Open the Singularity.jmp sample data table. There is a response Y, four predictors X1, X2, X3, and A, and five observations. The predictors are continuous except for A, which is nominal with four levels. Also note that there is a linear dependency among the continuous effects, namely, X3 = X1 + X2.

Compare the two reports (Fit Least Squares Reports for Model 1 (on left) and Model 2 (on right)). The Singularity Details report at the top of both reports displays the linear dependency, indicating that X1 = X3 - X2.

Now compare the Parameter Estimates reports for both models. Note, for example, that the estimate for X1 for Model 1 is –1.25 while for Model 2 it is 2.75. In both models, only two of the terms associated with effects are estimated, because there are only two model degrees of freedom. See the Analysis of Variance report. The estimates of the two terms that are estimated are labeled Biased while the remaining estimate is set to 0 and labeled Zeroed.

Portions of the report are shown in (Fit Least Squares Report for Model with X1 and A). The Singularity Details report shows that there is a linear dependency involving X1 and the three terms associated with the effect A. (For details about how a nominal effect is coded, see Details of Custom Test Example). The Analysis of Variance report shows that there are three model degrees of freedom. The Parameter Estimates report shows Biased estimates for the three terms X1, A[a], and A[b] and a Zeroed estimate for the fourth, A[c].

The Effect Tests report shows that X1 cannot be tested, because A must be entered first and A accounts for the three model degrees of freedom. However, A can be tested, but with only two degrees of freedom. (X1 must be entered first and it accounts for one of the model degrees of freedom.) The test for A is partial, so it must be interpreted with care.