Example of a prediction for a response surface design model
main topic     interpreting results     session command     see also 

In the fertilizer example, you generated a design, supplied the response data, and fit a linear model. Since this linear model suggested that a higher-order model is needed to adequately model the response surface, you fit the full quadratic model. The full quadratic provides a better fit, with the squared terms for nitrogen and phosphoric acid and the nitrogen by potash interaction being important. The example below is a continuation of this analysis. Now you want to use the model to generate a prediction for specific predictor values.

You do not need to re-analyze that response surface model. The worksheet contains the model for the prediction.

1    Open the worksheet CCD_EX1_MODEL.MTW.

2    Choose Stat > DOE > Response Surface > Predict.

3    In Response, choose BeanYield.

4    In the second drop-down list, choose Enter individual values.

5    In the variables table, enter the setting for each variable as shown below.

Nitrogen

PhosAcid

Potash

3

2

4

6    Click OK.

Session Window Output

Prediction for BeanYield

 

 

Regression Equation in Uncoded Units

 

BeanYield = 12.45 + 0.96 Nitrogen - 2.28 PhosAcid - 1.48 Potash - 0.268 Nitrogen*Nitrogen

            + 1.116 PhosAcid*PhosAcid - 0.239 Potash*Potash - 0.600 Nitrogen*PhosAcid

            + 0.695 Nitrogen*Potash + 0.306 PhosAcid*Potash

 

 

Variable  Setting

Nitrogen        3

PhosAcid        2

Potash          4

 

 

    Fit    SE Fit        95% CI              95% PI

10.2779  0.688285  (8.74427, 11.8115)  (7.58033, 12.9754)

Interpreting the results

Minitab uses the stored model to calculate that the predicted response value (fit) for the specified predictor values is 10.2779.

Additionally, the confidence interval indicates that you can be 95% confident that the mean yield at these predictor values is between 8.74427 and 11.8115. The prediction interval indicates that you can be 95% confident that a single new observation will fall between 7.58033 and 12.9754.

The prediction interval is always wider than the corresponding confidence interval because of the added uncertainty involved in predicting a single response versus the mean response.

This prediction is based on a model equation. Ensure that your model is adequate before interpreting the results.