# Example of Fit Poisson Model

A quality engineer is concerned about two types of defects in molded resin parts: discoloration and clumping. Discolored streaks in the final product can result from contamination in hoses and from abrasions to resin pellets. Clumping can occur when the process is run at higher temperatures and faster rates of transfer. The engineer identifies three possible predictor variables for the responses (defects). The engineer records the number of each type of defect in hour long sessions, while varying the predictor levels.

The engineer wants to study how several predictors affect discoloration defects in resin parts. Because the response variable describes the number of times that an event occurs in a finite observation space, the engineer fits a Poisson model.

1. Enter the sample data, ResinDefects.MTW.
2. Choose Stat > Regression > Poisson Regression > Fit Poisson Model.
3. In Response, enter 'Discoloration Defects'.
4. In Continuous predictors, enter 'Hours Since Cleanse' Temperature.
5. In Categorical predictors, enter 'Size of Screw'.
6. Click Graphs.
7. In Residuals for plots, select Standardized.
8. Under Residuals plots, select Four in one.
9. Click OK in each dialog box.

## Interpret the results

The plot of the standardized deviance residuals versus the fitted values shows a distinct curve. In the plot of the residuals versus order, the residuals in the middle tend to be higher than the residuals at the beginning and end of the data set. For these data, both patterns are because of a missing interaction term between the size of the screw and the temperature. The pattern is visible on the residuals versus order plot because the engineer did not collect the data in random order. The engineer refits the model with the interaction between temperature and the size of the screw to model the defects more accurately.

For the model with the interaction, the AIC is approximately 236, which is lower than the model without the interaction. The AIC criterion indicates that the model with the interaction is better than the model without the interaction. The curvature in the residuals versus fits plot is gone. The engineer decides to interpret this model rather than the model without the interaction.

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