# Example of Analyze Binary Response for Definitive Screening Design

Quality engineers want to improve a process that produces pretzels. Color is a key quality characteristic. The engineers use a definitive screening design to determine which potential factors affect the color of the pretzels. For the experiment, inspectors quickly sort small batches of pretzels into conforming and non-conforming categories.

1. Open the sample data, PretzelColor.MTW.
2. Choose Stat > DOE > Screening > Analyze Binary Response
3. In Event name, enter Event.
4. In Number of events, enter Passable Color.
5. In Number of trials, enter Trials.
6. Click Terms.
7. In Include the following terms, choose Full quadratic. Click OK.
8. Click Stepwise.
9. In Method, choose Forward information criteria.
10. Click OK in each dialog box.

## Interpret the results

The Pareto chart shows bars for the terms from the best model according to the AICc criterion. Two main effects are in the model: Bake Time (E) and Bake Temperature 2 (H). The model also includes the square term for Bake Time and the interaction effect between the two factors.

The engineers agree that this model matches their process knowledge. The engineers decide to use the model to plan further experimentation.

## Forward Selection of Terms

Achieved minimum AICc = 243.23

## Response Information

VariableValueCountEvent Name
Passable ColorEvent4235Event
Non-event765
TrialsTotal5000

## Coded Coefficients

TermCoefSE CoefVIF
Constant2.3940.145
Bake Time0.73490.05381.11
Bake Temperature 20.54510.05411.20
Bake Time*Bake Time-0.3840.1531.04
Bake Time*Bake Temperature 2-0.51060.05621.24

## Odds Ratios for Continuous Predictors

Unit of
Change
Odds Ratio95% CI
Bake Time2*(*, *)
Bake Temperature 215*(*, *)
Odds ratios are not calculated for predictors that are included in interaction terms because
these ratios depend on values of the other predictors in the interaction terms.

## Model Summary

Deviance
R-Sq
Deviance
AICAICcBIC
95.81%95.29%241.87243.23251.43

## Goodness-of-Fit Tests

TestDFChi-SquareP-Value
Deviance4532.280.922
Pearson4531.930.929
Hosmer-Lemeshow87.100.526

## Analysis of Variance

Model4737.452184.363737.450.000
Bake Time1203.236203.236203.240.000
Bake Temperature 21100.432100.432100.430.000
Bake Time*Bake Time16.7706.7706.770.009
Bake Time*Bake Temperature 2180.60580.60580.610.000
Error4532.2760.717
Total49769.728

## Regression Equation in Uncoded Units

 P(Event) = exp(Y')/(1 + exp(Y'))
 Y' = -11.984 + 3.361 Bake Time + 0.08740 Bake Temperature 2 - 0.0961 Bake Time*Bake Time- 0.01702 Bake Time*Bake Temperature 2

## Fits and Diagnostics for Unusual Observations

ObsObserved
Probability
FitResidStd Resid
10.98000.93762.02982.13R
70.98000.93961.95812.00R
240.90000.9497-2.0182-2.15R
R  Large residual