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The interpretation of the estimated coefficients depends on: the link function, reference and reference factor levels (see Setting reference levels). The estimated coefficient associated with a predictor (factor or covariate) represents the change in the link function for each unit change in the predictor, while all other predictors are held constant. A unit change in a factor refers to a comparison of a certain level to the reference level.
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:
Continuous predictors
If the magnitude of the estimated coefficient is -0.1–0.1, then the coefficient for a predictor is an approximate estimate of the proportional change in the response for a 1-unit increase in the predictor. For example, a coefficient for time in seconds of 0.05 indicates that the count will increase by about 5% for each additional second.
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.
Categorical predictors with 1, 0 coding
If the magnitude of the estimated coefficient is -0.1–0.1, then the coefficient for a level is an approximate estimate of the proportional change in the response for the change from the reference level to the level of the coefficient. For example, a categorical variable has the levels Fast and Slow and the reference level is Slow. If the coefficient for Fast is -0.075 then a change in the variable from Slow to Fast decreases the count by about 7.5%.
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.
Categorical predictors with 1, 0, -1 coding
If the magnitude of the estimated coefficient is -0.1–0.1, then the coefficient for a level is an approximate estimate of the proportional change in the response for the change from the mean count to the level of the coefficient. For example, a categorical variable has the levels Before Change and After Change. If the coefficient for After Change is -0.04 then the count decreases by about 4% from the average count when the value is After Change.
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.
To change how you view the estimated coefficients, you can change the reference level in the Options subdialog box. See Setting reference levels.