Regression & Correlation

Durbin-Watson Table

The exact dL and dU bounds for testing whether your regression residuals are autocorrelated.

Significance level (α, one-tailed)

Hover or tap a cell to read off its dL / dU bounds.

dL – dU bounds, α = 0.05 — k predictors across, n down

n \ k	1	2	3	4	5
15	1.077–1.361	0.946–1.543	0.814–1.750	0.685–1.977	0.562–2.220
16	1.106–1.371	0.982–1.539	0.857–1.728	0.734–1.935	0.615–2.157
17	1.133–1.381	1.015–1.536	0.897–1.710	0.779–1.900	0.664–2.104
18	1.158–1.391	1.046–1.535	0.933–1.696	0.820–1.872	0.710–2.060
19	1.180–1.401	1.074–1.536	0.967–1.685	0.859–1.848	0.752–2.023
20	1.201–1.411	1.100–1.537	0.998–1.676	0.894–1.828	0.792–1.991
21	1.221–1.420	1.125–1.538	1.026–1.669	0.927–1.812	0.829–1.963
22	1.239–1.429	1.147–1.541	1.053–1.664	0.958–1.797	0.863–1.940
23	1.257–1.437	1.168–1.543	1.078–1.660	0.986–1.785	0.895–1.920
24	1.273–1.446	1.188–1.546	1.101–1.656	1.013–1.775	0.925–1.902
25	1.288–1.454	1.206–1.550	1.123–1.654	1.038–1.767	0.953–1.886
26	1.302–1.461	1.224–1.553	1.143–1.652	1.062–1.759	0.979–1.873
27	1.316–1.469	1.240–1.556	1.162–1.651	1.084–1.753	1.004–1.861
28	1.328–1.476	1.255–1.560	1.181–1.650	1.104–1.747	1.028–1.850
29	1.341–1.483	1.270–1.563	1.198–1.650	1.124–1.743	1.050–1.841
30	1.352–1.489	1.284–1.567	1.214–1.650	1.143–1.739	1.071–1.833
31	1.363–1.496	1.297–1.570	1.229–1.650	1.160–1.735	1.090–1.825
32	1.373–1.502	1.309–1.574	1.244–1.650	1.177–1.732	1.109–1.819
33	1.383–1.508	1.321–1.577	1.258–1.651	1.193–1.730	1.127–1.813
34	1.393–1.514	1.333–1.580	1.271–1.652	1.208–1.728	1.144–1.808
35	1.402–1.519	1.343–1.584	1.283–1.653	1.222–1.726	1.160–1.803
36	1.411–1.525	1.354–1.587	1.295–1.654	1.236–1.724	1.175–1.799
37	1.419–1.530	1.364–1.590	1.307–1.655	1.249–1.723	1.190–1.795
38	1.427–1.535	1.373–1.594	1.318–1.656	1.261–1.722	1.204–1.792
39	1.435–1.540	1.382–1.597	1.328–1.658	1.273–1.722	1.218–1.789
40	1.442–1.544	1.391–1.600	1.338–1.659	1.285–1.721	1.230–1.786
45	1.475–1.566	1.430–1.615	1.383–1.666	1.336–1.720	1.287–1.776
50	1.503–1.585	1.462–1.628	1.421–1.674	1.378–1.721	1.335–1.771
55	1.528–1.601	1.490–1.641	1.452–1.681	1.414–1.724	1.374–1.768
60	1.549–1.616	1.514–1.652	1.480–1.689	1.444–1.727	1.408–1.767
65	1.567–1.629	1.536–1.662	1.503–1.696	1.471–1.731	1.438–1.767
70	1.583–1.641	1.554–1.672	1.525–1.703	1.494–1.735	1.464–1.768
75	1.598–1.652	1.571–1.680	1.543–1.709	1.515–1.739	1.487–1.770
80	1.611–1.662	1.586–1.688	1.560–1.715	1.534–1.743	1.507–1.772
85	1.623–1.671	1.600–1.696	1.575–1.721	1.550–1.747	1.525–1.774
90	1.635–1.679	1.612–1.703	1.589–1.726	1.566–1.751	1.542–1.776
95	1.645–1.687	1.623–1.709	1.602–1.732	1.579–1.755	1.557–1.778
100	1.654–1.694	1.634–1.715	1.613–1.736	1.592–1.758	1.571–1.780

k is the number of predictors in your regression, excluding the intercept; n is the number of observations. Reject the null hypothesis of no positive autocorrelation if your Durbin-Watson statistic d is below dL; don't reject if d is above dU; the test is inconclusive if dL ≤ d ≤ dU. For negative autocorrelation, compare 4 − d to the same bounds. Every value is the exact solution via Imhof's method, verified against the published Savin-White extended Durbin-Watson tables.

How to use this tool

Compute your Durbin-Watson statistic, d, from the regression residuals in time order.
Choose your significance level, α.
Find your number of predictors, k (excluding the intercept), and number of observations, n.
If d < dL, reject the null of no positive autocorrelation. If d > dU, don't reject. In between, the test is inconclusive.

Formula Reference

Durbin-Watson statistic

d = Σ(eₜ − eₜ₋₁)² / Σeₜ²

Relationship to residual autocorrelation

d ≈ 2(1 − r), where r is the lag-1 autocorrelation of the residuals

Negative autocorrelation

compare 4 − d to the same dL, dU bounds

ArticleThe Durbin-Watson Test ArticleSimple Linear Regression ArticleTime Series Basics ToolTime Series Decomposition Tool ToolRegression Diagnostics Explorer GlossaryGlossary: Durbin-Watson Test

Frequently Asked Questions

Why does the table give two bounds instead of one critical value?+

The exact critical value depends on the specific regressor data (X), which differs from dataset to dataset. Durbin and Watson proved that no matter what X is, the true critical value always lies between dL and dU, which depend only on n and the number of predictors — giving a valid test with an occasional inconclusive zone rather than a single, dataset-independent exact answer.

What if my n or k isn't in the table?+

For an n between two listed rows, most textbooks recommend using the next smaller n as a conservative choice. Software that computes an exact p-value for your specific X (via the same Imhof method used to build this table) avoids the gap and the inconclusive zone entirely.

How were these bounds computed?+

Exactly, not simulated: the Durbin-Watson statistic's null distribution is a ratio of quadratic forms in normal variables with known eigenvalues, and its exact cumulative probability at any point is found via Imhof's (1961) numerical integration method. Every value in this table was checked against the published Savin-White extended Durbin-Watson tables.

Does a Durbin-Watson result near 2 guarantee the regression is fine?+

It specifically rules out first-order autocorrelation (correlation with the immediately preceding residual) — it says nothing about other problems like heteroscedasticity, nonlinearity, or autocorrelation at longer lags, which need their own diagnostics.

n \ k

1.077–1.361

0.946–1.543

0.814–1.750

0.685–1.977

0.562–2.220

1.106–1.371

0.982–1.539

0.857–1.728

0.734–1.935

0.615–2.157

1.133–1.381

1.015–1.536

0.897–1.710

0.779–1.900

0.664–2.104

1.158–1.391

1.046–1.535

0.933–1.696

0.820–1.872

0.710–2.060

1.180–1.401

1.074–1.536

0.967–1.685

0.859–1.848

0.752–2.023

1.201–1.411

1.100–1.537

0.998–1.676

0.894–1.828

0.792–1.991

1.221–1.420

1.125–1.538

1.026–1.669

0.927–1.812

0.829–1.963

1.239–1.429

1.147–1.541

1.053–1.664

0.958–1.797

0.863–1.940

1.257–1.437

1.168–1.543

1.078–1.660

0.986–1.785

0.895–1.920

1.273–1.446

1.188–1.546

1.101–1.656

1.013–1.775

0.925–1.902

1.288–1.454

1.206–1.550

1.123–1.654

1.038–1.767

0.953–1.886

1.302–1.461

1.224–1.553

1.143–1.652

1.062–1.759

0.979–1.873

1.316–1.469

1.240–1.556

1.162–1.651

1.084–1.753

1.004–1.861

1.328–1.476

1.255–1.560

1.181–1.650

1.104–1.747

1.028–1.850

1.341–1.483

1.270–1.563

1.198–1.650

1.124–1.743

1.050–1.841

1.352–1.489

1.284–1.567

1.214–1.650

1.143–1.739

1.071–1.833

1.363–1.496

1.297–1.570

1.229–1.650

1.160–1.735

1.090–1.825

1.373–1.502

1.309–1.574

1.244–1.650

1.177–1.732

1.109–1.819

1.383–1.508

1.321–1.577

1.258–1.651

1.193–1.730

1.127–1.813

1.393–1.514

1.333–1.580

1.271–1.652

1.208–1.728

1.144–1.808

1.402–1.519

1.343–1.584

1.283–1.653

1.222–1.726

1.160–1.803

1.411–1.525

1.354–1.587

1.295–1.654

1.236–1.724

1.175–1.799

1.419–1.530

1.364–1.590

1.307–1.655

1.249–1.723

1.190–1.795

1.427–1.535

1.373–1.594

1.318–1.656

1.261–1.722

1.204–1.792

1.435–1.540

1.382–1.597

1.328–1.658

1.273–1.722

1.218–1.789

1.442–1.544

1.391–1.600

1.338–1.659

1.285–1.721

1.230–1.786

1.475–1.566

1.430–1.615

1.383–1.666

1.336–1.720

1.287–1.776

1.503–1.585

1.462–1.628

1.421–1.674

1.378–1.721

1.335–1.771

1.528–1.601

1.490–1.641

1.452–1.681

1.414–1.724

1.374–1.768

1.549–1.616

1.514–1.652

1.480–1.689

1.444–1.727

1.408–1.767

1.567–1.629

1.536–1.662

1.503–1.696

1.471–1.731

1.438–1.767

1.583–1.641

1.554–1.672

1.525–1.703

1.494–1.735

1.464–1.768

1.598–1.652

1.571–1.680

1.543–1.709

1.515–1.739

1.487–1.770

1.611–1.662

1.586–1.688

1.560–1.715

1.534–1.743

1.507–1.772

1.623–1.671

1.600–1.696

1.575–1.721

1.550–1.747

1.525–1.774

1.635–1.679

1.612–1.703

1.589–1.726

1.566–1.751

1.542–1.776

1.645–1.687

1.623–1.709

1.602–1.732

1.579–1.755

1.557–1.778

100

1.654–1.694

1.634–1.715

1.613–1.736

1.592–1.758

1.571–1.780

How to use this tool

Compute your Durbin-Watson statistic, d, from the regression residuals in time order.

Choose your significance level, α.

Find your number of predictors, k (excluding the intercept), and number of observations, n.

If d < dL, reject the null of no positive autocorrelation. If d > dU, don't reject. In between, the test is inconclusive.

Frequently Asked Questions

Why does the table give two bounds instead of one critical value?+

What if my n or k isn't in the table?+

How were these bounds computed?+

Does a Durbin-Watson result near 2 guarantee the regression is fine?+