Example of a prediction for a Poisson model
main topic     interpreting results     session command     see also 

One product that a company makes are molded resin parts. The quality engineers know that contamination in pipes and abrasions during transfer through hoses can lead to discolored streaks in the final product. A larger screw passes the pellets through the hoses faster. With a new type of resin pellet, the engineers collect data on these discoloration defects to learn about the best way to transfer pellets. After the identification of a model, the engineers use the model to predict the value at different values of the predictors.

1    Open the worksheet 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' and Temperature.

5    In Categorical predictors, enter 'Size of Screw'.

6    Click Model.

7    In Predictors, select 'Temperature' and 'Size of Screw'.

8    For Interactions through order, choose 2.

9    Next to Interactions through order, click Add.

10  Click OK in both dialog boxes.

11  Choose Stat > Regression > Poisson Regression > Predict.

12  In Response, choose  'Discoloration Defects'.

13  In the second drop-down list, choose Enter individual values.

14  In the predictors table, complete the columns of the table as shown below.

Hours Since Cle

Temperature

Size of Screw

4

150

large

15    Click OK.

Session Window Output

 
 

Poisson Regression Analysis: Discoloratio versus Hours Since , Temperature, Size of Scre

 

 

Prediction for Discoloration Defects

 

 

Regression Equation

 

Discoloration Defects  =  exp(Y')

 

 

Y' = 4.5760 + 0.01798 Hours Since Cleanse - 0.003285 Temperature + 0.000000 Size of

     Screw_large - 0.5444 Size of Screw_small + 0.000000 Temperature*Size of Screw_large

     + 0.002804 Temperature*Size of Screw_small

 

 

Variable             Setting

Hours Since Cleanse        4

Temperature              150

Size of Screw          large

 

 

    Fit   SE Fit        95% CI

63.7604  1.91394  (60.1173, 67.6242)

Interpreting the results

Minitab uses the model information to calculate that the average number of discoloration defects is 63.7604.

Additionally, the confidence interval indicates that you can be 95% confident that the average number of defects is between 60.1173 and 67.6242.

This prediction is based on a model equation. You should be sure that your model is adequate before you use the prediction. In particular, the data contain values at only two temperatures. If the relationship between temperature and defects does not follow the model, then the interpolation to temperatures in the middle of the data is inaccurate.