Profiling the Fitted Model

Use the Profiler, Contour Profiler, or Surface Profiler to gain further insight into the fitted model. To select a profiler option, click on the red triangle menu next to Loglinear Variance Fit and select one of the options under the Profilers menu.

Example of Profiling the Fitted Model

For example, suppose that the goal was to find the factor settings that achieved a target of 35 for the response, but at the smallest variance. Fit the models and choose Profiler from the report menu. For example, Figure 9.7 shows the Profiler set up to match a target value for a mean and to minimize variance.

Select Help > Sample Data Library and open InjectionMolding.jmp.

Select Analyze > Fit Model.

Since the variables in the data table have preselected roles assigned to them, the launch window is already filled out.

Click Run.

From the red triangle menu next to Loglinear Variance Fit, select Profilers > Profiler.

From the red triangle menu next to Prediction Profiler, select Optimization and Desirability > Set Desirabilities.

In the Response Goal window that appears, change Maximize to Match Target.

Click OK.

In the second Response Goal window, click OK.

From the red triangle menu next to Prediction Profiler select Optimization and Desirability > Maximize Desirability.

10.

From the red triangle menu next to Prediction Profiler, select Prediction Intervals.

Figure 9.7 Profiler to Match Target and Minimize Variance with Prediction Intervals

One of the best ways to see the relationship between the mean and the variance (both modeled with the LogVariance personality) is through looking at the individual prediction confidence intervals about the mean. Regular confidence intervals (those shown by default in the Profiler) do not show information about the variance model as well as individual prediction confidence intervals do. Prediction intervals show both the mean and variance model in one graph.

If Y is the modeled response, and you want a prediction interval for a new observation at xn, then:

where:

s2|xn is the variance for the individual prediction at xn

s2Y|xn is the variance of the distribution of Y at xn

is the variance of the sampling distribution of

, and is also the variance for the mean.

Because the variance of the individual prediction contains the variance of the distribution of Y, the effects of the changing variance for Y can be seen. Not only are the individual prediction intervals wider, but they can change shape with a change in the variance effects.