Variances and Regression Residuals
Durbin-Watson Table: Critical Values dL and dU
Lower and upper bounds for the Durbin-Watson test for first-order autocorrelation in regression residuals.
- n = 6 to 200
- k′ = 1 to 10 regressors
- Calculator for any n
Durbin-Watson Table
Jump to a significance level below. Rows: number of observations n · Columns: number of regressors k′ (excluding the intercept), with dL and dU for each.
α = 0.05
| 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 | 1.963 | 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 |
α = 0.01
| 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 | 0.605 | 1.001 | 0.466 | 1.332 | 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 | 2.029 | 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 | 2.982 | 0.078 | 3.287 | — | — |
| 15 | 0.811 | 1.070 | 0.700 | 1.252 | 0.591 | 1.464 | 0.488 | 1.704 | 0.391 | 1.966 | 0.303 | 2.244 | 0.226 | 2.530 | 0.161 | 2.817 | 0.107 | 3.101 | 0.068 | 3.374 |
| 16 | 0.843 | 1.086 | 0.737 | 1.252 | 0.633 | 1.446 | 0.532 | 1.663 | 0.437 | 1.900 | 0.349 | 2.153 | 0.269 | 2.416 | 0.200 | 2.681 | 0.142 | 2.944 | 0.094 | 3.201 |
| 17 | 0.874 | 1.102 | 0.772 | 1.255 | 0.672 | 1.432 | 0.574 | 1.630 | 0.480 | 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 | 1.117 | 0.804 | 1.259 | 0.708 | 1.422 | 0.613 | 1.604 | 0.522 | 1.803 | 0.435 | 2.015 | 0.355 | 2.238 | 0.282 | 2.467 | 0.217 | 2.697 | 0.160 | 2.925 |
| 19 | 0.928 | 1.132 | 0.835 | 1.265 | 0.742 | 1.415 | 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 | 0.863 | 1.270 | 0.773 | 1.411 | 0.685 | 1.567 | 0.598 | 1.737 | 0.515 | 1.918 | 0.436 | 2.110 | 0.362 | 2.308 | 0.294 | 2.510 | 0.232 | 2.713 |
| 21 | 0.975 | 1.161 | 0.890 | 1.277 | 0.803 | 1.408 | 0.718 | 1.554 | 0.633 | 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 | 0.914 | 1.284 | 0.831 | 1.407 | 0.748 | 1.543 | 0.667 | 1.691 | 0.587 | 1.849 | 0.510 | 2.015 | 0.437 | 2.188 | 0.368 | 2.367 | 0.305 | 2.548 |
| 23 | 1.017 | 1.187 | 0.938 | 1.291 | 0.858 | 1.407 | 0.777 | 1.534 | 0.698 | 1.673 | 0.620 | 1.821 | 0.545 | 1.977 | 0.473 | 2.140 | 0.404 | 2.308 | 0.340 | 2.478 |
| 24 | 1.037 | 1.199 | 0.960 | 1.298 | 0.882 | 1.407 | 0.805 | 1.528 | 0.728 | 1.658 | 0.652 | 1.797 | 0.578 | 1.944 | 0.507 | 2.097 | 0.439 | 2.255 | 0.375 | 2.417 |
| 25 | 1.055 | 1.211 | 0.981 | 1.305 | 0.906 | 1.409 | 0.831 | 1.522 | 0.756 | 1.645 | 0.682 | 1.777 | 0.610 | 1.915 | 0.540 | 2.059 | 0.473 | 2.209 | 0.409 | 2.362 |
| 26 | 1.072 | 1.222 | 1.001 | 1.312 | 0.928 | 1.411 | 0.855 | 1.518 | 0.783 | 1.635 | 0.711 | 1.759 | 0.640 | 1.889 | 0.571 | 2.026 | 0.505 | 2.168 | 0.441 | 2.313 |
| 27 | 1.089 | 1.233 | 1.019 | 1.319 | 0.949 | 1.413 | 0.878 | 1.515 | 0.808 | 1.626 | 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 | 1.037 | 1.325 | 0.969 | 1.415 | 0.900 | 1.513 | 0.832 | 1.618 | 0.764 | 1.730 | 0.696 | 1.847 | 0.630 | 1.970 | 0.566 | 2.098 | 0.504 | 2.229 |
| 29 | 1.119 | 1.254 | 1.054 | 1.332 | 0.988 | 1.418 | 0.921 | 1.512 | 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 | 1.133 | 1.263 | 1.070 | 1.339 | 1.006 | 1.421 | 0.941 | 1.511 | 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 | 1.273 | 1.085 | 1.345 | 1.023 | 1.425 | 0.960 | 1.510 | 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 | 1.282 | 1.100 | 1.352 | 1.040 | 1.428 | 0.979 | 1.510 | 0.917 | 1.597 | 0.856 | 1.690 | 0.794 | 1.787 | 0.734 | 1.889 | 0.674 | 1.995 | 0.616 | 2.104 |
| 33 | 1.172 | 1.291 | 1.114 | 1.358 | 1.055 | 1.432 | 0.996 | 1.510 | 0.936 | 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 | 1.299 | 1.128 | 1.364 | 1.070 | 1.435 | 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 | 1.140 | 1.370 | 1.085 | 1.439 | 1.028 | 1.512 | 0.971 | 1.589 | 0.914 | 1.671 | 0.857 | 1.757 | 0.801 | 1.847 | 0.744 | 1.940 | 0.689 | 2.037 |
| 36 | 1.206 | 1.315 | 1.153 | 1.376 | 1.098 | 1.442 | 1.043 | 1.513 | 0.988 | 1.588 | 0.932 | 1.666 | 0.877 | 1.749 | 0.821 | 1.836 | 0.766 | 1.925 | 0.711 | 2.018 |
| 37 | 1.217 | 1.323 | 1.165 | 1.382 | 1.112 | 1.446 | 1.058 | 1.514 | 1.004 | 1.586 | 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 | 1.585 | 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 | 1.393 | 1.137 | 1.453 | 1.085 | 1.517 | 1.034 | 1.584 | 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 | 1.198 | 1.398 | 1.148 | 1.457 | 1.098 | 1.518 | 1.048 | 1.584 | 0.997 | 1.652 | 0.946 | 1.724 | 0.895 | 1.799 | 0.844 | 1.876 | 0.794 | 1.956 |
| 45 | 1.288 | 1.376 | 1.245 | 1.423 | 1.201 | 1.474 | 1.156 | 1.528 | 1.111 | 1.584 | 1.065 | 1.643 | 1.020 | 1.704 | 0.973 | 1.768 | 0.927 | 1.834 | 0.881 | 1.902 |
| 50 | 1.324 | 1.403 | 1.285 | 1.446 | 1.245 | 1.491 | 1.205 | 1.538 | 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 | 1.427 | 1.320 | 1.466 | 1.284 | 1.506 | 1.247 | 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 | 1.383 | 1.449 | 1.350 | 1.484 | 1.317 | 1.520 | 1.283 | 1.558 | 1.249 | 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 | 1.468 | 1.377 | 1.500 | 1.346 | 1.534 | 1.315 | 1.568 | 1.283 | 1.604 | 1.251 | 1.642 | 1.218 | 1.680 | 1.186 | 1.720 | 1.153 | 1.761 | 1.120 | 1.803 |
| 70 | 1.429 | 1.485 | 1.400 | 1.515 | 1.372 | 1.546 | 1.343 | 1.578 | 1.313 | 1.611 | 1.283 | 1.645 | 1.253 | 1.680 | 1.223 | 1.716 | 1.192 | 1.753 | 1.162 | 1.792 |
| 75 | 1.448 | 1.501 | 1.422 | 1.529 | 1.395 | 1.557 | 1.368 | 1.587 | 1.340 | 1.617 | 1.312 | 1.649 | 1.284 | 1.681 | 1.256 | 1.714 | 1.227 | 1.748 | 1.199 | 1.783 |
| 80 | 1.466 | 1.515 | 1.441 | 1.541 | 1.416 | 1.568 | 1.390 | 1.595 | 1.364 | 1.624 | 1.338 | 1.653 | 1.312 | 1.683 | 1.286 | 1.714 | 1.259 | 1.745 | 1.232 | 1.777 |
| 85 | 1.482 | 1.528 | 1.458 | 1.553 | 1.435 | 1.578 | 1.411 | 1.603 | 1.386 | 1.630 | 1.362 | 1.657 | 1.337 | 1.685 | 1.312 | 1.714 | 1.287 | 1.743 | 1.261 | 1.773 |
| 90 | 1.496 | 1.540 | 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 | 1.642 | 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 | 1.503 | 1.583 | 1.482 | 1.604 | 1.462 | 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 | 1.707 | 1.529 | 1.722 | 1.515 | 1.737 | 1.501 | 1.752 | 1.487 | 1.767 |
| 200 | 1.664 | 1.684 | 1.654 | 1.694 | 1.644 | 1.704 | 1.633 | 1.714 | 1.623 | 1.725 | 1.613 | 1.735 | 1.603 | 1.746 | 1.592 | 1.757 | 1.582 | 1.768 | 1.571 | 1.779 |
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How to read this table
- Fit the regression (with an intercept) and compute d = Σ(eₜ − eₜ₋₁)² / Σeₜ² from the residuals in time order.
- Find the row for n and the pair of columns for k′, the number of regressors not counting the intercept.
- If d < dL, there is significant positive autocorrelation. If d > dU, there is not. If dL ≤ d ≤ dU, the test is inconclusive.
- For negative autocorrelation, apply the same rules to 4 − d.
Worked example
A regression of weekly enrolment on 2 predictors over 30 weeks gives d = 1.21. Row 30, k′ = 2 gives dL = 1.284 and dU = 1.567. Because 1.21 < 1.284, the residuals show significant positive autocorrelation.
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Formula and how the values were computed
d = Σₜ (eₜ − eₜ₋₁)² / Σₜ eₜ² · d ≈ 2(1 − ρ̂)
Bounds are computed exactly (Imhof's method) from the bounding distributions of Durbin and Watson, using the eigenvalues 2(1 − cos(πj/n)) of the difference matrix. They reproduce the Savin and White (1977) tables to three decimals.
Frequently asked questions
Why is there an inconclusive region?
The exact distribution of d depends on the regressors. dL and dU bound it for any design, so between them the answer depends on your particular X. Software can compute the exact p-value for your design.
When is the Durbin-Watson test not valid?
When the model includes a lagged dependent variable or has no intercept. Use the Breusch-Godfrey test or Durbin's h instead.