Rebuilding Critical Values of Durbin-Watson Test by Sufficient Statistic in the Multivariate Regression and First-Order Autogressive Error Model Without Intercept

This paper establishes a Durbin-Watson test statistic with sufficiency and rebuilds the probability table for hypothesis testing in the multivariate regression model without intercept because the Durbin-Watson test which has numerous problems first established in a multiple regression model with first-order autoregressive error by Durbin and Watson (1950). The paper shows that the independent variables, hypothesized autocorrelation coefficient of error and sample sizes have the influence on the shapes and coefficients of probability distribution and critical values in the Durbin-Watson test. First, the multi-collinearity causes the distortion on probability distribution. Second, the changes of independent variable values represent different shapes of probability distribution and critical values in the Durbin-Watson test. Third, the sample sizes induce in the effect of law of large number and asymptotic normality, so there is no gray area in the Durbin-Watson test table when the samples are large enough. Even in the case of small samples there is no gray area