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Jul 21, 2014 6:05 AM
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Solution

Bwanders,

The numbers for Y in the Prediction Profiler are coming from the prediction formula for your model. You can see the estimated model by looking at the Parameter Estimates. In your particular case, because there is no replication, the model is a perfect fit for the data. However, when you are trying to minimize the Y response, the prediction profiler searches the design space and finds a location with a negative predicted Y.

Linear regression assumes a continuous response, so a negative value is just fine as far as linear regression is concerned. If you wish to restrict the predictions to only positive results, a different modeling technique should be used that can enforce that restriction. However, the real culprit here is that the combination that provides that negative Y prediction is an extrapolation. The location that minimizes Y is the first set of conditions in your table except it is X1 Type = B instead of A. You never ran that combination. When you have a low level of X1, switching to X1 Type = B will lower the response (see the Prediction Profiler). In this case, low enough to give a negative value. The trends are what was shown in the data you did collect, but leads to an extrapolation because not all combinations were collected. My guess is that if you were to actually run that condition you would get a very low Y value.

Dan Obermiller

1 REPLY

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Bwanders,

The numbers for Y in the Prediction Profiler are coming from the prediction formula for your model. You can see the estimated model by looking at the Parameter Estimates. In your particular case, because there is no replication, the model is a perfect fit for the data. However, when you are trying to minimize the Y response, the prediction profiler searches the design space and finds a location with a negative predicted Y.

Linear regression assumes a continuous response, so a negative value is just fine as far as linear regression is concerned. If you wish to restrict the predictions to only positive results, a different modeling technique should be used that can enforce that restriction. However, the real culprit here is that the combination that provides that negative Y prediction is an extrapolation. The location that minimizes Y is the first set of conditions in your table except it is X1 Type = B instead of A. You never ran that combination. When you have a low level of X1, switching to X1 Type = B will lower the response (see the Prediction Profiler). In this case, low enough to give a negative value. The trends are what was shown in the data you did collect, but leads to an extrapolation because not all combinations were collected. My guess is that if you were to actually run that condition you would get a very low Y value.

Dan Obermiller