Modeling and Multivariate Methods - SAS

126 Fitting Standard Least Squares Models Chapter 3
Singularity Details
The random submatrix from the EMS table is inverted and multiplied into the mean squares to obtain
variance component estimates. These estimates are usually (but not necessarily) positive. The variance
component estimate for the residual is the Mean Square Error.
Note that the CV of the variance components is initially hidden in the Variance Components Estimates
report. To reveal it, right-click (or hold down CTRL and click on the Macintosh) and select Columns > CV
from the menu that appears.
Singularity Details
When there are linear dependencies between model effects, the Singularity Details report appears.
Figure 3.51 Singularity Details Report
Examples with Statistical Details
The examples in this section are based on the following example:
1. Open the Drug.jmp sample data table.
2. Select Analyze > Fit Model.
3. Select y and click Y.
4. Select Drug and click Add.
5. Click Run.
One-Way Analysis of Variance with Contrasts
In a one-way analysis of variance, a different mean is fit to each of the different sample (response) groups, as
identified by a nominal variable. To specify the model for JMP, select a continuous Y and a nominal X
variable, such as Drug. In this example, Drug has values a, d, and f. The standard least squares fitting
method translates this specification into a linear model as follows: The nominal variables define a sequence
of dummy variables, which have only values 1, 0, and –1. The linear model is written as follows:
y i
= β 0
+ β 1
x 1i
+ β 2
x 2i
+ ε i
where:
– y i is the observed response in the i th trial
– x 1i is the level of the first predictor variable in the i th trial