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.

- Enter the sample data, ResinDefects.MTW.
- Choose .
- In Response, enter 'Discoloration Defects'.
- In Continuous predictors, enter 'Hours Since Cleanse' Temperature.
- In Categorical predictors, enter 'Size of Screw'.
- Click Graphs.
- In Residuals for plots, select Standardized.
- Under Residuals plots, select Four in one.
- Click OK in each dialog box.

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.

Link function | Natural log |
---|---|

Categorical predictor coding | (1, 0) |

Rows used | 36 |

Discoloration Defects | = | exp(Y') |
---|

Size of Screw | |||
---|---|---|---|

large | Y' | = | 4.398 + 0.01798 Hours Since Cleanse - 0.001974 Temperature |

small | Y' | = | 4.244 + 0.01798 Hours Since Cleanse - 0.001974 Temperature |

Term | Coef | SE Coef | Z-Value | P-Value | VIF |
---|---|---|---|---|---|

Constant | 4.3982 | 0.0628 | 70.02 | 0.000 | |

Hours Since Cleanse | 0.01798 | 0.00826 | 2.18 | 0.029 | 1.00 |

Temperature | -0.001974 | 0.000318 | -6.20 | 0.000 | 1.00 |

Size of Screw | |||||

small | -0.1546 | 0.0427 | -3.62 | 0.000 | 1.00 |

Deviance R-Sq | Deviance R-Sq(adj) | AIC | AICc | BIC |
---|---|---|---|---|

64.20% | 60.80% | 253.29 | 254.58 | 259.62 |

Test | DF | Estimate | Mean | Chi-Square | P-Value |
---|---|---|---|---|---|

Deviance | 32 | 31.60722 | 0.98773 | 31.61 | 0.486 |

Pearson | 32 | 31.26713 | 0.97710 | 31.27 | 0.503 |

Wald Test | |||
---|---|---|---|

Source | DF | Chi-Square | P-Value |

Regression | 3 | 56.29 | 0.000 |

Hours Since Cleanse | 1 | 4.74 | 0.029 |

Temperature | 1 | 38.46 | 0.000 |

Size of Screw | 1 | 13.09 | 0.000 |

Obs | Discoloration Defects | Fit | Resid | Std Resid | |
---|---|---|---|---|---|

33 | 43.00 | 58.18 | -2.09 | -2.18 | R |

- Press Ctrl+E, or click the Edit Last Dialog button on the Standard toolbar.
- Click Model.
- In Predictors, select Temperature and 'Size of Screw'.
- Next to Interactions through order, choose 2 and click Add.
- Click OK in each dialog box.

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 notices that some coefficients have VIF values that are > 5. In this case, an analysis with standardized continuous predictors to reduce the effect of collinearity gives the same conclusions about the statistical significance of the terms in the model. (For more information, go to Multicollinearity in regression.) The engineer decides to interpret this model rather than the model without the interaction.

Link function | Natural log |
---|---|

Categorical predictor coding | (1, 0) |

Rows used | 36 |

Discoloration Defects | = | exp(Y') |
---|

Size of Screw | |||
---|---|---|---|

large | Y' | = | 4.576 + 0.01798 Hours Since Cleanse - 0.003285 Temperature |

small | Y' | = | 4.032 + 0.01798 Hours Since Cleanse - 0.000481 Temperature |

Term | Coef | SE Coef | Z-Value | P-Value | VIF |
---|---|---|---|---|---|

Constant | 4.5760 | 0.0736 | 62.15 | 0.000 | |

Hours Since Cleanse | 0.01798 | 0.00826 | 2.18 | 0.029 | 1.00 |

Temperature | -0.003285 | 0.000441 | -7.46 | 0.000 | 1.92 |

Size of Screw | |||||

small | -0.5444 | 0.0990 | -5.50 | 0.000 | 5.37 |

Temperature*Size of Screw | |||||

small | 0.002804 | 0.000640 | 4.38 | 0.000 | 6.64 |

Deviance R-Sq | Deviance R-Sq(adj) | AIC | AICc | BIC |
---|---|---|---|---|

85.99% | 81.46% | 236.05 | 238.05 | 243.97 |

Test | DF | Estimate | Mean | Chi-Square | P-Value |
---|---|---|---|---|---|

Deviance | 31 | 12.36598 | 0.39890 | 12.37 | 0.999 |

Pearson | 31 | 12.31611 | 0.39729 | 12.32 | 0.999 |

Wald Test | |||
---|---|---|---|

Source | DF | Chi-Square | P-Value |

Regression | 4 | 78.77 | 0.000 |

Hours Since Cleanse | 1 | 4.74 | 0.029 |

Temperature | 1 | 55.60 | 0.000 |

Size of Screw | 1 | 30.21 | 0.000 |

Temperature*Size of Screw | 1 | 19.17 | 0.000 |