Example of Analyze Binary Response for Response Surface Design

A clean room engineer analyzes a response surface design to determine how seal time, temperature, and pressure affect the seal quality of the sealed trays. The response is binary—whether the seal is intact or not—in a sample of 800 tray seals.

The engineer collects data and analyzes the design to determine which factors impact seal strength.

  1. Open the sample data, TraySeal.MTW.
  2. Choose Stat > DOE > Response Surface > Analyze Binary Response.
  3. In Event name, enter Event.
  4. In Number of events, enter Sealed.
  5. In Number of trials, enter Samples.
  6. Click Terms.
  7. Under Include the following terms, choose Full quadratic.
  8. Click OK.
  9. Click Graphs.
  10. Under Residual Plots, select Four in one.
  11. Click OK in each dialog box.

Interpret the results

In the Analysis of Variance table, the p-values for Temperature, Pressure and Temperature*Temperature are significant. The engineer can consider reducing the model to remove the terms that are not significant. For more information, go to Model reduction.

The Deviance R2 value shows that the model explains 97.47% of the total deviance in the response, which indicates that the model fits the data well.

The Pareto plot of the effects allow you to visually identify the important effects and compare the relative magnitude of the various effects. In addition, you can see that the largest effect is Temperature*Temperature (BB) because it extends the farthest.

Response Surface Binary Logistic Regression: Sealed versus Time, Temperature, ...

Method Link function Logit Rows used 15
Response Information Event Variable Value Count Name Sealed Event 9637 Event Non-event 2363 Samples Total 12000
Coded Coefficients Term Coef SE Coef VIF Constant 3.021 0.384 Time 0.210 0.139 18.53 Temperature 0.641 0.159 19.53 Pressure 0.420 0.211 70.48 Time*Time -0.0735 0.0482 1.01 Temperature*Temperature 0.2988 0.0517 1.17 Pressure*Pressure -0.0022 0.0277 70.24 Time*Temperature -0.0092 0.0505 1.14 Time*Pressure 0.0417 0.0342 18.12 Temperature*Pressure -0.0521 0.0396 19.24
Odds Ratios for Continuous Predictors Unit of Odds 95% Change Ratio CI Time 1.0 * (*, *) Temperature 25.0 * (*, *) Pressure 7.5 * (*, *) 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 97.47% 96.50% 140.64 195.64 147.72
Goodness-of-Fit Tests Test DF Chi-Square P-Value Deviance 5 23.40 0.000 Pearson 5 23.88 0.000 Hosmer-Lemeshow 5 7.47 0.188
Analysis of Variance Source DF Adj Dev Adj Mean Chi-Square P-Value Model 9 903.478 100.386 903.48 0.000 Time 1 2.303 2.303 2.30 0.129 Temperature 1 16.388 16.388 16.39 0.000 Pressure 1 3.966 3.966 3.97 0.046 Time*Time 1 2.331 2.331 2.33 0.127 Temperature*Temperature 1 34.012 34.012 34.01 0.000 Pressure*Pressure 1 0.006 0.006 0.01 0.937 Time*Temperature 1 0.033 0.033 0.03 0.856 Time*Pressure 1 1.490 1.490 1.49 0.222 Temperature*Pressure 1 1.731 1.731 1.73 0.188 Error 5 23.404 4.681 Total 14 926.882
Regression Equation in Uncoded Units P(Event) = exp(Y')/(1 + exp(Y')) Y' = 17.77 + 0.348 Time - 0.1918 Temperature + 0.1146 Pressure - 0.0735 Time*Time + 0.000478 Temperature*Temperature - 0.000039 Pressure*Pressure - 0.00037 Time*Temperature + 0.00556 Time*Pressure - 0.000278 Temperature*Pressure
Fits and Diagnostics for Unusual Observations Observed Obs Probability Fit Resid Std Resid 1 0.7113 0.6856 1.5722 4.45 R 3 0.9025 0.8879 1.3370 2.50 R 7 0.9675 0.9565 1.5927 2.17 R 8 0.6737 0.6884 -0.8891 -2.44 R 10 0.5550 0.5660 -0.6265 -2.07 R 11 0.9025 0.9281 -2.6700 -4.20 R 12 0.8413 0.8633 -1.7806 -3.54 R 15 0.7113 0.6892 1.3592 3.64 R R Large residual
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