Durbin watson tables

Appendix A Durbin-Watson Significance Tables The Durbin-Watson test statistic tests the null hypothesis that the residuals from an ordinary least-squares regression are not autocorrelated against the alternative that the residuals follow an AR1 process The Durbin-Watson statistic ranges in value from to A value near indicates non-autocorrelation; a value toward indicates positive autocorrelation; a value toward indicates negative autocorrelation Because of the dependence of any computed Durbin-Watson value on the associated data matrix, exact critical values of the Durbin-Watson statistic are not tabulated for all possible cases Instead, Durbin and Watson established upper and lower bounds for the critical values Typically, tabulated bounds are used to test the hypothesis of zero autocorrelation against the alternative of positive first-order autocorrelation, since positive autocorrelation is seen much more frequently in practice than negative autocorrelation To use the table, you must cross-reference the sample size against the number of regressors, excluding the constant from the count of the number of regressors The conventional Durbin-Watson tables are not applicable when you not have a constant term in the regression Instead, you must refer to an appropriate set of Durbin-Watson tables The conventional Durbin-Watson tables are also not applicable when a lagged dependent variable appears among the regressors Durbin has proposed alternative test procedures for this case Statisticians have compiled Durbin-Watson tables from some special cases, including: „ Regressions with a full set of quarterly seasonal dummies „ Regressions with an intercept and a linear trend variable (CURVEFIT MODEL=LINEAR) „ Regressions with a full set of quarterly seasonal dummies and a linear trend variable Appendix A In addition to obtaining the Durbin-Watson statistic for residuals from REGRESSION, you should also plot the ACF and PACF of the residuals series The plots might suggest either that the residuals are random, or that they follow some ARMA process If the residuals resemble an AR1 process, you can estimate an appropriate regression using the AREG procedure If the residuals follow any ARMA process, you can estimate an appropriate regression using the ARIMA procedure In this appendix, we have reproduced two sets of tables Savin and White (1977) present tables for sample sizes ranging from to 200 and for to 20 regressors for models in which an intercept is included Farebrother (1980) presents tables for sample sizes ranging from to 200 and for to 21 regressors for models in which an intercept is not included Let’s consider an example of how to use the tables In Chapter 9, we look at the classic Durbin and Watson data set concerning consumption of spirits The sample size is 69, there are regressors, and there is an intercept term in the model The DurbinWatson test statistic value is 0.24878 We want to test the null hypothesis of zero autocorrelation in the residuals against the alternative that the residuals are positively autocorrelated at the 1% level of significance If you examine the Savin and White tables (Table A.2 and Table A.3), you will not find a row for sample size 69, so go to the next lowest sample size with a tabulated row, namely N=65 Since there are two regressors, find the column labeled k=2 Cross-referencing the indicated row and column, you will find that the printed bounds are dL = 1.377 and dU = 1.500 If the observed value of the test statistic is less than the tabulated lower bound, then you should reject the null hypothesis of non-autocorrelated errors in favor of the hypothesis of positive first-order autocorrelation Since 0.24878 is less than 1.377, we reject the null hypothesis If the test statistic value were greater than dU, we would not reject the null hypothesis A third outcome is also possible If the test statistic value lies between dL and dU, the test is inconclusive In this context, you might err on the side of conservatism and not reject the null hypothesis For models with an intercept, if the observed test statistic value is greater than 2, then you want to test the null hypothesis against the alternative hypothesis of negative first-order autocorrelation To this, compute the quantity 4-d and compare this value with the tabulated values of dL and dU as if you were testing for positive autocorrelation When the regression does not contain an intercept term, refer to Farebrother‚Äôs tabulated values of the ‚Äúminimal bound,‚Äù denoted dM (Table A.4 and Table A.5), instead of Savin and White‚Äôs lower bound dL In this instance, the upper bound is Durbin-Watson Significance Tables the conventional bound dU found in the Savin and White tables To test for negative first-order autocorrelation, use Table A.6 and Table A.7 To continue with our example, had we run a regression with no intercept term, we would cross-reference N equals 65 and k equals in Farebrother‚Äôs table The tabulated 1% minimal bound is 1.348 4 Appendix A Table A-1 Models with an intercept (from Savin and White) Durbin-Watson Statistic: Per Cent Significance Points of dL and dU k’*=1 k’=2 k’=3 k’=4 k’=5 k’=6 k’=7 k’=8 k’=9 k’=10 n 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 dL 0.390 0.435 0.497 0.554 0.604 0.653 0.697 0.738 0.776 0.811 0.844 0.873 0.902 0.928 0.952 0.975 0.997 1.017 1.037 1.055 dU 1.142 1.036 1.003 0.998 1.001 1.010 1.023 1.038 1.054 1.070 1.086 1.102 1.118 1.133 1.147 1.161 1.174 1.186 1.199 1.210 dL 0.294 0.345 0.408 0.466 0.519 0.569 0.616 0.660 0.700 0.738 0.773 0.805 0.835 0.862 0.889 0.915 0.938 0.959 0.981 dU 1.676 1.489 1.389 1.333 1.297 1.274 1.261 1.254 1.252 1.253 1.255 1.259 1.264 1.270 1.276 1.284 1.290 1.298 1.305 dL 0.229 0.279 0.340 0.396 0.449 0.499 0.547 0.591 0.633 0.672 0.708 0.742 0.774 0.803 0.832 0.858 0.881 0.906 dU 2.102 1.875 1.733 1.640 1.575 1.526 1.490 1.465 1.447 1.432 1.422 1.416 1.410 1.408 1.407 1.407 1.407 1.408 dL 0.183 0.230 0.286 0.339 0.391 0.441 0.487 0.532 0.574 0.614 0.650 0.684 0.718 0.748 0.777 0.805 0.832 dU 2.433 2.193 2.030 1.913 1.826 1.757 1.705 1.664 1.631 1.604 1.583 1.567 1.554 1.543 1.535 1.527 1.521 dL 0.150 0.193 0.244 0.294 0.343 0.390 0.437 0.481 0.522 0.561 0.598 0.634 0.666 0.699 0.728 0.756 dU 2.690 2.453 2.280 2.150 2.049 1.967 1.901 1.847 1.803 1.767 1.736 1.712 1.691 1.674 1.659 1.645 dL 0.124 0.164 0.211 0.257 0.303 0.349 0.393 0.435 0.476 0.515 0.552 0.587 0.620 0.652 0.682 dU 2.892 2.665 2.490 2.354 2.244 2.153 2.078 2.015 1.963 1.918 1.881 1.849 1.821 1.797 1.776 dL 0.105 0.140 0.183 0.226 0.269 0.313 0.355 0.396 0.436 0.474 0.510 0.545 0.578 0.610 dU 3.053 2.838 2.667 2.530 2.416 2.319 2.238 2.169 2.110 2.059 2.015 1.977 1.944 1.915 dL 0.090 0.122 0.161 0.200 0.241 0.282 0.322 0.362 0.400 0.437 0.473 0.507 0.540 dU 3.182 2.981 2.817 2.681 2.566 2.467 2.381 2.308 2.244 2.188 2.140 2.097 2.059 dL 0.078 0.107 0.142 0.179 0.216 0.255 0.294 0.331 0.368 0.404 0.439 0.473 dU 3.287 3.101 2.944 2.811 2.697 2.597 2.510 2.434 2.367 2.308 2.255 2.209 dL 0.068 0.094 0.127 0.160 0.196 0.232 0.268 0.304 0.340 0.375 0.409 dU 3.374 3.201 3.053 2.925 2.813 2.174 2.625 2.548 2.479 2.417 2.362 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 150 200 1.072 1.088 1.104 1.119 1.134 1.147 1.160 1.171 1.184 1.195 1.205 1.217 1.227 1.237 1.246 1.288 1.324 1.356 1.382 1.407 1.429 1.448 1.465 1.481 1.496 1.510 1.522 1.611 1.664 1.222 1.232 1.244 1.254 1.264 1.274 1.283 1.291 1.298 1.307 1.315 1.322 1.330 1.337 1.344 1.376 1.403 1.428 1.449 1.467 1.485 1.501 1.514 1.529 1.541 1.552 1.562 1.637 1.684 1.000 1.019 1.036 1.053 1.070 1.085 1.100 1.114 1.128 1.141 1.153 1.164 1.176 1.187 1.197 1.245 1.285 1.320 1.351 1.377 1.400 1.422 1.440 1.458 1.474 1.489 1.502 1.598 1.653 1.311 1.318 1.325 1.332 1.339 1.345 1.351 1.358 1.364 1.370 1.376 1.383 1.388 1.392 1.398 1.424 1.445 1.466 1.484 1.500 1.514 1.529 1.541 1.553 1.563 1.573 1.582 1.651 1.693 0.928 0.948 0.969 0.988 1.006 1.022 1.039 1.055 1.070 1.085 1.098 1.112 1.124 1.137 1.149 1.201 1.245 1.284 1.317 1.346 1.372 1.395 1.416 1.434 1.452 1.468 1.482 1.584 1.643 1.410 1.413 1.414 1.418 1.421 1.425 1.428 1.432 1.436 1.439 1.442 1.446 1.449 1.452 1.456 1.474 1.491 1.505 1.520 1.534 1.546 1.557 1.568 1.577 1.587 1.596 1.604 1.665 1.704 0.855 0.878 0.901 0.921 0.941 0.960 0.978 0.995 1.012 1.028 1.043 1.058 1.072 1.085 1.098 1.156 1.206 1.246 1.283 1.314 1.343 1.368 1.390 1.411 1.429 1.446 1.461 1.571 1.633 1.517 1.514 1.512 1.511 1.510 1.509 1.509 1.510 1.511 1.512 1.513 1.514 1.515 1.517 1.518 1.528 1.537 1.548 1.559 1.568 1.577 1.586 1.595 1.603 1.611 1.618 1.625 1.679 1.715 0.782 0.808 0.832 0.855 0.877 0.897 0.917 0.935 0.954 0.971 0.987 1.004 1.019 1.033 1.047 1.111 1.164 1.209 1.248 1.283 1.313 1.340 1.364 1.386 1.406 1.425 1.441 1.557 1.623 1.635 1.625 1.618 1.611 1.606 1.601 1.597 1.594 1.591 1.589 1.587 1.585 1.584 1.583 1.583 1.583 1.587 1.592 1.598 1.604 1.611 1.617 1.624 1.630 1.636 1.641 1.647 1.693 1.725 0.711 0.738 0.764 0.788 0.812 0.834 0.856 0.876 0.896 0.914 0.932 0.950 0.966 0.982 0.997 1.065 1.123 1.172 1.214 1.251 1.283 1.313 1.338 1.362 1.383 1.403 1.421 1.543 1.613 1.759 1.743 1.729 1.718 1.707 1.698 1.690 1.683 1.677 1.671 1.666 1.662 1.658 1.655 1.652 1.643 1.639 1.638 1.639 1.642 1.645 1.649 1.653 1.657 1.661 1.666 1.670 1.708 1.735 0.640 0.669 0.696 0.723 0.748 0.772 0.794 0.816 0.837 0.857 0.877 0.895 0.913 0.930 0.946 1.019 1.081 1.134 1.179 1.218 1.253 1.284 1.312 1.337 1.360 1.381 1.400 1.530 1.603 1.889 1.867 1.847 1.830 1.814 1.800 1.788 1.776 1.766 1.757 1.749 1.742 1.735 1.729 1.724 1.704 1.692 1.685 1.682 1.680 1.680 1.682 1.683 1.685 1.687 1.690 1.693 1.722 1.746 0.572 0.602 0.630 0.658 0.684 0.710 0.734 0.757 0.779 0.800 0.821 0.841 0.860 0.878 0.895 0.974 1.039 1.095 1.144 1.186 1.223 1.256 1.285 1.312 1.336 1.358 1.378 1.515 1.592 2.026 1.997 1.970 1.947 1.925 1.906 1.889 1.874 1.860 1.847 1.836 1.825 1.816 1.807 1.799 1.768 1.748 1.734 1.726 1.720 1.716 1.714 1.714 1.714 1.714 1.715 1.717 1.737 1.757 0.505 0.536 0.566 0.595 0.622 0.649 0.674 0.698 0.722 0.744 0.766 0.787 0.807 0.826 0.844 0.927 0.997 1.057 1.108 1.153 1.192 1.227 1.259 1.287 1.312 1.336 1.357 1.501 1.582 2.168 2.131 2.098 2.068 2.041 2.017 1.995 1.975 1.957 1.940 1.925 1.911 1.899 1.887 1.876 1.834 1.805 1.785 1.771 1.761 1.754 1.748 1.745 1.743 1.741 1.741 1.741 1.752 1.768 0.441 0.473 0.504 0.533 0.562 0.589 0.615 0.641 0.665 0.689 0.711 0.733 0.754 0.774 0.749 0.881 0.955 1.018 1.072 1.120 1.162 1.199 1.232 1.262 1.288 1.313 1.335 1.486 1.571 2.313 2.269 2.229 2.193 2.160 2.131 2.104 2.080 2.057 2.037 2.018 2.001 1.985 1.970 1.956 1.902 1.864 1.837 1.817 1.802 1.792 1.783 1.777 1.773 1.769 1.767 1.765 1.767 1.779 *k’ is the number of regressors excluding the intercept Durbin-Watson Significance Tables k’*=11 n 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 150 200 dL 0.060 0.084 0.113 0.145 0.178 0.212 0.246 0.281 0.315 0.348 0.381 0.413 0.444 0.474 0.503 0.531 0.558 0.585 0.610 0.634 0.658 0.680 0.702 0.723 0.744 0.835 0.913 0.979 1.037 1.087 1.131 1.170 1.205 1.236 1.264 1.290 1.314 1.473 1.561 dU 3.446 3.286 3.146 3.023 2.914 2.817 2.729 2.651 2.580 2.517 2.460 2.409 2.363 2.321 2.283 2.248 2.216 2.187 2.160 2.136 2.113 2.092 2.073 2.055 2.039 1.972 1.925 1.891 1.865 1.845 1.831 1.819 1.810 1.803 1.798 1.793 1.790 1.783 1.791 k’=12 dL 0.053 0.075 0.102 0.131 0.162 0.194 0.227 0.260 0.292 0.324 0.356 0.387 0.417 0.447 0.475 0.503 0.530 0.556 0.581 0.605 0.628 0.651 0.673 0.694 0.790 0.871 0.940 1.001 1.053 1.099 1.141 1.177 1.210 1.240 1.267 1.292 1.458 1.550 dU 3.506 3.358 3.227 3.109 3.004 2.909 2.822 2.744 2.674 2.610 2.552 2.499 2.451 2.407 2.367 2.330 2.296 2.266 2.237 2.210 2.186 2.164 2.143 2.123 2.044 1.987 1.945 1.914 1.889 1.870 1.856 1.844 1.834 1.827 1.821 1.816 1.799 1.801 k’=13 dL 0.047 0.067 0.092 0.119 0.148 0.178 0.209 0.240 0.272 0.303 0.333 0.363 0.393 0.422 0.450 0.477 0.503 0.529 0.554 0.578 0.601 0.623 0.645 0.744 0.829 0.902 0.965 1.020 1.068 1.111 1.150 1.184 1.215 1.244 1.270 1.444 1.539 dU 3.557 3.420 3.297 3.185 3.084 2.991 2.906 2.829 2.758 2.694 2.635 2.582 2.533 2.487 2.446 2.408 2.373 2.340 2.310 2.282 2.256 2.232 2.210 2.118 2.051 2.002 1.964 1.934 1.911 1.893 1.878 1.866 1.856 1.848 1.841 1.814 1.813 k’=14 dL 0.043 0.061 0.084 0.109 0.136 0.165 0.194 0.224 0.253 0.283 0.313 0.342 0.371 0.399 0.426 0.452 0.478 0.504 0.528 0.552 0.575 0.597 0.700 0.787 0.863 0.929 0.986 1.037 1.082 1.122 1.158 1.191 1.221 1.248 1.429 1.528 dU 3.601 3.474 3.358 3.252 3.155 3.065 2.982 2.906 2.836 2.772 2.713 2.659 2.609 2.563 2.520 2.481 2.444 2.410 2.379 2.350 2.323 2.297 2.193 2.116 2.059 2.015 1.980 1.953 1.931 1.913 1.898 1.886 1.876 1.868 1.830 1.824 k’=15 dL 0.038 0.055 0.077 0.100 0.125 0.152 0.180 0.208 0.237 0.266 0.294 0.322 0.350 0.377 0.404 0.430 0.455 0.480 0.504 0.528 0.551 0.655 0.746 0.825 0.893 0.953 1.005 1.052 1.094 1.132 1.166 1.197 1.225 1.414 1.518 *k’ is the number of regressors excluding the intercept dU 3.639 3.521 3.412 3.311 3.218 3.131 3.050 2.976 2.907 2.843 2.785 2.730 2.680 2.633 2.590 2.550 2.512 2.477 2.445 2.414 2.386 2.269 2.182 2.117 2.067 2.027 1.995 1.970 1.949 1.931 1.917 1.905 1.895 1.847 1.836 k’=16 dL 0.035 0.050 0.070 0.092 0.116 0.141 0.167 0.194 0.222 0.249 0.277 0.304 0.331 0.357 0.383 0.409 0.434 0.458 0.482 0.505 0.612 0.705 0.786 0.857 0.919 0.974 1.023 1.066 1.106 1.141 1.174 1.203 1.400 1.507 dU 3.671 3.562 3.459 3.363 3.274 3.191 3.113 3.040 2.972 2.909 2.851 2.797 2.746 2.699 2.655 2.614 2.576 2.540 2.507 2.476 2.346 2.250 2.176 2.120 2.075 2.038 2.009 1.984 1.965 1.948 1.943 1.922 1.863 1.847 k’=17 dL 0.032 0.046 0.065 0.085 0.107 0.131 0.156 0.182 0.208 0.234 0.261 0.287 0.313 0.339 0.364 0.389 0.414 0.438 0.461 0.570 0.665 0.748 0.822 0.886 0.943 0.993 1.039 1.080 1.116 1.150 1.181 1.385 1.495 dU 3.700 3.597 3.501 3.410 3.325 3.245 3.169 3.098 3.032 2.970 2.912 2.858 2.808 2.761 2.717 2.675 2.637 2.600 2.566 2.424 2.318 2.237 2.173 2.123 2.082 2.049 2.022 1.999 1.979 1.963 1.949 1.880 1.860 k’=18 dL 0.029 0.043 0.060 0.079 0.100 0.122 0.146 0.171 0.193 0.221 0.246 0.272 0.297 0.322 0.347 0.371 0.395 0.418 0.528 0.625 0.711 0.786 0.852 0.911 0.964 1.011 1.053 1.091 1.126 1.158 1.370 1.484 dU 3.725 3.629 3.538 3.452 3.371 3.294 3.220 3.152 3.087 3.026 2.969 2.915 2.865 2.818 2.774 2.733 2.694 2.657 2.503 2.387 2.298 2.227 2.172 2.127 2.090 2.059 2.033 2.012 1.993 1.977 1.897 1.871 k’=19 dL 0.027 0.039 0.055 0.073 0.093 0.114 0.137 0.160 0.184 0.209 0.233 0.257 0.282 0.306 0.330 0.354 0.377 0.488 0.586 0.674 0.751 0.819 0.880 0.934 0.983 1.027 1.066 1.102 1.136 1.355 1.474 dU 3.747 3.657 3.572 3.490 3.412 3.338 3.267 3.201 3.137 3.078 3.022 2.969 2.919 2.872 2.828 2.787 2.748 2.582 2.456 2.359 2.283 2.221 2.172 2.131 2.097 2.068 2.044 2.023 2.006 1.913 1.883 k’=20 dL 0.025 0.036 0.051 0.068 0.087 0.107 0.128 0.151 0.174 0.197 0.221 0.244 0.268 0.291 0.315 0.338 0.448 0.548 0.637 0.716 0.789 0.849 0.905 0.955 1.000 1.041 1.079 1.113 1.340 1.462 dU 3.766 3.682 3.602 3.524 3.450 3.379 3.311 3.246 3.184 3.126 3.071 3.019 2.969 2.923 2.879 2.838 2.661 2.526 2.421 2.338 2.272 2.217 2.172 2.135 2.104 2.077 2.054 2.034 1.931 1.896 Appendix A Table A-2 Models with an intercept (from Savin and White) Durbin-Watson Statistic: Per Cent Significance Points of dL and dU k’*=1 k’=2 k’=3 k’=4 k’=5 k’=6 k’=7 k’=8 k’=9 k’=10 n 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 dL 0.610 0.700 0.763 0.824 0.879 0.927 0.971 1.010 1.045 1.077 1.106 1.133 1.158 1.180 1.201 1.221 1.239 1.257 1.273 1.288 dU 1.400 1.356 1.332 1.320 1.320 1.324 1.331 1.340 1.350 1.361 1.371 1.381 1.391 1.401 1.411 1.420 1.429 1.437 1.446 1.454 dL 0.467 0.559 0.629 0.697 0.758 0.812 0.861 0.905 0.946 0.982 1.015 1.046 1.074 1.100 1.125 1.147 1.168 1.188 1.206 dU 1.896 1.777 1.699 1.641 1.604 1.579 1.562 1.551 1.543 1.539 1.536 1.535 1.536 1.537 1.538 1.541 1.543 1.546 1.550 dL 0.367 0.455 0.525 0.595 0.658 0.715 0.767 0.814 0.857 0.897 0.933 0.967 0.998 1.026 1.053 1.078 1.101 1.123 dU 2.287 2.128 2.016 1.928 1.864 1.816 1.779 1.750 1.728 1.710 1.696 1.685 1.676 1.669 1.664 1.660 1.656 1.654 dL 0.296 0.376 0.444 0.512 0.574 0.632 0.685 0.734 0.779 0.820 0.859 0.894 0.927 0.958 0.986 1.013 1.038 dU 2.588 2.414 2.283 2.177 2.094 2.030 1.977 1.935 1.900 1.872 1.848 1.828 1.812 1.797 1.785 1.775 1.767 dL 0.243 0.315 0.380 0.444 0.505 0.562 0.615 0.664 0.710 0.752 0.792 0.829 0.863 0.895 0.925 0.953 dU 2.822 2.645 2.506 2.390 2.296 2.220 2.157 2.104 2.060 2.023 1.991 1.964 1.940 1.920 1.902 1.886 dL 0.203 0.268 0.328 0.389 0.447 0.502 0.554 0.603 0.649 0.691 0.731 0.769 0.804 0.837 0.868 dU 3.004 2.832 2.692 2.572 2.471 2.388 2.318 2.258 2.206 2.162 2.124 2.090 2.061 2.035 2.013 dL 0.171 0.230 0.286 0.343 0.398 0.451 0.502 0.549 0.595 0.637 0.677 0.715 0.750 0.784 dU 3.149 2.985 2.848 2.727 2.624 2.537 2.461 2.396 2.339 2.290 2.246 2.208 2.174 2.144 dL 0.147 0.200 0.251 0.304 0.356 0.407 0.456 0.502 0.546 0.588 0.628 0.666 0.702 dU 3.266 3.111 2.979 2.860 2.757 2.668 2.589 2.521 2.461 2.407 2.360 2.318 2.280 dL 0.127 0.175 0.222 0.272 0.321 0.369 0.416 0.461 0.504 0.545 0.584 0.621 dU 3.360 3.216 3.090 2.975 2.873 2.783 2.704 2.633 2.571 2.514 2.464 2.419 dL 0.111 0.155 0.198 0.244 0.290 0.336 0.380 0.424 0.465 0.506 0.544 dU 3.438 3.304 3.184 3.073 2.974 2.885 2.806 2.735 2.670 2.613 2.560 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 150 200 1.302 1.316 1.328 1.341 1.352 1.363 1.373 1.383 1.393 1.402 1.411 1.419 1.427 1.435 1.442 1.475 1.503 1.528 1.549 1.567 1.583 1.598 1.611 1.624 1.635 1.645 1.654 1.720 1.758 1.461 1.469 1.476 1.483 1.489 1.496 1.502 1.508 1.514 1.519 1.525 1.530 1.535 1.540 1.544 1.566 1.585 1.601 1.616 1.629 1.641 1.652 1.662 1.671 1.679 1.687 1.694 1.747 1.779 1.224 1.240 1.255 1.270 1.284 1.297 1.309 1.321 1.333 1.343 1.354 1.364 1.373 1.382 1.391 1.430 1.462 1.490 1.514 1.536 1.554 1.571 1.586 1.600 1.612 1.623 1.634 1.706 1.748 1.553 1.556 1.560 1.563 1.567 1.570 1.574 1.577 1.580 1.584 1.587 1.590 1.594 1.597 1.600 1.615 1.628 1.641 1.652 1.662 1.672 1.680 1.688 1.696 1.703 1.709 1.715 1.760 1.789 1.143 1.162 1.181 1.198 1.214 1.229 1.244 1.258 1.271 1.283 1.295 1.307 1.318 1.328 1.338 1.383 1.421 1.452 1.480 1.503 1.525 1.543 1.560 1.575 1.589 1.602 1.613 1.693 1.738 1.652 1.651 1.650 1.650 1.650 1.650 1.650 1.651 1.652 1.653 1.654 1.655 1.656 1.658 1.659 1.666 1.674 1.681 1.689 1.696 1.703 1.709 1.715 1.721 1.726 1.732 1.736 1.774 1.799 1.062 1.084 1.104 1.124 1.143 1.160 1.177 1.193 1.208 1.222 1.236 1.249 1.261 1.273 1.285 1.336 1.378 1.414 1.444 1.471 1.494 1.515 1.534 1.550 1.566 1.579 1.592 1.679 1.728 1.759 1.753 1.747 1.743 1.739 1.735 1.732 1.730 1.728 1.726 1.724 1.723 1.722 1.722 1.721 1.720 1.721 1.724 1.727 1.731 1.735 1.739 1.743 1.747 1.751 1.755 1.758 1.788 1.809 0.979 1.004 1.028 1.050 1.071 1.090 1.109 1.127 1.144 1.160 1.175 1.190 1.204 1.218 1.230 1.287 1.335 1.374 1.408 1.438 1.464 1.487 1.507 1.525 1.542 1.557 1.571 1.665 1.718 1.873 1.861 1.850 1.841 1.833 1.825 1.819 1.813 1.808 1.803 1.799 1.795 1.792 1.789 1.786 1.776 1.771 1.768 1.767 1.767 1.768 1.770 1.772 1.774 1.776 1.778 1.780 1.802 1.820 0.897 0.925 0.951 0.975 0.998 1.020 1.041 1.061 1.079 1.097 1.114 1.131 1.146 1.161 1.175 1.238 1.291 1.334 1.372 1.404 1.433 1.458 1.480 1.500 1.518 1.535 1.550 1.651 1.707 1.992 1.974 1.959 1.944 1.931 1.920 1.909 1.900 1.891 1.884 1.876 1.870 1.864 1.859 1.854 1.835 1.822 1.814 1.808 1.805 1.802 1.801 1.801 1.801 1.801 1.802 1.803 1.817 1.831 0.816 0.845 0.874 0.900 0.926 0.950 0.972 0.994 1.015 1.034 1.053 1.071 1.088 1.104 1.120 1.189 1.246 1.294 1.335 1.370 1.401 1.428 1.453 1.474 1.494 1.512 1.528 1.637 1.697 2.117 2.093 2.071 2.052 2.034 2.018 2.004 1.991 1.978 1.967 1.957 1.948 1.939 1.932 1.924 1.895 1.875 1.861 1.850 1.843 1.838 1.834 1.831 1.829 1.827 1.827 1.826 1.832 1.841 0.735 0.767 0.798 0.826 0.854 0.879 0.904 0.927 0.950 0.971 0.991 1.011 1.029 1.047 1.064 1.139 1.201 1.253 1.298 1.336 1.369 1.399 1.425 1.448 1.469 1.489 1.506 1.622 1.686 2.246 2.216 2.188 2.164 2.141 2.120 2.102 2.085 2.069 2.054 2.041 2.029 2.017 2.007 1.997 1.958 1.930 1.909 1.894 1.882 1.874 1.867 1.861 1.857 1.854 1.852 1.850 1.846 1.852 0.657 0.691 0.723 0.753 0.782 0.810 0.836 0.861 0.885 0.908 0.930 0.951 0.970 0.990 1.008 1.089 1.156 1.212 1.260 1.301 1.337 1.369 1.397 1.422 1.445 1.465 1.484 1.608 1.675 2.379 2.342 2.309 2.278 2.251 2.226 2.203 2.181 2.162 2.144 2.127 2.112 2.098 2.085 2.072 2.022 1.986 1.959 1.939 1.923 1.910 1.901 1.893 1.886 1.881 1.877 1.874 1.862 1.863 0.581 0.616 0.649 0.681 0.712 0.741 0.769 0.796 0.821 0.845 0.868 0.891 0.912 0.932 0.952 1.038 1.110 1.170 1.222 1.266 1.305 1.339 1.369 1.396 1.420 1.442 1.462 1.593 1.665 2.513 2.470 2.431 2.396 2.363 2.333 2.306 2.281 2.257 2.236 2.216 2.197 2.180 2.164 2.149 2.088 2.044 2.010 1.984 1.964 1.948 1.935 1.925 1.916 1.909 1.903 1.898 1.877 1.874 *k’ is the number of regressors excluding the intercept Durbin-Watson Significance Tables k’*=11 n 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 150 200 dL 0.098 0.138 0.177 0.220 0.263 0.307 0.349 0.391 0.431 0.470 0.508 0.544 0.578 0.612 0.643 0.674 0.703 0.731 0.758 0.783 0.808 0.831 0.854 0.875 0.896 0.988 1.064 1.129 1.184 1.231 1.272 1.308 1.340 1.369 1.395 1.418 1.439 1.579 1.654 dU 3.503 3.378 3.265 3.159 3.063 2.976 2.897 2.826 2.761 2.702 2.649 2.600 2.555 2.515 2.477 2.443 2.411 2.382 2.355 2.330 2.306 2.285 2.265 2.246 2.228 2.156 2.103 2.062 2.031 2.006 1.987 1.970 1.957 1.946 1.937 1.930 1.923 1.892 1.885 k’=12 dL 0.087 0.123 0.160 0.200 0.240 0.281 0.322 0.362 0.400 0.438 0.475 0.510 0.544 0.577 0.608 0.638 0.668 0.695 0.722 0.748 0.772 0.796 0.819 0.840 0.938 1.019 1.087 1.145 1.195 1.239 1.277 1.311 1.342 1.369 1.394 1.416 1.564 1.643 dU 3.557 3.441 3.335 3.234 3.141 3.057 2.979 2.908 2.844 2.784 2.730 2.680 2.634 2.592 2.553 2.517 2.484 2.454 2.425 2.398 2.374 2.351 2.329 2.309 2.225 2.163 2.116 2.079 2.049 2.026 2.006 1.991 1.977 1.966 1.956 1.948 1.908 1.896 k’=13 dL 0.078 0.111 0.145 0.182 0.220 0.259 0.297 0.335 0.373 0.409 0.445 0.479 0.512 0.545 0.576 0.606 0.634 0.662 0.689 0.714 0.739 0.763 0.785 0.887 0.973 1.045 1.106 1.160 1.206 1.247 1.283 1.315 1.344 1.370 1.393 1.550 1.632 dU 3.603 3.496 3.395 3.300 3.211 3.128 3.053 2.983 2.919 2.859 2.805 2.755 2.708 2.665 2.625 2.588 2.554 2.521 2.492 2.464 2.438 2.413 2.391 2.296 2.225 2.170 2.127 2.093 2.066 2.043 2.024 2.009 1.995 1.984 1.974 1.924 1.908 k’=14 dL 0.070 0.100 0.132 0.166 0.202 0.239 0.275 0.312 0.348 0.383 0.418 0.451 0.484 0.515 0.546 0.575 0.604 0.631 0.657 0.683 0.707 0.731 0.838 0.927 1.003 1.068 1.124 1.172 1.215 1.253 1.287 1.318 1.345 1.371 1.535 1.621 dU 3.642 3.542 3.448 3.358 3.272 3.193 3.119 3.051 2.987 2.928 2.874 2.823 2.776 2.733 2.692 2.654 2.619 2.586 2.555 2.526 2.499 2.473 2.367 2.287 2.225 2.177 2.138 2.106 2.080 2.059 2.040 2.025 2.012 2.000 1.940 1.919 k’=15 dL 0.063 0.091 0.120 0.153 0.186 0.221 0.256 0.291 0.325 0.359 0.392 0.425 0.457 0.488 0.518 0.547 0.575 0.602 0.628 0.653 0.678 0.788 0.882 0.961 1.029 1.088 1.139 1.184 1.224 1.260 1.292 1.321 1.347 1.519 1.610 *K’ is the number of regressors excluding the intercept dU 3.676 3.583 3.495 3.409 3.327 3.251 3.179 3.112 3.050 2.992 2.937 2.887 2.840 2.796 2.754 2.716 2.680 2.646 2.614 2.585 2.557 2.439 2.350 2.281 2.227 2.183 2.148 2.118 2.093 2.073 2.055 2.040 2.026 1.956 1.931 k’=16 dL 0.058 0.083 0.110 0.141 0.172 0.205 0.238 0.271 0.305 0.337 0.370 0.401 0.432 0.462 0.492 0.520 0.548 0.575 0.600 0.626 0.740 0.836 0.919 0.990 1.052 1.105 1.153 1.195 1.232 1.266 1.296 1.324 1.504 1.599 dU 3.705 3.619 3.535 3.454 3.376 3.303 3.233 3.168 3.107 3.050 2.996 2.946 2.899 2.854 2.813 2.774 2.738 2.703 2.671 2.641 2.512 2.414 2.338 2.278 2.229 2.189 2.156 2.129 2.105 2.085 2.068 2.053 1.972 1.943 k’=17 dL 0.052 0.076 0.101 0.130 0.160 0.191 0.222 0.254 0.286 0.317 0.349 0.379 0.409 0.439 0.467 0.495 0.522 0.549 0.575 0.692 0.792 0.877 0.951 1.016 1.072 1.121 1.165 1.205 1.240 1.271 1.301 1.489 1.588 dU 3.731 3.650 3.572 3.494 3.420 3.349 3.283 3.219 3.160 3.103 3.050 3.000 2.954 2.910 2.868 2.829 2.792 2.757 2.724 2.586 2.479 2.396 2.330 2.276 2.232 2.195 2.165 2.139 2.116 2.097 2.080 1.989 1.955 k’=18 dL 0.048 0.070 0.094 0.120 0.149 0.178 0.208 0.238 0.269 0.299 0.329 0.359 0.388 0.417 0.445 0.472 0.499 0.525 0.644 0.747 0.836 0.913 0.980 1.038 1.090 1.136 1.177 1.213 1.247 1.277 1.474 1.576 dU 3.753 3.678 3.604 3.531 3.460 3.392 3.327 3.266 3.208 3.153 3.100 3.051 3.005 2.961 2.920 2.880 2.843 2.808 2.659 2.544 2.454 2.382 2.323 2.275 2.235 2.201 2.172 2.148 2.126 2.108 2.006 1.967 k’=19 dL 0.044 0.065 0.087 0.112 0.138 0.166 0.195 0.224 0.253 0.283 0.312 0.340 0.369 0.397 0.424 0.451 0.477 0.598 0.703 0.795 0.874 0.944 1.005 1.058 1.106 1.149 1.187 1.222 1.253 1.458 1.565 dU 3.773 3.702 3.632 3.563 3.495 3.431 3.368 3.309 3.252 3.198 3.147 3.099 3.053 3.009 2.968 2.929 2.829 2.733 2.610 2.512 2.434 2.371 2.318 2.275 2.238 2.206 2.179 2.156 2.135 2.023 1.979 k’=20 dL 0.041 0.060 0.081 0.104 0.129 0.156 0.183 0.211 0.239 0.267 0.295 0.323 0.351 0.378 0.404 0.430 0.553 0.660 0.754 0.836 0.908 0.971 1.027 1.076 1.121 1.160 1.197 1.229 1.443 1.554 dU 3.790 3.724 3.658 3.592 3.528 3.465 3.406 3.348 3.293 3.240 3.190 3.142 3.097 3.054 3.013 2.974 2.807 2.675 2.571 2.487 2.419 2.362 2.315 2.275 2.241 2.211 2.186 2.164 2.040 1.991 Appendix A Table A-3 Models with no intercept (from Farebrother): Positive serial correlation Durbin-Watson One Per Cent Minimal Bound N K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 150 200 0.001 0.034 0.127 0.233 0.322 0.398 0.469 0.534 0.591 0.643 0.691 0.733 0.773 0.809 0.842 0.873 0.901 0.928 0.952 0.976 0.997 1.018 1.037 1.056 1.073 1.089 1.105 1.120 1.134 1.147 1.160 1.173 1.185 1.196 1.207 1.217 1.228 1.237 1.247 1.289 1.325 1.356 1.383 1.408 1.429 1.448 1.466 1.482 1.497 1.510 1.523 1.611 1.664 0.000 0.022 0.089 0.175 0.253 0.324 0.394 0.457 0.515 0.568 0.617 0.662 0.703 0.741 0.776 0.808 0.839 0.867 0.893 0.918 0.942 0.964 0.984 1.004 1.023 1.040 1.057 1.073 1.088 1.103 1.117 1.130 1.143 1.155 1.167 1.178 1.189 1.200 1.247 1.287 1.321 1.351 1.378 1.401 1.423 1.442 1.459 1.475 1.490 1.503 1.598 1.654 0.000 0.014 0.065 0.135 0.202 0.268 0.333 0.394 0.451 0.503 0.552 0.598 0.640 0.679 0.715 0.749 0.780 0.810 0.838 0.864 0.889 0.912 0.934 0.955 0.974 0.993 1.011 1.028 1.044 1.060 1.075 1.089 1.102 1.116 1.128 1.140 1.152 1.204 1.248 1.286 1.319 1.348 1.373 1.396 1.417 1.436 1.453 1.469 1.483 1.585 1.644 0.000 0.010 0.049 0.106 0.164 0.223 0.284 0.341 0.396 0.448 0.496 0.541 0.583 0.623 0.660 0.694 0.727 0.757 0.786 0.813 0.839 0.863 0.886 0.908 0.929 0.948 0.967 0.985 1.002 1.018 1.034 1.049 1.063 1.077 1.090 1.103 1.160 1.208 1.250 1.285 1.317 1.345 1.369 1.392 1.412 1.431 1.448 1.463 1.571 1.634 0.000 0.008 0.038 0.086 0.136 0.189 0.244 0.298 0.350 0.400 0.447 0.491 0.533 0.572 0.609 0.644 0.677 0.709 0.738 0.766 0.792 0.817 0.841 0.864 0.885 0.905 0.925 0.944 0.961 0.978 0.995 1.010 1.026 1.040 1.054 1.116 1.168 1.213 1.252 1.286 1.316 1.342 1.367 1.388 1.408 1.426 1.443 1.558 1.624 0.000 0.006 0.031 0.070 0.114 0.161 0.212 0.262 0.311 0.358 0.404 0.447 0.488 0.527 0.564 0.599 0.632 0.664 0.693 0.722 0.749 0.774 0.798 0.822 0.844 0.865 0.885 0.904 0.923 0.940 0.957 0.974 0.989 1.004 1.071 1.128 1.176 1.218 1.254 1.286 1.315 1.341 1.364 1.385 1.405 1.422 1.544 1.613 0.000 0.005 0.025 0.059 0.097 0.139 0.185 0.232 0.278 0.323 0.366 0.408 0.448 0.486 0.523 0.558 0.591 0.622 0.652 0.681 0.708 0.734 0.759 0.782 0.805 0.826 0.847 0.867 0.886 0.904 0.921 0.938 0.954 1.026 1.087 1.139 1.183 1.222 1.257 1.287 1.315 1.340 1.362 1.383 1.402 1.530 1.603 0.000 0.004 0.021 0.050 0.083 0.121 0.163 0.206 0.249 0.292 0.333 0.374 0.413 0.450 0.486 0.520 0.553 0.584 0.614 0.643 0.670 0.696 0.721 0.745 0.768 0.790 0.811 0.831 0.850 0.869 0.887 0.904 0.981 1.046 1.101 1.149 1.190 1.227 1.260 1.289 1.315 1.339 1.361 1.381 1.516 1.593 0.000 0.003 0.018 0.043 0.072 0.107 0.145 0.184 0.225 0.265 0.304 0.343 0.381 0.417 0.452 0.486 0.518 0.549 0.579 0.607 0.635 0.661 0.686 0.710 0.733 0.755 0.777 0.797 0.817 0.836 0.854 0.936 1.004 1.063 1.114 1.158 1.197 1.231 1.262 1.290 1.315 1.338 1.359 1.502 1.582 0.000 0.003 0.015 0.037 0.063 0.094 0.129 0.166 0.204 0.241 0.279 0.316 0.352 0.387 0.421 0.454 0.486 0.517 0.546 0.574 0.602 0.628 0.653 0.677 0.700 0.723 0.744 0.765 0.785 0.804 0.890 0.963 1.025 1.078 1.125 1.166 1.203 1.236 1.265 1.292 1.316 1.338 1.488 1.572 K=10 K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20 K=21 0.000 0.002 0.013 0.032 0.056 0.084 0.116 0.150 0.185 0.221 0.257 0.292 0.327 0.361 0.394 0.426 0.457 0.487 0.516 0.544 0.571 0.597 0.622 0.646 0.669 0.692 0.713 0.734 0.754 0.845 0.921 0.987 1.043 1.092 1.136 1.174 1.209 1.240 1.268 1.293 1.317 1.474 1.561 0.000 0.002 0.011 0.028 0.050 0.075 0.105 0.136 0.169 0.203 0.237 0.270 0.304 0.336 0.368 0.400 0.430 0.460 0.488 0.516 0.542 0.568 0.593 0.617 0.640 0.663 0.684 0.705 0.800 0.880 0.948 1.008 1.059 1.105 1.146 1.182 1.214 1.244 1.271 1.295 1.460 1.551 0.000 0.002 0.010 0.025 0.044 0.068 0.095 0.124 0.155 0.187 0.219 0.251 0.283 0.314 0.345 0.376 0.405 0.434 0.462 0.489 0.516 0.541 0.566 0.590 0.613 0.635 0.657 0.755 0.838 0.910 0.972 1.026 1.074 1.117 1.155 1.189 1.220 1.248 1.273 1.445 1.540 0.000 0.002 0.009 0.023 0.040 0.062 0.087 0.114 0.143 0.172 0.203 0.233 0.264 0.294 0.324 0.354 0.383 0.411 0.438 0.465 0.491 0.516 0.540 0.564 0.587 0.609 0.710 0.797 0.872 0.936 0.993 1.043 1.088 1.127 1.163 1.195 1.225 1.251 1.431 1.529 0.000 0.001 0.008 0.020 0.036 0.056 0.079 0.104 0.131 0.160 0.189 0.218 0.247 0.276 0.305 0.334 0.362 0.389 0.416 0.442 0.467 0.492 0.516 0.540 0.562 0.666 0.756 0.833 0.901 0.960 1.012 1.058 1.100 1.137 1.171 1.201 1.229 1.416 1.519 0.000 0.001 0.007 0.018 0.033 0.051 0.073 0.096 0.122 0.148 0.176 0.204 0.232 0.260 0.288 0.315 0.342 0.369 0.395 0.421 0.446 0.470 0.494 0.517 0.623 0.715 0.796 0.865 0.927 0.981 1.029 1.072 1.111 1.146 1.178 1.207 1.402 1.508 0.000 0.001 0.006 0.017 0.030 0.047 0.067 0.089 0.113 0.138 0.164 0.191 0.217 0.244 0.271 0.298 0.324 0.350 0.376 0.401 0.425 0.449 0.473 0.581 0.675 0.758 0.830 0.894 0.950 1.000 1.045 1.085 1.121 1.155 1.185 1.387 1.497 0.000 0.001 0.006 0.015 0.027 0.043 0.062 0.083 0.105 0.129 0.154 0.179 0.205 0.230 0.256 0.282 0.308 0.333 0.358 0.382 0.406 0.430 0.539 0.636 0.721 0.795 0.861 0.919 0.971 1.017 1.059 1.097 1.131 1.162 1.372 1.486 0.000 0.001 0.005 0.014 0.025 0.040 0.057 0.077 0.098 0.120 0.144 0.168 0.193 0.218 0.243 0.268 0.292 0.317 0.341 0.365 0.388 0.499 0.597 0.684 0.760 0.828 0.888 0.941 0.989 1.033 1.072 1.108 1.140 1.357 1.475 0.000 0.001 0.005 0.013 0.023 0.037 0.053 0.071 0.091 0.113 0.135 0.158 0.182 0.206 0.230 0.254 0.278 0.302 0.325 0.349 0.459 0.559 0.647 0.725 0.795 0.857 0.912 0.962 1.006 1.047 1.084 1.118 1.342 1.434 0.000 0.001 0.004 0.012 0.022 0.034 0.050 0.067 0.086 0.106 0.127 0.149 0.172 0.195 0.218 0.241 0.265 0.288 0.311 0.421 0.521 0.611 0.691 0.762 0.826 0.883 0.934 0.980 1.022 1.060 1.095 1.327 1.453 0.000 0.001 0.004 0.011 0.020 0.032 0.046 0.062 0.080 0.100 0.120 0.141 0.163 0.185 0.207 0.230 0.252 0.275 0.384 0.485 0.576 0.657 0.730 0.795 0.854 0.907 0.954 0.997 1.037 1.072 1.312 1.442 Durbin-Watson Significance Tables Table A-4 Models with no intercept (from Farebrother): Positive serial correlation Durbin-Watson Five Per Cent Minimal Bound N 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 K=0 0.012 0.168 0.355 0.478 0.584 0.677 0.754 0.820 0.877 0.927 0.972 1.012 1.047 1.079 1.109 1.136 1.160 1.183 1.204 1.224 1.242 1.259 1.275 1.290 1.304 1.318 1.330 1.342 1.354 1.365 1.375 1.385 1.394 1.403 1.412 1.420 1.428 1.436 1.443 1.476 1.504 1.528 1.549 K=1 0.006 0.105 0.248 0.358 0.462 0.556 0.635 0.706 0.768 0.823 0.872 0.916 0.955 0.992 1.024 1.055 1.082 1.108 1.132 1.154 1.175 1.194 1.212 1.229 1.245 1.260 1.275 1.288 1.301 1.313 1.325 1.336 1.347 1.357 1.367 1.376 1.385 1.394 1.432 1.464 1.492 1.516 K=2 0.004 0.070 0.180 0.275 0.371 0.460 0.539 0.610 0.674 0.731 0.783 0.829 0.872 0.911 0.946 0.979 1.010 1.038 1.064 1.088 1.111 1.132 1.152 1.171 1.188 1.205 1.221 1.236 1.250 1.264 1.277 1.289 1.301 1.312 1.323 1.333 1.343 1.387 1.424 1.455 1.482 K=3 0.002 0.050 0.136 0.217 0.303 0.385 0.460 0.530 0.593 0.651 0.704 0.752 0.797 0.837 0.875 0.910 0.942 0.972 1.000 1.026 1.050 1.073 1.094 1.115 1.134 1.152 1.169 1.185 1.201 1.216 1.230 1.243 1.256 1.268 1.280 1.291 1.341 1.382 1.417 1.447 K=4 0.002 0.037 0.106 0.175 0.251 0.326 0.397 0.464 0.525 0.583 0.635 0.684 0.729 0.771 0.810 0.846 0.879 0.911 0.940 0.967 0.993 1.017 1.040 1.062 1.082 1.101 1.120 1.137 1.153 1.169 1.184 1.199 1.212 1.225 1.238 1.294 1.340 1.379 1.412 K=5 0.001 0.029 0.085 0.143 0.211 0.279 0.345 0.408 0.467 0.523 0.575 0.624 0.669 0.711 0.751 0.787 0.822 0.854 0.884 0.913 0.940 0.965 0.989 1.011 1.033 1.053 1.072 1.091 1.108 1.125 1.141 1.156 1.170 1.184 1.246 1.297 1.340 1.376 K=6 0.001 0.023 0.069 0.120 0.180 0.241 0.302 0.361 0.418 0.472 0.523 0.570 0.615 0.657 0.697 0.734 0.769 0.802 0.833 0.862 0.889 0.916 0.940 0.964 0.986 1.007 1.027 1.046 1.064 1.082 1.099 1.114 1.130 1.197 1.253 1.300 1.340 K=7 0.001 0.019 0.058 0.101 0.154 0.210 0.266 0.322 0.376 0.427 0.476 0.523 0.567 0.609 0.648 0.685 0.720 0.753 0.785 0.815 0.843 0.869 0.895 0.919 0.942 0.963 0.984 1.004 1.023 1.041 1.058 1.075 1.148 1.209 1.260 1.303 K=8 0.001 0.016 0.049 0.087 0.134 0.185 0.237 0.288 0.339 0.388 0.436 0.481 0.524 0.565 0.604 0.641 0.676 0.709 0.741 0.770 0.799 0.826 0.852 0.876 0.900 0.922 0.943 0.964 0.983 1.002 1.020 1.099 1.164 1.219 1.266 K=9 0.001 0.013 0.042 0.075 0.118 0.164 0.211 0.260 0.307 0.354 0.400 0.443 0.485 0.525 0.563 0.600 0.635 0.668 0.699 0.729 0.758 0.785 0.811 0.836 0.860 0.883 0.905 0.925 0.945 0.965 1.049 1.120 1.179 1.229 K=10 0.001 0.011 0.036 0.066 0.104 0.146 0.190 0.235 0.280 0.324 0.368 0.410 0.450 0.489 0.527 0.563 0.597 0.630 0.661 0.691 0.720 0.747 0.774 0.799 0.823 0.846 0.868 0.889 0.909 1.000 1.075 1.138 1.191 K=11 0.001 0.010 0.031 0.058 0.093 0.131 0.171 0.213 0.256 0.298 0.339 0.380 0.419 0.457 0.493 0.529 0.562 0.595 0.626 0.653 0.684 0.712 0.738 0.763 0.787 0.811 0.833 0.854 0.950 1.029 1.096 1.153 K=12 0.001 0.008 0.028 0.052 0.083 0.118 0.156 0.195 0.235 0.274 0.314 0.353 0.390 0.427 0.463 0.497 0.530 0.562 0.593 0.623 0.651 0.678 0.705 0.730 0.754 0.778 0.800 0.900 0.984 1.055 1.115 K=13 0.001 0.007 0.025 0.046 0.075 0.107 0.142 0.178 0.216 0.254 0.291 0.328 0.365 0.400 0.435 0.468 0.501 0.532 0.563 0.592 0.620 0.647 0.673 0.698 0.723 0.746 0.851 0.939 1.013 1.077 K=14 0.000 0.007 0.022 0.041 0.067 0.097 0.130 0.164 0.199 0.235 0.271 0.306 0.341 0.376 0.409 0.442 0.474 0.504 0.534 0.563 0.591 0.618 0.644 0.669 0.693 0.802 0.894 0.972 1.038 K=15 0.000 0.006 0.020 0.037 0.061 0.089 0.119 0.151 0.184 0.218 0.252 0.286 0.320 0.353 0.386 0.418 0.449 0.479 0.508 0.536 0.564 0.590 0.616 0.641 0.753 0.849 0.930 1.000 K=16 0.000 0.005 0.018 0.034 0.056 0.081 0.110 0.140 0.171 0.203 0.236 0.268 0.301 0.333 0.364 0.395 0.425 0.455 0.483 0.511 0.538 0.564 0.590 0.706 0.804 0.889 0.962 K=17 0.000 0.005 0.016 0.031 0.051 0.075 0.101 0.130 0.159 0.190 0.221 0.252 0.283 0.314 0.344 0.374 0.404 0.432 0.460 0.488 0.514 0.540 0.658 0.760 0.848 0.923 K=18 0.000 0.004 0.015 0.028 0.047 0.069 0.094 0.120 0.148 0.177 0.207 0.237 0.267 0.297 0.326 0.355 0.384 0.412 0.439 0.466 0.492 0.612 0.717 0.807 0.885 K=19 0.000 0.004 0.014 0.026 0.044 0.064 0.087 0.112 0.139 0.166 0.195 0.223 0.252 0.280 0.309 0.337 0.365 0.392 0.419 0.445 0.567 0.674 0.766 0.847 K=20 0.000 0.004 0.012 0.024 0.040 0.060 0.081 0.105 0.130 0.156 0.183 0.211 0.238 0.266 0.293 0.321 0.347 0.374 0.400 0.523 0.631 0.726 0.810 K=21 0.000 0.003 0.011 0.022 0.037 0.055 0.076 0.098 0.122 0.147 0.173 0.199 0.225 0.252 0.279 0.305 0.331 0.357 0.480 0.590 0.687 0.772 65 70 75 80 85 90 95 100 150 200 1.568 1.584 1.599 1.612 1.624 1.635 1.645 1.654 1.720 1.759 1.537 1.555 1.572 1.587 1.600 1.613 1.624 1.634 1.706 1.748 1.505 1.526 1.545 1.561 1.576 1.590 1.603 1.614 1.693 1.738 1.474 1.497 1.517 1.536 1.552 1.567 1.581 1.593 1.679 1.728 1.441 1.467 1.489 1.509 1.527 1.544 1.559 1.573 1.666 1.718 1.408 1.436 1.461 1.483 1.502 1.520 1.537 1.551 1.652 1.708 1.375 1.405 1.432 1.456 1.477 1.497 1.514 1.530 1.638 1.697 1.341 1.374 1.403 1.429 1.452 1.472 1.491 1.508 1.624 1.687 1.307 1.342 1.373 1.401 1.426 1.448 1.468 1.487 1.609 1.676 1.272 1.310 1.344 1.373 1.400 1.423 1.445 1.465 1.595 1.666 1.238 1.278 1.313 1.345 1.373 1.399 1.422 1.442 1.580 1.655 1.202 1.245 1.283 1.317 1.347 1.373 1.398 1.420 1.566 1.644 1.167 1.213 1.253 1.288 1.320 1.348 1.374 1.397 1.551 1.633 1.132 1.180 1.222 1.259 1.293 1.323 1.350 1.374 1.536 1.622 1.096 1.147 1.191 1.230 1.266 1.297 1.326 1.352 1.521 1.611 1.061 1.113 1.160 1.201 1.238 1.271 1.301 1.328 1.506 1.600 1.025 1.080 1.129 1.172 1.211 1.245 1.277 1.305 1.491 1.589 0.989 1.047 1.098 1.143 1.183 1.219 1.252 1.282 1.476 1.578 0.953 1.013 1.066 1.113 1.155 1.193 1.227 1.258 1.461 1.567 0.918 0.980 1.035 1.084 1.128 1.167 1.202 1.235 1.445 1.556 0.882 0.947 1.004 1.054 1.100 1.141 1.177 1.211 1.430 1.544 0.847 0.914 0.972 1.025 1.072 1.114 1.152 1.187 1.414 1.533 10 Appendix A Table A-5 Models with no intercept (from Farebrother): Negative serial correlation Durbin-Watson Ninety Five Per Cent Minimal Bound N 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 K=0 1.988 2.761 2.871 2.857 2.844 2.828 2.805 2.783 2.762 2.742 2.723 2.705 2.688 2.672 2.657 2.644 2.631 2.618 2.607 2.596 2.585 2.575 2.566 2.557 1.073 1.089 1.105 1.120 1.134 1.147 1.160 1.173 1.185 1.196 1.207 1.217 1.228 1.237 1.247 1.289 1.325 1.356 1.383 K=1 0.994 1.836 2.178 2.320 2.398 2.453 2.483 2.501 2.511 2.516 2.518 2.517 2.515 2.512 2.508 2.504 2.499 2.494 2.489 2.484 2.479 2.474 2.470 1.004 1.023 1.040 1.057 1.073 1.088 1.103 1.117 1.130 1.143 1.155 1.167 1.178 1.189 1.200 1.247 1.287 1.321 1.351 K=2 0.582 1.267 1.655 1.871 2.008 2.110 2.181 2.231 2.268 2.296 2.316 2.332 2.344 2.353 2.359 2.364 2.368 2.370 2.372 2.373 2.373 2.373 0.934 0.955 0.974 0.993 1.011 1.028 1.044 1.060 1.075 1.089 1.102 1.116 1.128 1.140 1.152 1.204 1.248 1.286 1.319 K=3 0.380 0.917 1.283 1.521 1.687 1.816 1.913 1.987 2.044 2.090 2.126 2.155 2.179 2.199 2.215 2.228 2.239 2.249 2.257 2.263 2.269 0.863 0.886 0.908 0.929 0.948 0.967 0.985 1.002 1.018 1.034 1.049 1.063 1.077 1.090 1.103 1.160 1.208 1.250 1.285 K=4 0.266 0.690 1.017 1.251 1.427 1.569 1.682 1.771 1.843 1.902 1.950 1.990 2.024 2.053 2.077 2.098 2.116 2.131 2.145 2.156 0.792 0.817 0.841 0.864 0.885 0.905 0.925 0.944 0.961 0.978 0.995 1.010 1.026 1.040 1.054 1.116 1.168 1.213 1.252 K=5 0.197 0.537 0.823 1.044 1.218 1.364 1.484 1.582 1.664 1.732 1.789 1.838 1.880 1.916 1.947 1.974 1.998 2.019 2.037 0.722 0.749 0.774 0.798 0.822 0.844 0.865 0.885 0.904 0.923 0.940 0.957 0.974 0.989 1.004 1.071 1.128 1.176 1.218 K=6 0.151 0.429 0.678 0.881 1.049 1.193 1.316 1.419 1.506 1.580 1.644 1.699 1.747 1.789 1.825 1.858 1.886 1.912 0.652 0.681 0.708 0.734 0.759 0.782 0.805 0.826 0.847 0.867 0.886 0.904 0.921 0.938 0.954 1.026 1.087 1.139 1.183 K=7 0.120 0.350 0.567 0.752 0.911 1.051 1.172 1.276 1.367 1.445 1.513 1.573 1.625 1.671 1.712 1.749 1.782 0.584 0.614 0.643 0.670 0.696 0.721 0.745 0.768 0.790 0.811 0.831 0.850 0.869 0.887 0.904 0.981 1.046 1.101 1.149 K=8 0.097 0.291 0.481 0.649 0.797 0.931 1.049 1.153 1.244 1.324 1.395 1.457 1.513 1.563 1.607 1.647 0.518 0.549 0.579 0.607 0.635 0.661 0.686 0.710 0.733 0.755 0.777 0.797 0.817 0.836 0.854 0.936 1.004 1.063 1.114 K=9 0.080 0.245 0.413 0.565 0.703 0.829 0.944 1.045 1.136 1.216 1.289 1.353 1.411 1.463 1.510 0.454 0.486 0.517 0.546 0.574 0.602 0.628 0.653 0.677 0.700 0.723 0.744 0.765 0.785 0.804 0.890 0.963 1.025 1.078 K=10 0.068 0.210 0.358 0.497 0.624 0.743 0.852 0.951 1.040 1.120 1.193 1.258 1.318 1.371 0.394 0.426 0.457 0.487 0.516 0.544 0.571 0.597 0.622 0.646 0.669 0.692 0.713 0.734 0.754 0.845 0.921 0.987 1.043 K=11 0.058 0.181 0.314 0.439 0.557 0.669 0.773 0.868 0.955 1.034 1.107 1.172 1.232 0.336 0.368 0.400 0.430 0.460 0.488 0.516 0.542 0.568 0.593 0.617 0.640 0.663 0.684 0.705 0.800 0.880 0.948 1.008 K=12 0.050 0.158 0.277 0.391 0.501 0.605 0.704 0.796 0.880 0.957 1.029 1.094 0.283 0.314 0.345 0.376 0.405 0.434 0.462 0.489 0.516 0.541 0.566 0.590 0.613 0.635 0.657 0.755 0.838 0.910 0.972 K=13 0.043 0.139 0.246 0.351 0.452 0.550 0.644 0.731 0.813 0.888 0.958 0.233 0.264 0.294 0.324 0.354 0.383 0.411 0.438 0.465 0.491 0.516 0.540 0.564 0.587 0.609 0.710 0.797 0.872 0.936 K=14 0.038 0.124 0.220 0.316 0.410 0.502 0.591 0.674 0.753 0.826 0.189 0.218 0.247 0.276 0.305 0.334 0.362 0.389 0.416 0.442 0.467 0.492 0.516 0.540 0.562 0.666 0.756 0.833 0.901 K=15 0.034 0.110 0.198 0.286 0.373 0.460 0.544 0.623 0.699 0.148 0.176 0.204 0.232 0.260 0.288 0.315 0.342 0.369 0.395 0.421 0.446 0.470 0.494 0.517 0.623 0.715 0.796 0.865 K=16 0.030 0.099 0.179 0.260 0.341 0.422 0.502 0.578 0.113 0.138 0.164 0.191 0.217 0.244 0.271 0.298 0.324 0.350 0.376 0.401 0.425 0.449 0.473 0.581 0.675 0.758 0.830 K=17 0.027 0.090 0.162 0.238 0.313 0.389 0.465 0.083 0.105 0.129 0.154 0.179 0.205 0.230 0.256 0.282 0.308 0.333 0.358 0.382 0.406 0.430 0.539 0.636 0.721 0.795 K=18 0.025 0.081 0.148 0.218 0.289 0.360 0.057 0.077 0.098 0.120 0.144 0.168 0.193 0.218 0.243 0.268 0.292 0.317 0.341 0.365 0.388 0.499 0.597 0.684 0.760 K=19 0.022 0.074 0.136 0.201 0.267 0.037 0.053 0.071 0.091 0.113 0.135 0.158 0.182 0.206 0.230 0.254 0.278 0.302 0.325 0.349 0.459 0.559 0.647 0.725 K=20 0.020 0.068 0.125 0.185 0.022 0.034 0.050 0.067 0.086 0.106 0.127 0.149 0.172 0.195 0.218 0.241 0.265 0.288 0.311 0.421 0.521 0.611 0.691 K=21 0.019 0.062 0.115 0.011 0.020 0.032 0.046 0.062 0.080 0.100 0.120 0.141 0.163 0.185 0.207 0.230 0.252 0.275 0.384 0.485 0.576 0.657 65 1.408 70 1.429 75 1.448 80 1.466 85 1.482 90 1.497 95 1.510 100 1.523 150 1.611 200 1.664 1.378 1.401 1.423 1.442 1.459 1.475 1.490 1.503 1.598 1.654 1.348 1.373 1.396 1.417 1.436 1.453 1.469 1.483 1.585 1.644 1.317 1.345 1.369 1.392 1.412 1.431 1.448 1.463 1.571 1.634 1.286 1.316 1.342 1.367 1.388 1.408 1.426 1.443 1.558 1.624 1.254 1.286 1.315 1.341 1.364 1.385 1.405 1.422 1.544 1.613 1.222 1.257 1.287 1.315 1.340 1.362 1.383 1.402 1.530 1.603 1.190 1.227 1.260 1.289 1.315 1.339 1.361 1.381 1.516 1.593 1.158 1.197 1.231 1.262 1.290 1.315 1.338 1.359 1.502 1.582 1.125 1.166 1.203 1.236 1.265 1.292 1.316 1.338 1.488 1.572 1.092 1.136 1.174 1.209 1.240 1.268 1.293 1.317 1.474 1.561 1.059 1.105 1.146 1.182 1.214 1.244 1.271 1.295 1.460 1.551 1.026 1.074 1.117 1.155 1.189 1.220 1.248 1.273 1.445 1.540 0.993 1.043 1.088 1.127 1.163 1.195 1.225 1.251 1.431 1.529 0.960 1.012 1.058 1.100 1.137 1.171 1.201 1.229 1.416 1.519 0.927 0.981 1.029 1.072 1.111 1.146 1.178 1.207 1.402 1.508 0.894 0.950 1.000 1.045 1.085 1.121 1.155 1.185 1.387 1.497 0.861 0.919 0.971 1.017 1.059 1.097 1.131 1.162 1.372 1.486 0.828 0.888 0.941 0.989 1.033 1.072 1.108 1.140 1.357 1.475 0.795 0.857 0.912 0.962 1.006 1.047 1.084 1.118 1.342 1.464 0.762 0.826 0.883 0.934 0.980 1.022 1.060 1.095 1.327 1.453 0.730 0.795 0.854 0.907 0.954 0.997 1.037 1.072 1.312 1.442 11 Durbin-Watson Significance Tables Table A-6 Models with no intercept (from Farebrother): Negative serial correlation Durbin-Watson Ninety Nine Per Cent Minimal Bound N 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 K=0 1.999 2.951 3.221 3.261 3.235 3.198 3.166 3.133 3.101 3.071 3.043 3.017 2.992 2.969 2.948 2.927 2.908 2.890 2.874 2.858 2.842 2.828 2.814 2.801 2.789 2.777 2.766 2.755 2.745 2.735 2.725 2.716 2.707 2.699 2.690 2.683 2.675 2.667 2.660 2.628 2.600 2.575 2.553 K=1 0.999 1.967 2.462 2.682 2.776 2.817 2.837 2.847 2.847 2.843 2.836 2.828 2.818 2.808 2.797 2.787 2.776 2.766 2.756 2.746 2.736 2.727 2.717 2.709 2.700 2.692 2.684 2.676 2.668 2.661 2.654 2.647 2.640 2.634 2.627 2.621 2.615 2.609 2.583 2.559 2.538 2.519 K=2 0.586 1.359 1.878 2.177 2.347 2.448 2.514 2.560 2.592 2.612 2.626 2.635 2.640 2.643 2.644 2.643 2.641 2.638 2.635 2.631 2.627 2.623 2.618 2.614 2.609 2.604 2.600 2.595 2.590 2.586 2.581 2.576 2.572 2.567 2.563 2.559 2.555 2.535 2.516 2.500 2.484 K=3 0.382 0.983 1.459 1.776 1.983 2.121 2.220 2.294 2.349 2.391 2.423 2.447 2.466 2.480 2.492 2.500 2.506 2.511 2.515 2.517 2.518 2.519 2.519 2.519 2.518 2.517 2.515 2.514 2.512 2.510 2.508 2.506 2.503 2.501 2.499 2.496 2.484 2.471 2.459 2.448 K=4 0.268 0.740 1.158 1.465 1.684 1.842 1.961 2.054 2.127 2.185 2.231 2.269 2.299 2.324 2.344 2.361 2.375 2.387 2.396 2.404 2.411 2.416 2.421 2.425 2.428 2.430 2.432 2.433 2.434 2.435 2.435 2.435 2.435 2.435 2.434 2.430 2.424 2.417 2.409 K=5 0.198 0.576 0.937 1.224 1.441 1.607 1.737 1.842 1.928 1.997 2.055 2.102 2.142 2.176 2.204 2.228 2.249 2.267 2.282 2.295 2.306 2.316 2.325 2.332 2.339 2.344 2.349 2.353 2.357 2.360 2.363 2.365 2.367 2.369 2.374 2.374 2.373 2.370 K=6 0.153 0.460 0.773 1.035 1.244 1.410 1.544 1.656 1.749 1.827 1.893 1.948 1.996 2.036 2.071 2.102 2.128 2.151 2.171 2.189 2.205 2.219 2.231 2.242 2.252 2.260 2.268 2.275 2.281 2.287 2.292 2.296 2.300 2.315 2.323 2.327 2.329 K=7 0.121 0.375 0.647 0.885 1.082 1.244 1.379 1.494 1.591 1.675 1.746 1.807 1.861 1.907 1.947 1.983 2.014 2.042 2.066 2.088 2.107 2.125 2.140 2.155 2.167 2.179 2.189 2.199 2.207 2.215 2.222 2.229 2.253 2.269 2.280 2.286 K=8 0.098 0.312 0.549 0.764 0.948 1.104 1.237 1.351 1.451 1.538 1.613 1.678 1.736 1.786 1.831 1.871 1.906 1.938 1.966 1.991 2.014 2.035 2.053 2.070 2.086 2.100 2.113 2.124 2.135 2.145 2.154 2.190 2.214 2.231 2.242 K=9 0.081 0.263 0.471 0.666 0.837 0.985 1.114 1.227 1.327 1.415 1.492 1.561 1.621 1.675 1.723 1.766 1.805 1.839 1.871 1.899 1.925 1.948 1.970 1.989 2.007 2.023 2.038 2.052 2.065 2.077 2.124 2.157 2.180 2.197 K=10 0.069 0.225 0.409 0.585 0.743 0.883 1.007 1.118 1.217 1.305 1.384 1.454 1.516 1.572 1.623 1.669 1.710 1.747 1.781 1.812 1.840 1.866 1.889 1.911 1.931 1.950 1.967 1.982 1.997 2.056 2.098 2.128 2.151 K=11 0.059 0.195 0.358 0.517 0.664 0.796 0.915 1.022 1.119 1.207 1.285 1.356 1.420 1.478 1.530 1.577 1.621 1.660 1.696 1.729 1.759 1.787 1.813 1.837 1.859 1.879 1.898 1.915 1.986 2.037 2.075 2.103 K=12 0.051 0.170 0.316 0.461 0.597 0.721 0.834 0.937 1.032 1.118 1.196 1.267 1.331 1.390 1.444 1.493 1.537 1.579 1.616 1.651 1.683 1.713 1.740 1.765 1.789 1.811 1.831 1.914 1.975 2.020 2.054 K=13 0.044 0.150 0.281 0.413 0.539 0.656 0.763 0.862 0.954 1.038 1.115 1.186 1.250 1.309 1.364 1.414 1.460 1.502 1.541 1.577 1.611 1.642 1.670 1.697 1.722 1.746 1.841 1.911 1.964 2.004 K=14 0.039 0.133 0.251 0.372 0.489 0.598 0.700 0.796 0.884 0.966 1.042 1.111 1.176 1.235 1.290 1.340 1.387 1.430 1.470 1.507 1.542 1.574 1.604 1.632 1.659 1.767 1.847 1.907 1.954 K=15 0.035 0.119 0.226 0.337 0.446 0.548 0.645 0.736 0.821 0.901 0.975 1.043 1.107 1.166 1.221 1.272 1.319 1.363 1.404 1.442 1.477 1.510 1.541 1.570 1.691 1.781 1.849 1.902 K=16 0.031 0.107 0.204 0.307 0.408 0.504 0.596 0.683 0.765 0.842 0.914 0.981 1.044 1.102 1.157 1.208 1.255 1.299 1.341 1.379 1.416 1.450 1.482 1.614 1.714 1.790 1.849 K=17 0.028 0.096 0.185 0.280 0.374 0.465 0.552 0.635 0.714 0.788 0.858 0.924 0.986 1.043 1.097 1.148 1.196 1.240 1.282 1.321 1.358 1.392 1.537 1.646 1.730 1.796 K=18 0.025 0.087 0.169 0.257 0.345 0.430 0.512 0.592 0.667 0.739 0.807 0.872 0.932 0.989 1.042 1.093 1.140 1.184 1.226 1.266 1.303 1.459 1.578 1.669 1.742 K=19 0.023 0.080 0.155 0.237 0.319 0.399 0.477 0.553 0.625 0.695 0.761 0.823 0.882 0.938 0.991 1.041 1.088 1.132 1.174 1.213 1.381 1.509 1.608 1.687 K=20 0.021 0.073 0.143 0.218 0.295 0.371 0.445 0.517 0.587 0.654 0.718 0.779 0.836 0.891 0.943 0.992 1.039 1.083 1.124 1.302 1.439 1.546 1.631 K=21 0.019 0.067 0.132 0.202 0.274 0.346 0.416 0.485 0.552 0.617 0.678 0.737 0.794 0.847 0.898 0.947 0.993 1.036 1.224 1.370 1.484 1.576 65 70 75 80 85 90 95 100 150 200 2.534 2.516 2.500 2.486 2.473 2.460 2.449 2.438 2.363 2.317 2.503 2.487 2.473 2.461 2.449 2.438 2.428 2.418 2.349 2.307 2.470 2.458 2.446 2.436 2.425 2.415 2.406 2.398 2.336 2.296 2.437 2.427 2.417 2.408 2.399 2.391 2.384 2.377 2.322 2.286 2.402 2.395 2.387 2.380 2.374 2.367 2.361 2.355 2.308 2.276 2.366 2.361 2.357 2.352 2.347 2.342 2.338 2.333 2.294 2.265 2.329 2.327 2.325 2.323 2.320 2.317 2.314 2.310 2.279 2.255 2.290 2.292 2.293 2.293 2.292 2.291 2.289 2.287 2.265 2.244 2.250 2.256 2.260 2.262 2.263 2.264 2.264 2.264 2.250 2.233 2.210 2.219 2.226 2.231 2.234 2.237 2.239 2.240 2.235 2.222 2.168 2.181 2.191 2.198 2.204 2.209 2.212 2.215 2.220 2.211 2.125 2.142 2.155 2.165 2.174 2.181 2.186 2.190 2.204 2.200 2.081 2.102 2.118 2.132 2.143 2.152 2.159 2.165 2.188 2.189 2.036 2.061 2.081 2.098 2.111 2.122 2.131 2.139 2.173 2.177 1.990 2.020 2.043 2.063 2.079 2.092 2.103 2.113 2.156 2.166 1.944 1.977 2.005 2.027 2.046 2.061 2.075 2.086 2.140 2.154 1.896 1.934 1.965 1.991 2.012 2.030 2.046 2.059 2.124 2.142 1.848 1.891 1.926 1.954 1.979 1.999 2.016 2.031 2.107 2.131 1.799 1.846 1.885 1.917 1.944 1.967 1.986 2.003 2.090 2.119 1.750 1.802 1.844 1.879 1.909 1.935 1.956 1.975 2.073 2.106 1.700 1.756 1.802 1.841 1.874 1.902 1.926 1.946 2.056 2.094 1.650 1.710 1.760 1.803 1.838 1.869 1.895 1.917 2.039 2.082 ... 0.954 0.997 1.037 1.072 1.312 1.442 Durbin- Watson Significance Tables Table A-4 Models with no intercept (from Farebrother): Positive serial correlation Durbin- Watson Five Per Cent Minimal Bound... 0.997 1.037 1.072 1.312 1.442 11 Durbin- Watson Significance Tables Table A-6 Models with no intercept (from Farebrother): Negative serial correlation Durbin- Watson Ninety Nine Per Cent Minimal... lower bound dL In this instance, the upper bound is Durbin- Watson Significance Tables the conventional bound dU found in the Savin and White tables To test for negative first-order autocorrelation,