# Durbin-Watson Table

In the following tables n is the sample size and k is the number of independent variables. See Autocorrelation for details.

Alpha = .01

Alpha = .05

### 44 Responses to Durbin-Watson Table

1. Harel says:

Dear Dr. Zaiontz. I was wondering, how to interpret bounds for Durbin-Watson test (dU, dL) if dU is greater than 2.0. I know that it is an extreme case, but just want to know…

For example, for alpha=0.01 if n=13 and k=8 than dU=3.182, dL=0.090. Then 4-dU=0.818, 4-dL=3.91… Does it mean that between 0.090 and 3.190 test is inconlusive? It is quite strange situation, I know that there is plenty of tests better than Durbin-Watson one, but it is nice to know such details.

Greetings from Central Europe.

• Charles says:

Good to hear someone from Central Europe and thanks for your kind words about the website.
The bounds for the Durbin-Watson test are indeed strange. If the test produces a value between dL and dU, i.e. between .818 and 3.10 in this case, then yes the test is inconclusive.
Charles

2. Cheng says:

Hi Charles,

Thank you for your excellent website.
Can I confirm that the k in durbin watson table excludes intercept.
Thanks

• Charles says:

Hi Cheng,
The tables are for the case where there is an intercept, but k does not include the intercept. Thus if k = 2, there are 2 independent variables plus an intercept.
Charles

Thanks for this!

4. Olga says:

Hi Charles,

thank you for all the info on this website!
I was wondering where you got those tables from? I noticed that in Durbin & Watson’s paper from 1951 (Testing for serial correlation), they only go up to an N = 100 (and I am particularly interested in higher N’s). Is there another paper that I have been missing?

Thank you!

Olga

• Charles says:
• Olga says:

Hi Charles,

thanks for the quick reply! When I click on the link, it required authorization. Do you know if there’s another source I could click on? Thanks again!

Olga

• Charles says:

Olga, no I don’t.
Charles

5. Thank you, Charles!
Great job.
I appreciate you spending time to have this important table available.
Warmest regards,
Francisco

If I want to know for n=41, how can I know value

• Charles says:

You need to interpolate the values in the table between the entries for 40 and the entries for 45. This is explained on the webpage
Interpolation
Alternatively, you can use the Real Statistics functions DLowerCrit and DUpperCrit
Charles

If a (one period) auto-correlation adjustment is made, does the adjustment count as an additional k (independent) variable in evaluating DW limits. Thanks

• Charles says:

What sort of (one period) auto-correlation adjustment are your referring to? Are you referring to differencing?
Charles

8. Joel says:

please i have TTF- TIME TO FAILURES values as follows; 28,52,42,8,14,13,47,38,25,12,50,42. How do i know my n and k so to check on DW table for du and dl.
Thanks

Hy charles, can I know how the table of durbin watson for n=204

10. Fiona says:

Hi Charles,

How if I want to know the value for n = 665?

11. zhyan says:

How can I find DL and DU for n=48 with 4 independent variable

• Charles says:

Zhyan,
This depends on the alpha value, but if alpha = .05, then the table has values for n=45 and n=50 and you will need to interpolate between these values to get the answer you are looking for. See the following webpage for details abouit interpolation:
Interpolation
Charles

12. Merin says:

can you help me to explain how to interpolate for n=205?

• Charles says:

Merin,

You won’t be able to interpolate for values of n larger than 200 since the table provided on the website only goes up to n = 200.

The following are the table values for n = 210 and alpha = .05. You can now interpolate between n = 200 and n = 210. In fact, the linear interpolations are simply the average of the values for n = 200 and n = 210 for any given value of k

n k dL dU
210 1 1.76445 1.78358
210 2 1.75483 1.79326
210 3 1.74513 1.80305
210 4 1.73537 1.81295
210 5 1.72554 1.82294
210 6 1.71563 1.83305
210 7 1.70566 1.84325
210 8 1.69561 1.85355
210 9 1.6855 1.86394
210 10 1.67532 1.87445
210 11 1.66508 1.88505
210 12 1.65478 1.89574
210 13 1.64441 1.90653
210 14 1.63398 1.91742
210 15 1.62348 1.92839
210 16 1.61293 1.93947
210 17 1.60232 1.95063
210 18 1.59165 1.96188
210 19 1.58094 1.97323
210 20 1.57015 1.98467

Charles

• Merin says:

ok thank you so much .. that helpfull

13. sawsan says:

what is the dl and du for 258 observations with 40 independent variables at 5%, noting that the 32 of these 40 idependent variable are dummy variables used for the fixed effect model.

• Charles says:

Sawsan,
I have not seen any tables of critical values with more than 20 independent variables. I will look into creating an approximation for such critical values.
Charles

14. Joe Henry says:

Charles,

I have a time sequence of 48 numbers (quarterly crime stats in fact). DW test statistic calculates as 1.632. The alpha=5% lower and upper bounds for k=1 n=48 (interpolated) are 1.492 & 1.577. As d is > than du there is failure to reject the null of no auto-correlation. When checking against the alpha=1% bounds the interpolated lower and upper bounds are 1.310 & 1.392. d is now even farther from the upper critical value. However as the 1% test is a more rigorous test, I would have intuitively thought that the 1% upper bound would move towards the value of 2 (no auto-correlation) rather than away from it. Why is the 1% test less demanding than the 5% one for a DW test of a hypothesis?

Joe

• Charles says:

Joe,
When alpha = 1% it should be easier to retain the null hypothesis than when alpha = 5%. This is indeed the case.
When alpha = 1% it should be harder to reject the null hypothesis than when alpha = 5%. This is indeed the case.
Charles

15. Diva says:

Hello, can you help me to get dl and du for 1346 samples, 3 variables, and alpha 0.5? Thank you.

• Charles says:

Diva,
Here are the values for 1300 and 1350. You will need to interpolate to get the value for 1346 (although obviously it will be pretty close to the value for 1350). I assume that alpha is .05 (and not .5) and that 3 variables means in addition to the constant term.
n = 1300: dl = 1.90420 and du = 1.91345
n = 1350: dl = 1.90607 and du = 1.91498
You can also use the Real Statistics functions DLowerCrit and DUpperCrit.
Charles

16. Mark says:

Hi Charles,

I have data of 1.176 households over 13 weeks in my dataset, which makes 25.288 lines of data. I have 22 explanatory variables in my model + an intercept. My DW statistic is 1.511.
How can I test whether autocorrelation is an issue?

Thanks,
Mark

17. Linda says:

Hy Charles,
thats very great articles.
but I want to ask you something.
My teacher give me some homework, and there’s n >200. how if i want to know the value from n = 240?

thanks before.

18. Eric says:

hi charles
can you tell me n=304

19. maya says:

Hi Mr. Charles,

How if I want to know the value for n = 440?

20. deva says:

Hi Mr. Charles,
I want to ask you something. If n=100 , k=4 and DW statistics is 2.310, is there an autocorrelation? how to determine it? thanks

• Charles says:

Deva,
The critical values for n = 100, k = 4 and alpha = .05 are shown in the table.
See the following webpage for how to interpret the results:
Autocorrelation
Charles

21. my DW is equal to 2,172232

• Charles says: