For a testable hypothesis , the Wald F statistic is computed as
where is a contrast vector or matrix that you specify, is the vector of regression parameters, is the estimated regression coefficients, is the estimated covariance matrix of , rank() is the rank of , and is a matrix such that
has the same number of columns as
has full row rank
the rank of equals the rank of the matrix
all rows of are estimable functions
the Wald F statistic computed by using the matrix is equivalent to the Wald F statistic computed by using the matrix with any row deleted that is a linear combination of previous rows
If is a full-rank matrix and all rows of are estimable functions, then is the same as . It is possible that matrix cannot be constructed for a given set of linear contrasts, in which case the contrasts are not testable.
If the DF=NONE option in the MODEL statement is specified, then the procedure performs a chi-square significance test.