Table D5a

DURBIN-WATSON d STATISTIC: SIGNIFICANCE POINTS OF dL AND du AT 0.05 LEVEL OF SIGNIFICANCE

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

8 0.763 1.332 0.559 1.777 0.368 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 0.658 1.604 0.595 1.928 0.444 2.283 0.316 2.645 0.203 3.005 ________

12 0.971 1.331 0.812 1.579 0.658 1.864 0.512 2.177 0.379 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 0.445 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 2.472 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 2.257 0.502 2.461 0.407 2.667 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 0.692 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 0.732 2.124 0.637 2.290 0.547 2.460 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 2.734

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 0.751 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 2.012 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 1.958 0.874 2.071 0.798 2.188 0.723 2.309 0.650 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 0.682 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 0.795 2.281

34 1.393 1.514 1.333 1.580 1.271 1.652 1.208 1.728 1.144 1.808 1.080 1.891 1.015 1.979 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 1.877 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 2.198

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 1.837 1.369 1.873 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 1.746 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 1.847 1.608 1.862 1.594 1.877

200 1.758 1.778 1.748 1.789 1.738 1.799 1.728 1.810 1.718 1.820 1.707 1.831 1.697 1.841 1.686 1.852 1.675 1.863 1.665 1.874

APPENDIX D: STATISTICAL TABLES 971

n dL du dL du dL du dL du dL du dL du dL du dL du dL du dL du

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 2.892 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 1.986 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 1.929 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

Source: This table is an extension of the original Durbin-Watson table and is reproduced from N. E. Savin and K. J. White, "The Durbin-Watson Test for Serial Correlation with Extreme Small Samples or Many Regressors," Econometrica, vol. 45, November 1977, pp. 1989-96 and as corrected by R. W. Farebrother, Econometrica, vol. 48, September 1980, p. 1554. Reprinted by permission of the Econometric Society.

Note: n = number of observations, k = number of explanatory variables excluding the constant term.

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