image\LOGOBIG.gifExample of a response optimization experiment for regression models
main topic     interpreting results     session command     see also  

Solar energy studies indicate that the important factors for total heat flux (HeatFlux) from homes are the position of the focal points in the east, south, and north directions. Additionally, these focal points are significant predictors for the amount of solar radiation that the focal points receive (Insolation).

Your goal is to optimize both responses: HeatFlux and Insolation. You want to arrange the focal points to receive a sufficient amount of solar radiation but not to generate excessive heat.

You do not need to analyze these regression models. The worksheet contains the models for the response optimizer.

1    Open the worksheet FLUXINSOLATION.MTW.

2    Choose Stat > Regression > Regression > Response Optimizer.

3    For Insolation, choose Target and enter 750.

4    For HeatFlux, choose Target and enter 200.

5    Click OK in each dialog box.

Session Window Output

Response Optimization: Insolation, HeatFlux 

 

Parameters

 

Response    Goal     Lower  Target   Upper  Weight  Importance

Insolation  Target  568.55     750  909.45       1           1

HeatFlux    Target  181.50     200  278.70       1           1

 

 

Solution

 

                                   Insolation  HeatFlux     Composite

Solution  East     South  North           Fit       Fit  Desirability

1         31.9438  31.84  17.6683         750       200             1

 

 

Multiple Response Prediction

 

Variable  Setting

East      31.9438

South     31.84

North     17.6683

 

 

Response       Fit  SE Fit       95% CI            95% PI

Insolation   750.0    47.3  ( 652.7,  847.3)  ( 591.3,  908.7)

HeatFlux    200.00    6.68  (186.25, 213.75)  (177.58, 222.42)

Graph Window Output

Interpreting the results

The combined or composite desirability of these two responses is 1, which indicates an excellent solution.

To obtain this desirability, you would set the factor levels at the values shown under Multiple Response Prediction. That is, East would be set at 31.9438, South at 31.84, and North at 17.6683. The predicted responses for these settings are 750.0 for Insolation and 200.00 for HeatFlux. The confidence intervals and prediction intervals indicate the precision of these predictions.

If you want to adjust the factor settings of this initial solution, you can use the plot. Move the vertical bars to change the factor settings and see how the individual desirability (d) of the responses and the composite desirability change.

The response optimizer uses model equations. Ensure that your models are adequate before you interpret the results.