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 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.
Select Help > Sample Data Library and open Design Experiment/Borehole Sphere
Go back to the Borehole Sphere data table.
In the data grid, select the column headings for true model and Y Prediction Formula.
Right-click and select New Formula Column > Combine > Difference.
From the Borehole Sphere data table, select Graph > Profiler.
Select true model-Y Prediction Formula and click Y, Prediction Formula
Select Expand Intermediate Formulas.
Profiler Dialog for Borehole Sphere-Packing Data
Profiler for Bias of the Borehole GP Model with Y-axis Set at -30 to 30
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.
Distribution of the Prediction Bias

Help created on 9/19/2017