Prediction Variance Profile

The Prediction Variance Profile outline shows a profiler of the relative variance of prediction. Select the Optimization and Desirability > Maximize Desirability option from the red triangle next to Prediction Variance Profile to find the maximum value of the relative prediction variance over the design space. For details, see Maximize Desirability.

The Prediction Variance Profile plots the relative variance of prediction as a function of each factor at fixed values of the other factors. Prediction Variance Profiler shows the Prediction Variance Profile for the Bounce Data.jmp data table, located in the Design Experiment folder.

Prediction Variance Profiler

Relative Prediction Variance

For given settings of the factors, the prediction variance is the product of the error variance and a quantity that depends on the design and the factor settings. Before you run your experiment, the error variance is unknown, so the prediction variance is also unknown. However, the ratio of the prediction variance to the error variance is not a function of the error variance. This ratio, called the relative prediction variance, depends only on the design and the factor settings. Consequently, the relative variance of prediction can be calculated before acquiring the data. For details, see Relative Prediction Variance in Technical Details.

After you run your experiment and fit a least squares model, you can estimate the error variance using the mean squared error (MSE) of the model fit. You can estimate the actual variance of prediction at any setting by multiplying the relative variance of prediction at that setting.

It is ideal for the prediction variance to be small throughout the design space. Generally, the error variance drops as the sample size increases. In comparing designs, you may want to place the prediction variance profilers for two designs side-by-side. A design with lower prediction variance on average is preferred.

Maximize Desirability

You can also evaluate a design or compare designs in terms of the maximum relative prediction variance. Select the Optimization and Desirability > Maximize Desirability option from the red triangle next to Prediction Variance Profile. JMP uses a desirability function that maximizes the relative prediction variance. The value of the Variance displayed in the Prediction variance Profile is the worst (least desirable from a design point of view) value of the relative prediction variance.

Prediction Variance Profile Showing Maximum Variance shows the Prediction Variance Profile after Maximize Desirability was selected. The plot is for the Bounce Data.jmp sample data table, located in the Design Experiment folder. The largest value of the relative prediction variance is 1.395833. The plot also shows values of the factors that give this worst-case relative variance. However, keep in mind that many settings can lead to this same relative variance. See Prediction Variance Surface.

Prediction Variance Profile Showing Maximum Variance