160 1.803 1.097 1.884 1.034 1.967 0.971 2.054 0.908 2.144 0.845 2.236
36 1.411 1.525 1.354 1.587 1.295 1.654 1.236 1.724 1.175 1.799 1.114 1.876 1.053 1.957 0.991 2.041 0.930 2.127 0.868 2.216
37 1.419 1.530 1.364 1.590 1.307 1.655 1.249 1.723 1.190 1.795 1.131 1.870 1.071 1.948 1.011 2.029 0.951 2.112 0.891 2.197
38 1.427 1.535 1.373 1.594 1.318 1.656 1.261 1.722 1.204 1.792 1.146 1.864 1.088 1.939 1.029 2.017 0.970 2.098 0.912 2.180
39 1.435 1.540 1.382 1.597 1.328 1.658 1.273 1.722 1.218 1.789 1.161 1.859 1.104 1.932 1.047 2.007 0.990 2.085 0.932 2.164
40 1.442 1.544 1.391 1.600 1.338 1.659 1.285 1.721 1.230 1.786 1.175 1.854 1.120 1.924 1.064 1.997 1.008 2.072 0.952 2.149
45 1.475 1.566 1.430 1.615 1.383 1.666 1.336 1.720 1.287 1.776 1.238 1.835 1.189 1.895 1.139 1.958 1.089 2.022 1.038 2.088
50 1.503 1.585 1.462 1.628 1.421 1.674 1.378 1.721 1.335 1.771 1.291 1.822 1.246 1.875 1.201 1.930 1.156 1.986 1.110 2.044
55 1.528 1.601 1.490 1.641 1.452 1.681 1.414 1.724 1.374 1.768 1.334 1.814 1.294 1.861 1.253 1.909 1.212 1.959 1.170 2.010
60 1.549 1.616 1.514 1.652 1.480 1.689 1.444 1.727 1.408 1.767 1.372 1.808 1.335 1.850 1.298 1.894 1.260 1.939 1.222 1.984
65 1.567 1.629 1.536 1.662 1.503 1.696 1.471 1.731 1.438 1.767 1.404 1.805 1.370 1.843 1.336 1.882 1.301 1.923 1.266 1.964
70 1.583 1.641 1.554 1.672 1.525 1.703 1.494 1.735 1.464 1.768 1.433 1.802 1.401 1.838 1.369 1.874 1.337 1.910 1.305 1.948
75 1.598 1.652 1.571 1.680 1.543 1.709 1.515 1.739 1.487 1.770 1.458 1.801 1.428 1.834 1.399 1.867 1.369 1.901 1.339 1.935
80 1.611 1.662 1.586 1.688 1.560 1.715 1.534 1.743 1.507 1.772 1.480 1.801 1.453 1.831 1.425 1.861 1.397 1.893 1.369 1.925
85 1.624 1.671 1.600 1.696 1.575 1.721 1.550 1.747 1.525 1.774 1.500 1.801 1.474 1.829 1.448 1.857 1.422 1.886 1.396 1.916
90 1.635 1.679 1.612 1.703 1.589 1.726 1.566 1.751 1.542 1.776 1.518 1.801 1.494 1.827 1.469 1.854 1.445 1.881 1.420 1.909
95 1.645 1.687 1.623 1.709 1.602 1.732 1.579 1.755 1.557 1.778 1.535 1.802 1.512 1.827 1.489 1.852 1.465 1.877 1.442 1.903
100 1.654 1.694 1.634 1.715 1.613 1.736 1.592 1.758 1.571 1.780 1.550 1.803 1.528 1.826 1.506 1.850 1.484 1.874 1.462 1.898
150 1.720 1.747 1.706 1.760 1.693 1.774 1.679 1.788 1.665 1.802 1.651 1.817 1.637 1.832 1.622 1.846 1.608 1.862 1.593 1.877
200 1.758 1.779 1.748 1.789 1.738 1.799 1.728 1.809 1.718 1.820 1.707 1.831 1.697 1.841 1.686 1.852 1.675 1.863 1.665 1.874
16 0.098 3.503 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
17 0.138 3.378 0.087 3.557 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
18 0.177 3.265 0.123 3.441 0.078 3.603 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
19 0.220 3.159 0.160 3.335 0.111 3.496 0.070 3.642 —– —– —– —– —– —– —– —– —– —– —– —–
20 0.263 3.063 0.200 3.234 0.145 3.395 0.100 3.542 0.063 3.676 —– —– —– —– —– —– —– —– —– —–
21 0.307 2.976 0.240 3.141 0.182 3.300 0.132 3.448 0.091 3.583 0.058 3.705 —– —– —– —– —– —– —– —–
22 0.349 2.897 0.281 3.057 0.220 3.211 0.166 3.358 0.120 3.495 0.083 3.619 0.052 3.731 —– —– —– —– —– —–
23 0.391 2.826 0.322 2.979 0.259 3.128 0.202 3.272 0.153 3.409 0.110 3.535 0.076 3.650 0.048 3.753 —– —– —– —–
24 0.431 2.761 0.362 2.908 0.297 3.053 0.239 3.193 0.186 3.327 0.141 3.454 0.101 3.572 0.070 3.678 0.044 3.773 —– —–
25 0.470 2.702 0.400 2.844 0.335 2.983 0.275 3.119 0.221 3.251 0.172 3.376 0.130 3.494 0.094 3.604 0.065 3.702 0.041 3.790
26 0.508 2.649 0.438 2.784 0.373 2.919 0.312 3.051 0.256 3.179 0.205 3.303 0.160 3.420 0.120 3.531 0.087 3.632 0.060 3.724
27 0.544 2.600 0.475 2.730 0.409 2.859 0.348 2.987 0.291 3.112 0.238 3.233 0.191 3.349 0.149 3.460 0.112 3.563 0.081 3.658
28 0.578 2.555 0.510 2.680 0.445 2.805 0.383 2.928 0.325 3.050 0.271 3.168 0.222 3.283 0.178 3.392 0.138 3.495 0.104 3.592
29 0.612 2.515 0.544 2.634 0.479 2.755 0.418 2.874 0.359 2.992 0.305 3.107 0.254 3.219 0.208 3.327 0.166 3.431 0.129 3.528
30 0.643 2.477 0.577 2.592 0.512 2.708 0.451 2.823 0.392 2.937 0.337 3.050 0.286 3.160 0.238 3.266 0.195 3.368 0.156 3.465
31 0.674 2.443 0.608 2.553 0.545 2.665 0.484 2.776 0.425 2.887 0.370 2.996 0.317 3.103 0.269 3.208 0.224 3.309 0.183 3.406
32 0.703 2.411 0.638 2.517 0.576 2.625 0.515 2.733 0.457 2.840 0.401 2.946 0.349 3.050 0.299 3.153 0.253 3.252 0.211 3.348
33 0.731 2.382 0.668 2.484 0.606 2.588 0.546 2.692 0.488 2.796 0.432 2.899 0.379 3.000 0.329 3.100 0.283 3.198 0.239 3.293
34 0.758 2.355 0.695 2.454 0.634 2.554 0.575 2.654 0.518 2.754 0.462 2.854 0.409 2.954 0.359 3.051 0.312 3.147 0.267 3.240
35 0.783 2.330 0.722 2.425 0.662 2.521 0.604 2.619 0.547 2.716 0.492 2.813 0.439 2.910 0.388 3.005 0.340 3.099 0.295 3.190
36 0.808 2.306 0.748 2.398 0.689 2.492 0.631 2.586 0.575 2.680 0.520 2.774 0.467 2.868 0.417 2.961 0.369 3.053 0.323 3.142
37 0.831 2.285 0.772 2.374 0.714 2.464 0.657 2.555 0.602 2.646 0.548 2.738 0.495 2.829 0.445 2.920 0.397 3.009 0.351 3.097
38 0.854 2.265 0.796 2.351 0.739 2.438 0.683 2.526 0.628 2.614 0.575 2.703 0.522 2.792 0.472 2.880 0.424 2.968 0.378 3.054
39 0.875 2.246 0.819 2.329 0.763 2.413 0.707 2.499 0.653 2.585 0.600 2.671 0.549 2.757 0.499 2.843 0.451 2.929 0.404 3.013
40 0.896 2.228 0.840 2.309 0.785 2.391 0.731 2.473 0.678 2.557 0.626 2.641 0.575 2.724 0.525 2.808 0.477 2.829 0.430 2.974
45 0.988 2.156 0.938 2.225 0.887 2.296 0.838 2.367 0.788 2.439 0.740 2.512 0.692 2.586 0.644 2.659 0.598 2.733 0.553 2.807
50 1.064 2.103 1.019 2.163 0.973 2.225 0.927 2.287 0.882 2.350 0.836 2.414 0.792 2.479 0.747 2.544 0.703 2.610 0.660 2.675
55 1.129 2.062 1.087 2.116 1.045 2.170 1.003 2.225 0.961 2.281 0.919 2.338 0.877 2.396 0.836 2.454 0.795 2.512 0.754 2.571
60 1.184 2.031 1.145 2.079 1.106 2.127 1.068 2.177 1.029 2.227 0.990 2.278 0.951 2.330 0.913 2.382 0.874 2.434 0.836 2.487
65 1.231 2.006 1.195 2.049 1.160 2.093 1.124 2.138 1.088 2.183 1.052 2.229 1.016 2.276 0.980 2.323 0.944 2.371 0.908 2.419
70 1.272 1.987 1.239 2.026 1.206 2.066 1.172 2.106 1.139 2.148 1.105 2.189 1.072 2.232 1.038 2.275 1.005 2.318 0.971 2.362
75 1.308 1.970 1.277 2.006 1.247 2.043 1.215 2.080 1.184 2.118 1.153 2.156 1.121 2.195 1.090 2.235 1.058 2.275 1.027 2.315
80 1.340 1.957 1.311 1.991 1.283 2.024 1.253 2.059 1.224 2.093 1.195 2.129 1.165 2.165 1.136 2.201 1.106 2.238 1.076 2.275
85 1.369 1.946 1.342 1.977 1.315 2.009 1.287 2.040 1.260 2.073 1.232 2.105 1.205 2.139 1.177 2.172 1.149 2.206 1.121 2.241
90 1.395 1.937 1.369 1.966 1.344 1.995 1.318 2.025 1.292 2.055 1.266 2.085 1.240 2.116 1.213 2.148 1.187 2.179 1.160 2.211
95 1.418 1.930 1.394 1.956 1.370 1.984 1.345 2.012 1.321 2.040 1.296 2.068 1.271 2.097 1.247 2.126 1.222 2.156 1.197 2.186
100 1.439 1.923 1.416 1.948 1.393 1.974 1.371 2.000 1.347 2.026 1.324 2.053 1.301 2.080 1.277 2.108 1.253 2.135 1.229 2.164
150 1.579 1.892 1.564 1.908 1.550 1.924 1.535 1.940 1.519 1.956 1.504 1.972 1.489 1.989 1.474 2.006 1.458 2.023 1.443 2.040
200 1.654 1.885 1.643 1.896 1.632 1.908 1.621 1.919 1.610 1.931 1.599 1.943 1.588 1.955 1.576 1.967 1.565 1.979 1.554 1.991

Bảng A.3: Mô hình không có hệ số cắt, theo Farebrother(1980)

  • Sự tự tương quan dương
  • Thống kê DW ở mức ý nghĩa 1% (Minimal Bound)
N K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10 K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20 K=21
2 0.001 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
3 0.034 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
4 0.127 0.022 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
5 0.233 0.089 0.014 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
6 0.322 0.175 0.065 0.010 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
7 0.398 0.253 0.135 0.049 0.008 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
8 0.469 0.324 0.202 0.106 0.038 0.006 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
9 0.534 0.394 0.268 0.164 0.086 0.031 0.005 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
10 0.591 0.457 0.333 0.223 0.136 0.070 0.025 0.004 0.000 —– —– —– —– —– —– —– —– —– —– —– —– —–
11 0.643 0.515 0.394 0.284 0.189 0.114 0.059 0.021 0.003 0.000 —– —– —– —– —– —– —– —– —– —– —– —–
12 0.691 0.568 0.451 0.341 0.244 0.161 0.097 0.050 0.018 0.003 0.000 —– —– —– —– —– —– —– —– —– —– —–
13 0.733 0.617 0.503 0.396 0.298 0.212 0.139 0.083 0.043 0.015 0.002 0.000 —– —– —– —– —– —– —– —– —– —–
14 0.773 0.662 0.552 0.448 0.350 0.262 0.185 0.121 0.072 0.037 0.013 0.002 0.000 —– —– —– —– —– —– —– —– —–
15 0.809 0.703 0.598 0.496 0.400 0.311 0.232 0.163 0.107 0.063 0.032 0.011 0.002 0.000 —– —– —– —– —– —– —– —–
16 0.842 0.741 0.640 0.541 0.447 0.358 0.278 0.206 0.145 0.094 0.056 0.028 0.010 0.002 0.000 —– —– —– —– —– —– —–
17 0.873 0.776 0.679 0.583 0.491 0.404 0.323 0.249 0.184 0.129 0.084 0.050 0.025 0.009 0.001 0.000 —– —– —– —– —– —–
18 0.901 0.808 0.715 0.623 0.533 0.447 0.366 0.292 0.225 0.166 0.116 0.075 0.044 0.023 0.008 0.001 0.000 —– —– —– —– —–
19 0.928 0.839 0.749 0.660 0.572 0.488 0.408 0.333 0.265 0.204 0.150 0.105 0.068 0.040 0.020 0.007 0.001 0.000 —– —– —– —–
20 0.952 0.867 0.780 0.694 0.609 0.527 0.448 0.374 0.304 0.241 0.185 0.136 0.095 0.062 0.036 0.018 0.006 0.001 0.000 —– —– —–
21 0.976 0.893 0.810 0.727 0.644 0.564 0.486 0.413 0.343 0.279 0.221 0.169 0.124 0.087 0.056 0.033 0.017 0.006 0.001 0.000 —– —–
22 0.997 0.918 0.838 0.757 0.677 0.599 0.523 0.450 0.381 0.316 0.257 0.203 0.155 0.114 0.079 0.051 0.030 0.015 0.005 0.001 0.000 —–
23 1.018 0.942 0.864 0.786 0.709 0.632 0.558 0.486 0.417 0.352 0.292 0.237 0.187 0.143 0.104 0.073 0.047 0.027 0.014 0.005 0.001 0.000
24 1.037 0.964 0.889 0.813 0.738 0.664 0.591 0.520 0.452 0.387 0.327 0.270 0.219 0.172 0.131 0.096 0.067 0.043 0.025 0.013 0.004 0.001
25 1.056 0.984 0.912 0.839 0.766 0.693 0.622 0.553 0.486 0.421 0.361 0.304 0.251 0.203 0.160 0.122 0.089 0.062 0.040 0.023 0.012 0.004
26 1.073 1.004 0.934 0.863 0.792 0.722 0.652 0.584 0.518 0.454 0.394 0.336 0.283 0.233 0.189 0.148 0.113 0.083 0.057 0.037 0.022 0.011
27 1.089 1.023 0.955 0.886 0.817 0.749 0.681 0.614 0.549 0.486 0.426 0.368 0.314 0.264 0.218 0.176 0.138 0.105 0.077 0.053 0.034 0.020
28 1.105 1.040 0.974 0.908 0.841 0.774 0.708 0.643 0.579 0.517 0.457 0.400 0.345 0.294 0.247 0.204 0.164 0.129 0.098 0.071 0.050 0.032
29 1.120 1.057 0.993 0.929 0.864 0.798 0.734 0.670 0.607 0.546 0.487 0.430 0.376 0.324 0.276 0.232 0.191 0.154 0.120 0.091 0.067 0.046
30 1.134 1.073 1.011 0.948 0.885 0.822 0.759 0.696 0.635 0.574 0.516 0.460 0.405 0.354 0.305 0.260 0.217 0.179 0.144 0.113 0.086 0.062
31 1.147 1.088 1.028 0.967 0.905 0.844 0.782 0.721 0.661 0.602 0.544 0.488 0.434 0.383 0.334 0.288 0.244 0.205 0.168 0.135 0.106 0.080
32 1.160 1.103 1.044 0.985 0.925 0.865 0.805 0.745 0.686 0.628 0.571 0.516 0.462 0.411 0.362 0.315 0.271 0.230 0.193 0.158 0.127 0.100
33 1.173 1.117 1.060 1.002 0.944 0.885 0.826 0.768 0.710 0.653 0.597 0.542 0.489 0.438 0.389 0.342 0.298 0.256 0.218 0.182 0.149 0.120
34 1.185 1.130 1.075 1.018 0.961 0.904 0.847 0.790 0.733 0.677 0.622 0.568 0.516 0.465 0.416 0.369 0.324 0.282 0.243 0.206 0.172 0.141
35 1.196 1.143 1.089 1.034 0.978 0.923 0.867 0.811 0.755 0.700 0.646 0.593 0.541 0.491 0.442 0.395 0.350 0.308 0.268 0.230 0.195 0.163
36 1.207 1.155 1.102 1.049 0.995 0.940 0.886 0.831 0.777 0.723 0.669 0.617 0.566 0.516 0.467 0.421 0.376 0.333 0.292 0.254 0.218 0.185
37 1.217 1.167 1.116 1.063 1.010 0.957 0.904 0.850 0.797 0.744 0.692 0.640 0.590 0.540 0.492 0.446 0.401 0.358 0.317 0.278 0.241 0.207
38 1.228 1.178 1.128 1.077 1.026 0.974 0.921 0.869 0.817 0.765 0.713 0.663 0.613 0.564 0.516 0.470 0.425 0.382 0.341 0.302 0.265 0.230
39 1.237 1.189 1.140 1.090 1.040 0.989 0.938 0.887 0.836 0.785 0.734 0.684 0.635 0.587 0.540 0.494 0.449 0.406 0.365 0.325 0.288 0.252
40 1.247 1.200 1.152 1.103 1.054 1.004 0.954 0.904 0.854 0.804 0.754 0.705 0.657 0.609 0.562 0.517 0.473 0.430 0.388 0.349 0.311 0.275
45 1.289 1.247 1.204 1.160 1.116 1.071 1.026 0.981 0.936 0.890 0.845 0.800 0.755 0.710 0.666 0.623 0.581 0.539 0.499 0.459 0.421 0.384
50 1.325 1.287 1.248 1.208 1.168 1.128 1.087 1.046 1.004 0.963 0.921 0.880 0.838 0.797 0.756 0.715 0.675 0.636 0.597 0.559 0.521 0.485
55 1.356 1.321 1.286 1.250 1.213 1.176 1.139 1.101 1.063 1.025 0.987 0.948 0.910 0.872 0.833 0.796 0.758 0.721 0.684 0.647 0.611 0.576
60 1.383 1.351 1.319 1.285 1.252 1.218 1.183 1.149 1.114 1.078 1.043 1.008 0.972 0.936 0.901 0.865 0.830 0.795 0.760 0.725 0.691 0.657
65 1.408 1.378 1.348 1.317 1.286 1.254 1.222 1.190 1.158 1.125 1.092 1.059 1.026 0.993 0.960 0.927 0.894 0.861 0.828 0.795 0.762 0.730
70 1.429 1.401 1.373 1.345 1.316 1.286 1.257 1.227 1.197 1.166 1.136 1.105 1.074 1.043 1.012 0.981 0.950 0.919 0.888 0.857 0.826 0.795
75 1.448 1.423 1.396 1.369 1.342 1.315 1.287 1.260 1.231 1.203 1.174 1.146 1.117 1.088 1.058 1.029 1.000 0.971 0.941 0.912 0.883 0.854
80 1.466 1.442 1.417 1.392 1.367 1.341 1.315 1.289 1.262 1.236 1.209 1.182 1.155 1.127 1.100 1.072 1.045 1.017 0.989 0.962 0.934 0.907
85 1.482 1.459 1.436 1.412 1.388 1.364 1.340 1.315 1.290 1.265 1.240 1.214 1.189 1.163 1.137 1.111 1.085 1.059 1.033 1.006 0.980 0.954
90 1.497 1.475 1.453 1.431 1.408 1.385 1.362 1.339 1.315 1.292 1.268 1.244 1.220 1.195 1.171 1.146 1.121 1.097 1.072 1.047 1.022 0.997
95 1.510 1.490 1.469 1.448 1.426 1.405 1.383 1.361 1.338 1.316 1.293 1.271 1.248 1.225 1.201 1.178 1.155 1.131 1.108 1.084 1.060 1.037
100 1.523 1.503 1.483 1.463 1.443 1.422 1.402 1.381 1.359 1.338 1.317 1.295 1.273 1.251 1.229 1.207 1.185 1.162 1.140 1.118 1.095 1.072
150 1.611 1.598 1.585 1.571 1.558 1.544 1.530 1.516 1.502 1.488 1.474 1.460 1.445 1.431 1.416 1.402 1.387 1.372 1.357 1.342 1.327 1.312
200 1.664 1.654 1.644 1.634 1.624 1.613 1.603 1.593 1.582 1.572 1.561 1.551 1.540 1.529 1.519 1.508 1.497 1.486 1.475 1.434 1.453 1.442

Bảng A.4: Mô hình không có hệ số cắt, theo Farebrother(1980)

  • Sự tự tương quan dương
  • Thống kê DW ở mức ý nghĩa 5% (Minimal Bound)
N K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10 K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20 K=21
2 0.012 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
3 0.168 0.006 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
4 0.355 0.105 0.004 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
5 0.478 0.248 0.070 0.002 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
6 0.584 0.358 0.180 0.050 0.002 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
7 0.677 0.462 0.275 0.136 0.037 0.001 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
8 0.754 0.556 0.371 0.217 0.106 0.029 0.001 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
9 0.820 0.635 0.460 0.303 0.175 0.085 0.023 0.001 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
10 0.877 0.706 0.539 0.385 0.251 0.143 0.069 0.019 0.001 —– —– —– —– —– —– —– —– —– —– —– —– —–
11 0.927 0.768 0.610 0.460 0.326 0.211 0.120 0.058 0.016 0.001 —– —– —– —– —– —– —– —– —– —– —– —–
12 0.972 0.823 0.674 0.530 0.397 0.279 0.180 0.101 0.049 0.013 0.001 —– —– —– —– —– —– —– —– —– —– —–
13 1.012 0.872 0.731 0.593 0.464 0.345 0.241 0.154 0.087 0.042 0.011 0.001 —– —– —– —– —– —– —– —– —– —–
14 1.047 0.916 0.783 0.651 0.525 0.408 0.302 0.210 0.134 0.075 0.036 0.010 0.001 —– —– —– —– —– —– —– —– —–
15 1.079 0.955 0.829 0.704 0.583 0.467 0.361 0.266 0.185 0.118 0.066 0.031 0.008 0.001 —– —– —– —– —– —– —– —–
16 1.109 0.992 0.872 0.752 0.635 0.523 0.418 0.322 0.237 0.164 0.104 0.058 0.028 0.007 0.000 —– —– —– —– —– —– —–
17 1.136 1.024 0.911 0.797 0.684 0.575 0.472 0.376 0.288 0.211 0.146 0.093 0.052 0.025 0.007 0.000 —– —– —– —– —– —–
18 1.160 1.055 0.946 0.837 0.729 0.624 0.523 0.427 0.339 0.260 0.190 0.131 0.083 0.046 0.022 0.006 0.000 —– —– —– —– —–
19 1.183 1.082 0.979 0.875 0.771 0.669 0.570 0.476 0.388 0.307 0.235 0.171 0.118 0.075 0.041 0.020 0.005 0.000 —– —– —– —–
20 1.204 1.108 1.010 0.910 0.810 0.711 0.615 0.523 0.436 0.354 0.280 0.213 0.156 0.107 0.067 0.037 0.018 0.005 0.000 —– —– —–
21 1.224 1.132 1.038 0.942 0.846 0.751 0.657 0.567 0.481 0.400 0.324 0.256 0.195 0.142 0.097 0.061 0.034 0.016 0.004 0.000 —– —–
22 1.242 1.154 1.064 0.972 0.879 0.787 0.697 0.609 0.524 0.443 0.368 0.298 0.235 0.178 0.130 0.089 0.056 0.031 0.015 0.004 0.000 —–
23 1.259 1.175 1.088 1.000 0.911 0.822 0.734 0.648 0.565 0.485 0.410 0.339 0.274 0.216 0.164 0.119 0.081 0.051 0.028 0.014 0.004 0.000
24 1.275 1.194 1.111 1.026 0.940 0.854 0.769 0.685 0.604 0.525 0.450 0.380 0.314 0.254 0.199 0.151 0.110 0.075 0.047 0.026 0.012 0.003
25 1.290 1.212 1.132 1.050 0.967 0.884 0.802 0.720 0.641 0.563 0.489 0.419 0.353 0.291 0.235 0.184 0.140 0.101 0.069 0.044 0.024 0.011
26 1.304 1.229 1.152 1.073 0.993 0.913 0.833 0.753 0.676 0.600 0.527 0.457 0.390 0.328 0.271 0.218 0.171 0.130 0.094 0.064 0.040 0.022
27 1.318 1.245 1.171 1.094 1.017 0.940 0.862 0.785 0.709 0.635 0.563 0.493 0.427 0.365 0.306 0.252 0.203 0.159 0.120 0.087 0.060 0.037
28 1.330 1.260 1.188 1.115 1.040 0.965 0.889 0.815 0.741 0.668 0.597 0.529 0.463 0.400 0.341 0.286 0.236 0.190 0.148 0.112 0.081 0.055
29 1.342 1.275 1.205 1.134 1.062 0.989 0.916 0.843 0.770 0.699 0.630 0.562 0.497 0.435 0.376 0.320 0.268 0.221 0.177 0.139 0.105 0.076
30 1.354 1.288 1.221 1.152 1.082 1.011 0.940 0.869 0.799 0.729 0.661 0.595 0.530 0.468 0.409 0.353 0.301 0.252 0.207 0.166 0.130 0.098
31 1.365 1.301 1.236 1.169 1.101 1.033 0.964 0.895 0.826 0.758 0.691 0.626 0.562 0.501 0.442 0.386 0.333 0.283 0.237 0.195 0.156 0.122
32 1.375 1.313 1.250 1.185 1.120 1.053 0.986 0.919 0.852 0.785 0.720 0.653 0.593 0.532 0.474 0.418 0.364 0.314 0.267 0.223 0.183 0.147
33 1.385 1.325 1.264 1.201 1.137 1.072 1.007 0.942 0.876 0.811 0.747 0.684 0.623 0.563 0.504 0.449 0.395 0.344 0.297 0.252 0.211 0.173
34 1.394 1.336 1.277 1.216 1.153 1.091 1.027 0.963 0.900 0.836 0.774 0.712 0.651 0.592 0.534 0.479 0.425 0.374 0.326 0.280 0.238 0.199
35 1.403 1.347 1.289 1.230 1.169 1.108 1.046 0.984 0.922 0.860 0.799 0.738 0.678 0.620 0.563 0.508 0.455 0.404 0.355 0.309 0.266 0.225
36 1.412 1.357 1.301 1.243 1.184 1.125 1.064 1.004 0.943 0.883 0.823 0.763 0.705 0.647 0.591 0.536 0.483 0.432 0.384 0.337 0.293 0.252
37 1.420 1.367 1.312 1.256 1.199 1.141 1.082 1.023 0.964 0.905 0.846 0.787 0.730 0.673 0.618 0.564 0.511 0.460 0.412 0.365 0.321 0.279
38 1.428 1.376 1.323 1.268 1.212 1.156 1.099 1.041 0.983 0.925 0.868 0.811 0.754 0.698 0.644 0.590 0.538 0.488 0.439 0.392 0.347 0.305
39 1.436 1.385 1.333 1.280 1.225 1.170 1.114 1.058 1.002 0.945 0.889 0.833 0.778 0.723 0.669 0.616 0.564 0.514 0.466 0.419 0.374 0.331
40 1.443 1.394 1.343 1.291 1.238 1.184 1.130 1.075 1.020 0.965 0.909 0.854 0.800 0.746 0.693 0.641 0.590 0.540 0.492 0.445 0.400 0.357
45 1.476 1.432 1.387 1.341 1.294 1.246 1.197 1.148 1.099 1.049 1.000 0.950 0.900 0.851 0.802 0.753 0.706 0.658 0.612 0.567 0.523 0.480
50 1.504 1.464 1.424 1.382 1.340 1.297 1.253 1.209 1.164 1.120 1.075 1.029 0.984 0.939 0.894 0.849 0.804 0.760 0.717 0.674 0.631 0.590
55 1.528 1.492 1.455 1.417 1.379 1.340 1.300 1.260 1.219 1.179 1.138 1.096 1.055 1.013 0.972 0.930 0.889 0.848 0.807 0.766 0.726 0.687
60 1.549 1.516 1.482 1.447 1.412 1.376 1.340 1.303 1.266 1.229 1.191 1.153 1.115 1.077 1.038 1.000 0.962 0.923 0.885 0.847 0.810 0.772
65 1.568 1.537 1.505 1.474 1.441 1.408 1.375 1.341 1.307 1.272 1.238 1.202 1.167 1.132 1.096 1.061 1.025 0.989 0.953 0.918 0.882 0.847
70 1.584 1.555 1.526 1.497 1.467 1.436 1.405 1.374 1.342 1.310 1.278 1.245 1.213 1.180 1.147 1.113 1.080 1.047 1.013 0.980 0.947 0.914
75 1.599 1.572 1.545 1.517 1.489 1.461 1.432 1.403 1.373 1.344 1.313 1.283 1.253 1.222 1.191 1.160 1.129 1.098 1.066 1.035 1.004 0.972
80 1.612 1.587 1.561 1.536 1.509 1.483 1.456 1.429 1.401 1.373 1.345 1.317 1.288 1.259 1.230 1.201 1.172 1.143 1.113 1.084 1.054 1.025
85 1.624 1.600 1.576 1.552 1.527 1.502 1.477 1.452 1.426 1.400 1.373 1.347 1.320 1.293 1.266 1.238 1.211 1.183 1.155 1.128 1.100 1.072
90 1.635 1.613 1.590 1.567 1.544 1.520 1.497 1.472 1.448 1.423 1.399 1.373 1.348 1.323 1.297 1.271 1.245 1.219 1.193 1.167 1.141 1.114
95 1.645 1.624 1.603 1.581 1.559 1.537 1.514 1.491 1.468 1.445 1.422 1.398 1.374 1.350 1.326 1.301 1.277 1.252 1.227 1.202 1.177 1.152
100 1.654 1.634 1.614 1.593 1.573 1.551 1.530 1.508 1.487 1.465 1.442 1.420 1.397 1.374 1.352 1.328 1.305 1.282 1.258 1.235 1.211 1.187
150 1.720 1.706 1.693 1.679 1.666 1.652 1.638 1.624 1.609 1.595 1.580 1.566 1.551 1.536 1.521 1.506 1.491 1.476 1.461 1.445 1.430 1.414
200 1.759 1.748 1.738 1.728 1.718 1.708 1.697 1.687 1.676 1.666 1.655 1.644 1.633 1.622 1.611 1.600 1.589 1.578 1.567 1.556 1.544 1.533

Bảng A.5: Mô hình không có hệ số cắt, theo Farebrother(1980)

  • Sự tự tương quan âm
  • Thống kê DW ở mức ý nghĩa 95% (Minimal Bound)
N K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10 K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20 K=21
2 1.988 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
3 2.761 0.994 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
4 2.871 1.836 0.582 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
5 2.857 2.178 1.267 0.380 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
6 2.844 2.320 1.655 0.917 0.266 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
7 2.828 2.398 1.871 1.283 0.690 0.197 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
8 2.805 2.453 2.008 1.521 1.017 0.537 0.151 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
9 2.783 2.483 2.110 1.687 1.251 0.823 0.429 0.120 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
10 2.762 2.501 2.181 1.816 1.427 1.044 0.678 0.350 0.097 —– —– —– —– —– —– —– —– —– —– —– —– —–
11 2.742 2.511 2.231 1.913 1.569 1.218 0.881 0.567 0.291 0.080 —– —– —– —– —– —– —– —– —– —– —– —–
12 2.723 2.516 2.268 1.987 1.682 1.364 1.049 0.752 0.481 0.245 0.068 —– —– —– —– —– —– —– —– —– —– —–
13 2.705 2.518 2.296 2.044 1.771 1.484 1.193 0.911 0.649 0.413 0.210 0.058 —– —– —– —– —– —– —– —– —– —–
14 2.688 2.517 2.316 2.090 1.843 1.582 1.316 1.051 0.797 0.565 0.358 0.181 0.050 —– —– —– —– —– —– —– —– —–
15 2.672 2.515 2.332 2.126 1.902 1.664 1.419 1.172 0.931 0.703 0.497 0.314 0.158 0.043 —– —– —– —– —– —– —– —–
16 2.657 2.512 2.344 2.155 1.950 1.732 1.506 1.276 1.049 0.829 0.624 0.439 0.277 0.139 0.038 —– —– —– —– —– —– —–
17 2.644 2.508 2.353 2.179 1.990 1.789 1.580 1.367 1.153 0.944 0.743 0.557 0.391 0.246 0.124 0.034 —– —– —– —– —– —–
18 2.631 2.504 2.359 2.199 2.024 1.838 1.644 1.445 1.244 1.045 0.852 0.669 0.501 0.351 0.220 0.110 0.030 —– —– —– —– —–
19 2.618 2.499 2.364 2.215 2.053 1.880 1.699 1.513 1.324 1.136 0.951 0.773 0.605 0.452 0.316 0.198 0.099 0.027 —– —– —– —–
20 2.607 2.494 2.368 2.228 2.077 1.916 1.747 1.573 1.395 1.216 1.040 0.868 0.704 0.550 0.410 0.286 0.179 0.090 0.025 —– —– —–
21 2.596 2.489 2.370 2.239 2.098 1.947 1.789 1.625 1.457 1.289 1.120 0.955 0.796 0.644 0.502 0.373 0.260 0.162 0.081 0.022 —– —–
22 2.585 2.484 2.372 2.249 2.116 1.974 1.825 1.671 1.513 1.353 1.193 1.034 0.880 0.731 0.591 0.460 0.341 0.238 0.148 0.074 0.020 —–
23 2.575 2.479 2.373 2.257 2.131 1.998 1.858 1.712 1.563 1.411 1.258 1.107 0.957 0.813 0.674 0.544 0.422 0.313 0.218 0.136 0.068 0.019
24 2.566 2.474 2.373 2.263 2.145 2.019 1.886 1.749 1.607 1.463 1.318 1.172 1.029 0.888 0.753 0.623 0.502 0.389 0.289 0.201 0.125 0.062
25 2.557 2.470 2.373 2.269 2.156 2.037 1.912 1.782 1.647 1.510 1.371 1.232 1.094 0.958 0.826 0.699 0.578 0.465 0.360 0.267 0.185 0.115
26 1.073 1.004 0.934 0.863 0.792 0.722 0.652 0.584 0.518 0.454 0.394 0.336 0.283 0.233 0.189 0.148 0.113 0.083 0.057 0.037 0.022 0.011
27 1.089 1.023 0.955 0.886 0.817 0.749 0.681 0.614 0.549 0.486 0.426 0.368 0.314 0.264 0.218 0.176 0.138 0.105 0.077 0.053 0.034 0.020
28 1.105 1.040 0.974 0.908 0.841 0.774 0.708 0.643 0.579 0.517 0.457 0.400 0.345 0.294 0.247 0.204 0.164 0.129 0.098 0.071 0.050 0.032
29 1.120 1.057 0.993 0.929 0.864 0.798 0.734 0.670 0.607 0.546 0.487 0.430 0.376 0.324 0.276 0.232 0.191 0.154 0.120 0.091 0.067 0.046
30 1.134 1.073 1.011 0.948 0.885 0.822 0.759 0.696 0.635 0.574 0.516 0.460 0.405 0.354 0.305 0.260 0.217 0.179 0.144 0.113 0.086 0.062
31 1.147 1.088 1.028 0.967 0.905 0.844 0.782 0.721 0.661 0.602 0.544 0.488 0.434 0.383 0.334 0.288 0.244 0.205 0.168 0.135 0.106 0.080
32 1.160 1.103 1.044 0.985 0.925 0.865 0.805 0.745 0.686 0.628 0.571 0.516 0.462 0.411 0.362 0.315 0.271 0.230 0.193 0.158 0.127 0.100
33 1.173 1.117 1.060 1.002 0.944 0.885 0.826 0.768 0.710 0.653 0.597 0.542 0.489 0.438 0.389 0.342 0.298 0.256 0.218 0.182 0.149 0.120
34 1.185 1.130 1.075 1.018 0.961 0.904 0.847 0.790 0.733 0.677 0.622 0.568 0.516 0.465 0.416 0.369 0.324 0.282 0.243 0.206 0.172 0.141
35 1.196 1.143 1.089 1.034 0.978 0.923 0.867 0.811 0.755 0.700 0.646 0.593 0.541 0.491 0.442 0.395 0.350 0.308 0.268 0.230 0.195 0.163
36 1.207 1.155 1.102 1.049 0.995 0.940 0.886 0.831 0.777 0.723 0.669 0.617 0.566 0.516 0.467 0.421 0.376 0.333 0.292 0.254 0.218 0.185
37 1.217 1.167 1.116 1.063 1.010 0.957 0.904 0.850 0.797 0.744 0.692 0.640 0.590 0.540 0.492 0.446 0.401 0.358 0.317 0.278 0.241 0.207
38 1.228 1.178 1.128 1.077 1.026 0.974 0.921 0.869 0.817 0.765 0.713 0.663 0.613 0.564 0.516 0.470 0.425 0.382 0.341 0.302 0.265 0.230
39 1.237 1.189 1.140 1.090 1.040 0.989 0.938 0.887 0.836 0.785 0.734 0.684 0.635 0.587 0.540 0.494 0.449 0.406 0.365 0.325 0.288 0.252
40 1.247 1.200 1.152 1.103 1.054 1.004 0.954 0.904 0.854 0.804 0.754 0.705 0.657 0.609 0.562 0.517 0.473 0.430 0.388 0.349 0.311 0.275
45 1.289 1.247 1.204 1.160 1.116 1.071 1.026 0.981 0.936 0.890 0.845 0.800 0.755 0.710 0.666 0.623 0.581 0.539 0.499 0.459 0.421 0.384
50 1.325 1.287 1.248 1.208 1.168 1.128 1.087 1.046 1.004 0.963 0.921 0.880 0.838 0.797 0.756 0.715 0.675 0.636 0.597 0.559 0.521 0.485
55 1.356 1.321 1.286 1.250 1.213 1.176 1.139 1.101 1.063 1.025 0.987 0.948 0.910 0.872 0.833 0.796 0.758 0.721 0.684 0.647 0.611 0.576
60 1.383 1.351 1.319 1.285 1.252 1.218 1.183 1.149 1.114 1.078 1.043 1.008 0.972 0.936 0.901 0.865 0.830 0.795 0.760 0.725 0.691 0.657
65 1.408 1.378 1.348 1.317 1.286 1.254 1.222 1.190 1.158 1.125 1.092 1.059 1.026 0.993 0.960 0.927 0.894 0.861 0.828 0.795 0.762 0.730
70 1.429 1.401 1.373 1.345 1.316 1.286 1.257 1.227 1.197 1.166 1.136 1.105 1.074 1.043 1.012 0.981 0.950 0.919 0.888 0.857 0.826 0.795
75 1.448 1.423 1.396 1.369 1.342 1.315 1.287 1.260 1.231 1.203 1.174 1.146 1.117 1.088 1.058 1.029 1.000 0.971 0.941 0.912 0.883 0.854
80 1.466 1.442 1.417 1.392 1.367 1.341 1.315 1.289 1.262 1.236 1.209 1.182 1.155 1.127 1.100 1.072 1.045 1.017 0.989 0.962 0.934 0.907
85 1.482 1.459 1.436 1.412 1.388 1.364 1.340 1.315 1.290 1.265 1.240 1.214 1.189 1.163 1.137 1.111 1.085 1.059 1.033 1.006 0.980 0.954
90 1.497 1.475 1.453 1.431 1.408 1.385 1.362 1.339 1.315 1.292 1.268 1.244 1.220 1.195 1.171 1.146 1.121 1.097 1.072 1.047 1.022 0.997
95 1.510 1.490 1.469 1.448 1.426 1.405 1.383 1.361 1.338 1.316 1.293 1.271 1.248 1.225 1.201 1.178 1.155 1.131 1.108 1.084 1.060 1.037
100 1.523 1.503 1.483 1.463 1.443 1.422 1.402 1.381 1.359 1.338 1.317 1.295 1.273 1.251 1.229 1.207 1.185 1.162 1.140 1.118 1.095 1.072
150 1.611 1.598 1.585 1.571 1.558 1.544 1.530 1.516 1.502 1.488 1.474 1.460 1.445 1.431 1.416 1.402 1.387 1.372 1.357 1.342 1.327 1.312
200 1.664 1.654 1.644 1.634 1.624 1.613 1.603 1.593 1.582 1.572 1.561 1.551 1.540 1.529 1.519 1.508 1.497 1.486 1.475 1.464 1.453 1.442

Bảng A.6: Mô hình không có hệ số cắt, theo Farebrother(1980)

  • Sự tự tương quan âm
  • Thống kê DW ở mức ý nghĩa 99% (Minimal Bound)
N K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10 K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20 K=21
2 1.999 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
3 2.951 0.999 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
4 3.221 1.967 0.586 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
5 3.261 2.462 1.359 0.382 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
6 3.235 2.682 1.878 0.983 0.268 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
7 3.198 2.776 2.177 1.459 0.740 0.198 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
8 3.166 2.817 2.347 1.776 1.158 0.576 0.153 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–
9 3.133 2.837 2.448 1.983 1.465 0.937 0.460 0.121 —– —– —– —– —– —– —– —– —– —– —– —– —– —–
10 3.101 2.847 2.514 2.121 1.684 1.224 0.773 0.375 0.098 —– —– —– —– —– —– —– —– —– —– —– —– —–
11 3.071 2.847 2.560 2.220 1.842 1.441 1.035 0.647 0.312 0.081 —– —– —– —– —– —– —– —– —– —– —– —–
12 3.043 2.843 2.592 2.294 1.961 1.607 1.244 0.885 0.549 0.263 0.069 —– —– —– —– —– —– —– —– —– —– —–
13 3.017 2.836 2.612 2.349 2.054 1.737 1.410 1.082 0.764 0.471 0.225 0.059 —– —– —– —– —– —– —– —– —– —–
14 2.992 2.828 2.626 2.391 2.127 1.842 1.544 1.244 0.948 0.666 0.409 0.195 0.051 —– —– —– —– —– —– —– —– —–
15 2.969 2.818 2.635 2.423 2.185 1.928 1.656 1.379 1.104 0.837 0.585 0.358 0.170 0.044 —– —– —– —– —– —– —– —–
16 2.948 2.808 2.640 2.447 2.231 1.997 1.749 1.494 1.237 0.985 0.743 0.517 0.316 0.150 0.039 —– —– —– —– —– —– —–
17 2.927 2.797 2.643 2.466 2.269 2.055 1.827 1.591 1.351 1.114 0.883 0.664 0.461 0.281 0.133 0.035 —– —– —– —– —– —–
18 2.908 2.787 2.644 2.480 2.299 2.102 1.893 1.675 1.451 1.227 1.007 0.796 0.597 0.413 0.251 0.119 0.031 —– —– —– —– —–
19 2.890 2.776 2.643 2.492 2.324 2.142 1.948 1.746 1.538 1.327 1.118 0.915 0.721 0.539 0.372 0.226 0.107 0.028 —– —– —– —–
20 2.874 2.766 2.641 2.500 2.344 2.176 1.996 1.807 1.613 1.415 1.217 1.022 0.834 0.656 0.489 0.337 0.204 0.096 0.025 —– —– —–
21 2.858 2.756 2.638 2.506 2.361 2.204 2.036 1.861 1.678 1.492 1.305 1.119 0.937 0.763 0.598 0.446 0.307 0.185 0.087 0.023 —– —–
22 2.842 2.746 2.635 2.511 2.375 2.228 2.071 1.907 1.736 1.561 1.384 1.207 1.032 0.862 0.700 0.548 0.408 0.280 0.169 0.080 0.021 —–
23 2.828 2.736 2.631 2.515 2.387 2.249 2.102 1.947 1.786 1.621 1.454 1.285 1.118 0.954 0.796 0.645 0.504 0.374 0.257 0.155 0.073 0.019
24 2.814 2.727 2.627 2.517 2.396 2.267 2.128 1.983 1.831 1.675 1.516 1.356 1.196 1.038 0.884 0.736 0.596 0.465 0.345 0.237 0.143 0.067
25 2.801 2.717 2.623 2.518 2.404 2.282 2.151 2.014 1.871 1.723 1.572 1.420 1.267 1.115 0.966 0.821 0.683 0.552 0.430 0.319 0.218 0.132
26 2.789 2.709 2.618 2.519 2.411 2.295 2.171 2.042 1.906 1.766 1.623 1.478 1.331 1.186 1.042 0.901 0.765 0.635 0.512 0.399 0.295 0.202
27 2.777 2.700 2.614 2.519 2.416 2.306 2.189 2.066 1.938 1.805 1.669 1.530 1.390 1.250 1.111 0.975 0.842 0.714 0.592 0.477 0.371 0.274
28 2.766 2.692 2.609 2.519 2.421 2.316 2.205 2.088 1.966 1.839 1.710 1.577 1.444 1.309 1.176 1.043 0.914 0.788 0.667 0.553 0.445 0.346
29 2.755 2.684 2.604 2.518 2.425 2.325 2.219 2.107 1.991 1.871 1.747 1.621 1.493 1.364 1.235 1.107 0.981 0.858 0.739 0.625 0.517 0.416
30 2.745 2.676 2.600 2.517 2.428 2.332 2.231 2.125 2.014 1.899 1.781 1.660 1.537 1.414 1.290 1.166 1.044 0.924 0.807 0.695 0.587 0.485
31 2.735 2.668 2.595 2.515 2.430 2.339 2.242 2.140 2.035 1.925 1.812 1.696 1.579 1.460 1.340 1.221 1.102 0.986 0.872 0.761 0.654 0.552
32 2.725 2.661 2.590 2.514 2.432 2.344 2.252 2.155 2.053 1.948 1.840 1.729 1.616 1.502 1.387 1.272 1.157 1.043 0.932 0.823 0.718 0.617
33 2.716 2.654 2.586 2.512 2.433 2.349 2.260 2.167 2.070 1.970 1.866 1.759 1.651 1.541 1.430 1.319 1.208 1.097 0.989 0.882 0.779 0.678
34 2.707 2.647 2.581 2.510 2.434 2.353 2.268 2.179 2.086 1.989 1.889 1.787 1.683 1.577 1.470 1.363 1.255 1.148 1.042 0.938 0.836 0.737
35 2.699 2.640 2.576 2.508 2.435 2.357 2.275 2.189 2.100 2.007 1.911 1.813 1.713 1.611 1.507 1.404 1.299 1.196 1.093 0.991 0.891 0.794
36 2.690 2.634 2.572 2.506 2.435 2.360 2.281 2.199 2.113 2.023 1.931 1.837 1.740 1.642 1.542 1.442 1.341 1.240 1.140 1.041 0.943 0.847
37 2.683 2.627 2.567 2.503 2.435 2.363 2.287 2.207 2.124 2.038 1.950 1.859 1.765 1.670 1.574 1.477 1.379 1.282 1.184 1.088 0.992 0.898
38 2.675 2.621 2.563 2.501 2.435 2.365 2.292 2.215 2.135 2.052 1.967 1.879 1.789 1.697 1.604 1.510 1.416 1.321 1.226 1.132 1.039 0.947
39 2.667 2.615 2.559 2.499 2.435 2.367 2.296 2.222 2.145 2.065 1.982 1.898 1.811 1.722 1.632 1.541 1.450 1.358 1.266 1.174 1.083 0.993
40 2.660 2.609 2.555 2.496 2.434 2.369 2.300 2.229 2.154 2.077 1.997 1.915 1.831 1.746 1.659 1.570 1.482 1.392 1.303 1.213 1.124 1.036
45 2.628 2.583 2.535 2.484 2.430 2.374 2.315 2.253 2.190 2.124 2.056 1.986 1.914 1.841 1.767 1.691 1.614 1.537 1.459 1.381 1.302 1.224
50 2.600 2.559 2.516 2.471 2.424 2.374 2.323 2.269 2.214 2.157 2.098 2.037 1.975 1.911 1.847 1.781 1.714 1.646 1.578 1.509 1.439 1.370
55 2.575 2.538 2.500 2.459 2.417 2.373 2.327 2.280 2.231 2.180 2.128 2.075 2.020 1.964 1.907 1.849 1.790 1.730 1.669 1.608 1.546 1.484
60 2.553 2.519 2.484 2.448 2.409 2.370 2.329 2.286 2.242 2.197 2.151 2.103 2.054 2.004 1.954 1.902 1.849 1.796 1.742 1.687 1.631 1.576
65 2.534 2.503 2.470 2.437 2.402 2.366 2.329 2.290 2.250 2.210 2.168 2.125 2.081 2.036 1.990 1.944 1.896 1.848 1.799 1.750 1.700 1.650
70 2.516 2.487 2.458 2.427 2.395 2.361 2.327 2.292 2.256 2.219 2.181 2.142 2.102 2.061 2.020 1.977 1.934 1.891 1.846 1.802 1.756 1.710
75 2.500 2.473 2.446 2.417 2.387 2.357 2.325 2.293 2.260 2.226 2.191 2.155 2.118 2.081 2.043 2.005 1.965 1.926 1.885 1.844 1.802 1.760
80 2.486 2.461 2.436 2.408 2.380 2.352 2.323 2.293 2.262 2.231 2.198 2.165 2.132 2.098 2.063 2.027 1.991 1.954 1.917 1.879 1.841 1.803
85 2.473 2.449 2.425 2.399 2.374 2.347 2.320 2.292 2.263 2.234 2.204 2.174 2.143 2.111 2.079 2.046 2.012 1.979 1.944 1.909 1.874 1.838
90 2.460 2.438 2.415 2.391 2.367 2.342 2.317 2.291 2.264 2.237 2.209 2.181 2.152 2.122 2.092 2.061 2.030 1.999 1.967 1.935 1.902 1.869
95 2.449 2.428 2.406 2.384 2.361 2.338 2.314 2.289 2.264 2.239 2.212 2.186 2.159 2.131 2.103 2.075 2.046 2.016 1.986 1.956 1.926 1.895
100 2.438 2.418 2.398 2.377 2.355 2.333 2.310 2.287 2.264 2.240 2.215 2.190 2.165 2.139 2.113 2.086 2.059 2.031 2.003 1.975 1.946 1.917
150 2.363 2.349 2.336 2.322 2.308 2.294 2.279 2.265 2.250 2.235 2.220 2.204 2.188 2.173 2.156 2.140 2.124 2.107 2.090 2.073 2.056 2.039
200 2.317 2.307 2.296 2.286 2.276 2.265 2.255 2.244 2.233 2.222 2.211 2.200 2.189 2.177 2.166 2.154 2.142 2.131 2.119 2.106 2.094 2.082