Douglas R. White. 2007. Using the Durbin-Watson test with multiple regression | |||||||||||||||||||||||||||

Source of the Durban-Watson lookup table: | |||||||||||||||||||||||||||

The Durbin-Watson Test for Serial Correlation with Extreme Sample Sizes or Many Regressors | |||||||||||||||||||||||||||

N. E. Savin; Kenneth J. White | Consult article at Jstor for missing values if needed | http://links.jstor.org/sici?sici=0012-9682%28197711%2945%3A8%3C1989%3ATDTFSC%3E2.0.CO%3B2-D | |||||||||||||||||||||||||

Econometrica, Vol. 45, No. 8. (Nov., 1977), pp. 1989-1996. | Charted by Number of Independent Variables in the Regression Equation | ||||||||||||||||||||||||||

Variables= | 1 | Variables= | 2 | Variables= | 3 | Variables= | 4 | Variables= | 5 | Variables= | 6 | Variables= | 7 | Variables= | 8 | Variables= | 9 | Variables= | 10 | ||||||||

p<.05 | dL | dU | dL | dU | dL | dU | dL | dU | dL | dU | |||||||||||||||||

n | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 9 | 9 | 10 | 10 | |||||||

10 | 0.88 | 1.32 | 0.70 | 1.64 | 0.53 | 2.02 | 0.38 | 2.41 | na | na | |||||||||||||||||

20 | 1.20 | 1.41 | 1.10 | 1.54 | 1.00 | 1.68 | 0.79 | 1.99 | 0.69 | 1.99 | The Durban-Watson is out of date, but it is the only option now in Spss v14.0 | ||||||||||||||||

30 | 1.35 | 1.49 | 1.28 | 1.57 | 1.21 | 1.65 | 1.14 | 1.74 | 1.08 | 1.83 | D-W tests for correlation between a residual and the immediately preceding residual. | ||||||||||||||||

40 | 1.44 | 1.54 | 1.39 | 1.60 | 1.34 | 1.66 | 1.23 | 1.72 | 1.23 | 1.79 | The ordering of the observations should be: one-dimensional and directed | ||||||||||||||||

50 | 1.50 | 1.59 | 1.46 | 1.63 | 1.42 | 1.67 | 1.34 | 1.72 | 1.34 | 1.77 | (so that influence moves in only one direction along the line). | ||||||||||||||||

60 | 1.55 | 1.62 | 1.51 | 1.65 | 1.48 | 1.69 | 1.44 | 1.73 | 1.41 | 1.77 | For a time series, both of these conditions are met. | ||||||||||||||||

70 | 1.58 | 1.64 | 1.55 | 1.67 | 1.53 | 1.70 | 1.49 | 1.74 | 1.46 | 1.77 | The SCCS ordering does not meetl these conditions. | ||||||||||||||||

80 | 1.61 | 1.66 | 1.59 | 1.69 | 1.56 | 1.72 | 1.53 | 1.74 | 1.51 | 1.77 | For example, Thonga (3) is preceded by Kung Bushmen (2); but Thonga would be better paired with the culture that follows it in the list, Lozi (4). | ||||||||||||||||

90 | 1.64 | 1.68 | 1.61 | 1.70 | 1.59 | 1.73 | 1.57 | 1.75 | 1.54 | 1.78 | Contiguity relationships really can't be collapsed to a single order dimension because | ||||||||||||||||

100 | 1.65 | 1.69 | 1.64 | 1.72 | 1.61 | 1.74 | 1.59 | 1.76 | 1.57 | 1.78 | there are likely to be several cultures defined as contiguous to a given culture. | ||||||||||||||||

150 | 1.72 | 1.75 | 1.71 | 1.76 | 1.69 | 1.77 | 1.68 | 1.79 | 1.66 | 1.80 | Nonetheless, your regression may have serial correlation even on this limited criterion. | ||||||||||||||||

200 | 1.76 | 1.78 | 1.75 | 1.79 | 1.74 | 1.80 | 1.73 | 1.81 | 1.72 | 1.82 | But the test is not complete | ||||||||||||||||

p<.01 | READING THE TABLE: For any number of Independent Variables in your Regression Equation | ||||||||||||||||||||||||||

10 | 0.39 | 1.14 | 0.34 | 1.70 | There are two values to consider for Durbin-Watson: dL and dU (lesser and upper values) | ||||||||||||||||||||||

20 | |||||||||||||||||||||||||||

30 | If your Durbin-Watson value is less than the dL you have serial correlation | ||||||||||||||||||||||||||

40 | |||||||||||||||||||||||||||

50 | If your Durbin-Watson value is less than the dU you probably have serial correlation | ||||||||||||||||||||||||||

60 | (especially, in this case, if one of your independent variables is a measure of time) | ||||||||||||||||||||||||||

70 | |||||||||||||||||||||||||||

80 | Durbin-Watson is used in regression analysis with a constant term and one or more independent variables, | ||||||||||||||||||||||||||

90 | where the observations are consecutive, as in the Standard Cross-Cultural Sample or time series. | ||||||||||||||||||||||||||

100 | 1.52 | 1.56 | 1.48 | 1.60 | |||||||||||||||||||||||

150 | 1.61 | 1.64 | 1.58 | 1.67 | Using /Analyze/Regression/Linear in Spss, the Durbin-Watson calculation is done | ||||||||||||||||||||||

200 | 1.66 | 1.68 | 1.64 | 1.70 | when this option is clicked in the STATISTICS box | ||||||||||||||||||||||

The test results is between 0 and 4, with 2 meaning no serial correlation | |||||||||||||||||||||||||||

In cross-cultural research, the Durbin-Watson provides | Serial correlation means, for low values of, that adjacent cases are SIMILAR. | ||||||||||||||||||||||||||

information needed for determining whether the significance | However, if you subtract the values from 4, a resultant low value that is statistically significant | ||||||||||||||||||||||||||

of a finding should be lowered by reducing the effective sample size | means that adjacent cases are more DIVERSE that excected by change. | ||||||||||||||||||||||||||

because some of the cases act as nonindependent duplicates. | |||||||||||||||||||||||||||

This table was copied from Savin and White (1977) by DR White, 2007. | |||||||||||||||||||||||||||

The Excel file for this Durbin-Watson.htm is on this site and named Durbin-Watson.xls | |||||||||||||||||||||||||||

For a full treatment of this probblem see | http://www.mtsu.edu/~Eeaeff/662/c09.pdf | ||||||||||||||||||||||||||