Example of a prediction for a factorial design model
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A metals supplier is developing a new part to be incorporated into the production of a motor. They have studied the effects of three exterior coatings (ExCoat) and three alloys (Alloy) on the corrosion resistance (Resistance) of the new part.

Now, the supplier wants to use the factorial model to predict corrosion resistance for specific variable settings.

You do not need to re-analyze the factorial design. The worksheet contains the model for the prediction.

1    Open the worksheet METALPART_MODEL.MTW.

2    Choose Stat > DOE > Factorial > Predict.

3    In Response, choose Resistance.

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.

ExCoat

Alloy

Plastic

C

6    Click OK.

Session Window Output

Prediction for Resistance

 

 

Regression Equation

 

Resistance = 6.7389 - 0.2222 ExCoat_None - 0.0222 ExCoat_Paint + 0.2444 ExCoat_Plastic

             - 0.0722 Alloy_A - 0.1222 Alloy_B + 0.1944 Alloy_C + 0.0556 ExCoat*Alloy_None A

             - 0.0444 ExCoat*Alloy_None B - 0.0111 ExCoat*Alloy_None C

             + 0.0556 ExCoat*Alloy_Paint A - 0.0944 ExCoat*Alloy_Paint B

             + 0.0389 ExCoat*Alloy_Paint C - 0.1111 ExCoat*Alloy_Plastic A

             + 0.1389 ExCoat*Alloy_Plastic B - 0.0278 ExCoat*Alloy_Plastic C

 

Equation averaged over blocks.

 

 

Variable  Setting

ExCoat    Plastic

Alloy           C

 

Prediction is averaged over blocks.

 

 

 Fit     SE Fit        95% CI              95% PI

7.15  0.0968246  (6.92672, 7.37328)  (6.76327, 7.53673)

Interpreting the results

Minitab uses the regression equation to calculate that the predicted response value (fit) for the specified variable settings is 7.15.

Additionally, the confidence interval indicates that you can be 95% confident that the mean of the corrosion resistance at these settings is between 6.92672 and 7.37328. The prediction interval indicates that you can be 95% confident that a single new observation will fall between 6.76327 and 7.53673.

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.