Modeling and Multivariate Methods - SAS

44 Introduction to the Fit Model Platform Chapter 2
Construct Model Effects
Figure 2.5 Parameter Estimates Table
If you use the Prediction Formula option in the Save Columns submenu, a new data table column called
Pred Formula odor saves the prediction formula using the coefficients from the Parameter Estimates table.
The probability value of 0.0657 in the Analysis of Variance table indicates that the three-variable response
surface model is only marginally better than the sample mean.
Figure 2.6 Analysis of Variance Table
The response surface analysis also displays the Response Surface table and the Solution table (Figure 2.7).
The Solution table shows the critical values for the surface variables and indicates that the surface solution
point is a minimum for this example.
Canonical Curvature Table
The Canonical Curvature report, found under the Response Surface title, shows the eigenstructure
(Figure 2.7), which is useful for identifying the shape and orientation of the curvature, and results from the
eigenvalue decomposition of the matrix of second-order parameter estimates. The eigenvalues (given in the
first row of the Canonical Curvature table) are negative if the response surface shape curves back from a
maximum. The eigenvalues are positive if the surface shape curves up from a minimum. If the eigenvalues
are mixed, the surface is saddle shaped, curving up in one direction and down in another direction.
The eigenvectors listed beneath the eigenvalues show the orientations of the principal axes. In this example
the eigenvalues are positive, which indicates that the curvature bends up from a minimum. The direction
where the curvature is the greatest corresponds to the largest eigenvalue (48.8588) and the variable with the
largest component of the associated eigenvector (gl ratio). The direction with the eigenvalue of 31.1035 is
loaded more on temp, which has nearly as much curvature as that for gl ratio.
Sometimes a zero eigenvalue occurs. This means that along the direction described by the corresponding
eigenvector, the fitted surface is flat.