I have a D-W = 1.312 with a sample of 22 cases.
Is it a good value for running a multiple linear regression model?
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A DW of 1.312 suggests you have some positive auto-correlation. A "good" value is 2. Whether a value of 1.312 is a problem depends on your number of predictors. If you have 1 or 2 predictors (excluding the intercept), then your value is above the upper bound and you can't reject the null hypothesis (i.e., the DW is "OK" at the 0.05 level of significance). If you have more than 2 predictors you may have a problem. Of course, the sample size is small so the test has low power, and there may be a benefit of bootstrapping. See here for more information.