It is important to remember that deterministic data have no random component. The same input values generate the same output. As a result, p-values from fitted statistical models do not have their usual meanings. A large F statistic (low p-value) is an indication of an effect due to a model term. However, you cannot construct valid confidence intervals for effects or model predictions.
Often, the true model is not available in a simple analytical form. As a result, the prediction bias is known only at observed data points. However, in this example, the functional form of the true model is known. In the Borehole Sphere Packing.jmp data table, the true model column contains the formula of the known function. This formula enables you to profile the prediction bias over the factor input region.
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Click the red triangle next to Gaussian Process Model of Y and select Save Prediction Formula.
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Go back to the Borehole Sphere Packing.jmp data table.
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Right-click and select New Formula Column > Combine > Difference.
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Select Expand Intermediate Formulas.
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Figure 21.26 Profiler Dialog for Borehole Sphere-Packing Data
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Click OK.
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The profiler defaults to the center of the design region. If there were no bias, all profile traces would be constant between the value ranges of each factor. In this example, the variables logRw, Hu, and Hl show the largest effects on the bias.
You can use the profiler to explore the range of the prediction bias over the entire domain. To find points of minimum and maximum bias, select Optimization and Desirability > Desirability Functions from the Prediction Profiler red triangle menu. See Desirability Profiling and Optimization in the Profilers book. To evaluate the prediction bias over the design points, select Analyze > Distribution to see a distribution analysis.
Figure 21.28 Distribution of the Prediction Bias
