# 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.

### Screening Design Binary Logistic Regression: Passable Col versus Flour Protei, Water, ...

Method Link function Logit Rows used 50
Forward Selection of Terms Achieved minimum AICc = 243.23
Response Information Event Variable Value Count Name Passable Color Event 4235 Event Non-event 765 Trials Total 5000
Coded Coefficients Term Coef SE Coef VIF Constant 2.394 0.145 Bake Time 0.7349 0.0538 1.11 Bake Temperature 2 0.5451 0.0541 1.20 Bake Time*Bake Time -0.384 0.153 1.04 Bake Time*Bake Temperature 2 -0.5106 0.0562 1.24
Odds Ratios for Continuous Predictors Unit of Odds 95% Change Ratio CI Bake Time 2 * (*, *) Bake Temperature 2 15 * (*, *) 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 Deviance R-Sq R-Sq(adj) AIC AICc BIC 95.81% 95.29% 241.87 243.23 251.43
Goodness-of-Fit Tests Test DF Chi-Square P-Value Deviance 45 32.28 0.922 Pearson 45 31.93 0.929 Hosmer-Lemeshow 8 7.10 0.526
Analysis of Variance Source DF Adj Dev Adj Mean Chi-Square P-Value Model 4 737.452 184.363 737.45 0.000 Bake Time 1 203.236 203.236 203.24 0.000 Bake Temperature 2 1 100.432 100.432 100.43 0.000 Bake Time*Bake Time 1 6.770 6.770 6.77 0.009 Bake Time*Bake Temperature 2 1 80.605 80.605 80.61 0.000 Error 45 32.276 0.717 Total 49 769.728
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 Observed Obs Probability Fit Resid Std Resid 1 0.9800 0.9376 2.0298 2.13 R 7 0.9800 0.9396 1.9581 2.00 R 24 0.9000 0.9497 -2.0182 -2.15 R R Large residual
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