evidence that the error terms are negatively autocorrelated. If dL,α < (4 − d) < dU,α, the test is inconclusive. Negative serial correlation implies that a positive error for one observation increases the chance of a negative error for another observation and a negative error for one observation increases the chances of a positive error for another. The critical values, dL,α and dU,α, vary by level of significance (α) and the degrees of freedom in the regression equation. Their derivation is complex—statisticians typically obtain them from the appendices of statistical texts. If the design matrix of the regression is known, exact critical values for the distribution of under the null hypothesis of no serial correlation can be calculated. Under the null hypothesis is distributed as where n are the number of observations and k the number of regression variables; the are independent standard normal random variables; and the are the nonzero eigenvalues of where is the matrix that transforms the residuals into the statistic, i.e. . A number of computational algorithms for finding percentiles of this distribution are available. Although serial correlation does not affect the consistency of the estimated regression coefficients, it does affect our ability to conduct valid statistical tests. First, the F-statistic to test for overall significance of the regression may be inflated under positive serial correlation because the mean squared error (MSE) will tend to underestimate the population error variance. Second, positive serial correlation typically causes the ordinary least squares (OLS) standard errors for the regression coefficients to underestimate the true standard errors. As a consequence, if positive serial correlation is present in the regression, standard linear regression analysis will typically lead us to compute artificially small standard errors for the regression coefficient. These small standard errors will cause the estimated t-statistic to be inflated, suggesting significance where perhaps there is none. The inflated t-statistic, may in turn, lead us to incorrectly reject null hypotheses, about population values of the parameters of the regression model more often than we would if the standard errors were correctly estimated. If the Durbin–Watson statistic indicates the presence of serial correlation of the residuals, this can be remedied by using the Cochrane–Orcutt procedure. The Durbin–Watson statistic, while displayed by many regression analysis programs, is not applicable in certain situations. For instance, when lagged dependent variables are included in the explanatory variables, then it is inappropriate to use this test. Durbin's