The warning message: 

   Warning: The average covariance matrix for the SPEC test has been
            deemed singular which violates an assumption of the test.
            Use caution when interpreting the results of the test.

is issued when PROC REG detects a linear dependency (or near linear dependency) in one of the matrices used to calculate the chi-square statistic and degrees of freedom for the SPEC option – specifically, in the estimated matrix β_n which is defined in White (1980, middle pg 823).

Note that this violates Assumption #6 (pages 822-823 of White's paper), which states that the average covariance matrix is nonsingular. All results (chi-square and degrees of freedom) used to calculate the SPEC option should be suspect, just as when the assumptions for any test are violated. Note that all other results from PROC REG are unaffected by this problem.

Changing the independent effects listed in the MODEL statement or rescaling the data may circumvent the problem. Or, if you have SAS/ETS^® software licensed, you may want to try the WHITE or the BREUSCH= options in the FIT statement in PROC MODEL as an alternative test. These options, as well as the difference between them and the SPEC option in PROC REG, are discussed in Heteroscedasticity tests in the MODEL chapter of the SAS/ETS User's Guide.

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