rw = radius of borehole, 0.05 to 0.15 m
r = radius of influence, 100 to 50,000 m
Tu = transmissivity of upper aquifer, 63,070 to 115,600 m2/year
Hu = potentiometric head of upper aquifer, 990 to 1100 m
Tl = transmissivity of lower aquifer, 63.1 to 116 m2/year
Hl = potentiometric head of lower aquifer, 700 to 820 m
L = length of borehole, 1120 to 1680 m
Kw = hydraulic conductivity of borehole, 9855 to 12,045 m/year
 1 Select DOE > Space Filling Design.
 2 Click the red triangle icon on the Space Filling Design title bar and select Load Factors.
 3 Select Help > Sample Data Library and open Design Experiment/Borehole Factors.jmp (Factors Panel with Factor Values Loaded for Borehole Example).
Factors Panel with Factor Values Loaded for Borehole Example
Note: The logarithm of r and rw are used in the following discussion.
 4 Click Continue.
 5
Space-Filling Design Method Panel Showing 32 Runs
 6 Click the Sphere Packing button to produce the design.
 7 Click Make Table to make a table showing the design settings for the experiment.
To see a completed data table for this example, select Help > Sample Data Library and open Design Experiment/ Borehole Sphere Packing.jmp. Because the designs are generated from a random seed, the settings that you obtain will differ from those shown in the completed table.
The Borehole Sphere Packing.jmp data table contains a Fit Model script that you can use to analyze the data. Columns containing the true model, the prediction formula, and the prediction bias are included in the data table.
It is important to remember that deterministic data have no random component. 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 make valid confidence intervals about the size of the effects or about predictions made using the model.
 • A stepwise regression of the response, log y, versus the full quadratic model in the eight factors, led to the prediction formula column.
 • The prediction bias column is the difference between the true model column and the prediction formula column.
 • The prediction bias is relatively small for each of the experimental points. This indicates that the model fits the data well.
In this case, the true model column contains a formula that allows profiling the prediction bias to find its value anywhere in the region of the data. To understand the prediction bias in this example:
 1 Select Graph > Profiler.
 2 Highlight the prediction bias column and click the Y, Prediction Formula button.
 3 Check the Expand Intermediate Formulas box, as shown at the bottom on the Profiler dialog in Profiler Dialog and Profile of the Prediction Bias in the Borehole Sphere-Packing Data. The prediction bias formula is a function of columns that are also created by formulas.
 4 Click OK.
The profile plots at the bottom in Profiler Dialog and Profile of the Prediction Bias in the Borehole Sphere-Packing Data show the prediction bias at the center of the design region. If there were no bias, the profile traces would be constant between the value ranges of each factor. In this example, the variables Hu and Hl show nonlinear effects.
Distribution of the Prediction Bias
The top plot in Prediction Plots Showing Maximum and Minimum Bias over Factor Domains shows the maximum bias (2.91) over the entire domain of the factors. The plot at the bottom shows the comparable minimum bias (–4.84). This gives a range of 7.75. This is more than three times the size of the range over the observed data.
Prediction Plots Showing Maximum and Minimum Bias over Factor Domains
 • Cross validation refits the data to the model while holding back a subset of the points and looks at the error in estimating those points.
 • Verification runs (new runs performed) at different settings to assess the lack of fit of the empirical model.