  In statistics, the Durbin-Watson test is always employed to detect the
presence of serial correlation of residuals from a least squares regression
analysis. However, the Durbin-Watson statistic is only suitable for ordered
time or spatial series. If the variables comprise cross-sectional data coming
from spatial random sampling, the Durbin-Watson will be ineffectual because the
value of Durbin-Watson's statistic depends on the sequences of data point
arrangement. Based on the ideas from spatial autocorrelation, this paper
presents two new statistics for testing serial correlation of residuals from
least squares regression based on spatial samples. By analogy with the new form
of Moran's index, an autocorrelation coefficient is defined with a standardized
residual vector and a normalized spatial weight matrix. Then on the analogy of
the Durbin-Watson statistic, a serial correlation index is constructed. As a
case, the two statistics are applied to the spatial sample of 29 China's
regions. These results show that the new spatial autocorrelation model can be
used to test the serial correlation of residuals from regression analysis. In
practice, the new statistics can make up for the deficiency of the
Durbin-Watson test.
