# Interpret the key results for Fit Poisson Model

Complete the following steps to interpret a Poisson regression model. Key output includes the p-value, coefficients, model summary statistics, and the residual plots.

## Step 1: Determine whether the association between the response and the term is statistically significant

To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that there is no association between the term and the response. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association exists when there is no actual association.
P-value ≤ α: The association is statistically significant
If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the response variable and the term.
P-value > α: The association is not statistically significant
If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the response variable and the term. You may want to refit the model without the term.
If there are multiple predictors without a statistically significant association with the response, you can reduce the model by removing terms one at a time. For more information on removing terms from the model, go to Model reduction.
If a model term is statistically significant, the interpretation depends on the type of term. The interpretations are as follows:
• If a continuous predictor is significant, you can conclude that the coefficient for the predictor is different from zero.
• If a categorical predictor is significant, you can conclude that not all of the levels have the same mean number of events.
• If an interaction term is significant, you can conclude that the relationship between the predictor and the number of events depends on the other predictors in the term.
• If a polynomial term is significant, you can conclude that the relationship between a predictor and the number of events depends on the magnitude of the predictor.

## Step 2: Determine whether the model does not fit the data

Use the goodness-of-fit tests to determine whether the predicted numbers of events deviate from the observed numbers of events in a way that the Poisson distribution does not predict. If the p-value for the goodness-of-fit test is lower than your chosen significance level, you can reject the null hypothesis that the Poisson distribution provides a good fit. This list provides common reasons for deviations: