Poisson regression examines the relationship between one or more predictor variables and a response that counts occurrences. The regression equation explains how the number of occurrences changes as the predictor variables change.

The log link provides the most natural interpretation of the estimated coefficients and is therefore the default link in Minitab. A summary of the interpretation follows:

·    If the magnitude of the estimated coefficient is -0.1–0.1, then the coefficient is an approximate estimate of the proportional change in the response for a 1-unit change in the predictor. For example, a coefficient of 0.05 indicates that the count will increase by about 5% for a 1-unit increase in the predictor.

·     As the magnitude of the estimated coefficient increases, the approximation to the proportional change worsens. To find the proportional change in the response, calculate eβ−1.

For the resin defect data, the model uses the natural log link function. The coefficient for the time since the last cleanse is small and positive, which indicates that the number of defects increases by 1.8% for each hour of time that passes. The coefficient for temperature is small and negative, which indicates that the number of defects decreases by about 0.2% for each increase of 1 degree in temperature.

The coefficient for the size of the screw is further from 0 than -0.1, so a calculation before interpretation is helpful. The calculation e-0.1546-1 = -0.1432. The calculation for the categorical predictor shows that the change from the large screw to the small screw decreases the number of defects by about 14%.