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In these results, the dosage is statistically significant at the significance level of 0. You can conclude that changes in the dosage are associated with changes in the probability that the event occurs. Assess the coefficient to determine whether a change in a predictor variable makes the event more likely or less likely. The relationship between the coefficient and the probability depends on several aspects of the analysis, including the link function.

Generally, positive coefficients indicate that the event becomes more likely as the predictor increases. Negative coefficients indicate that the event becomes less likely as the predictor increases. For more information, go to Coefficients and Regression equation. The coefficient for Dose is 3. In these results, the model uses the dosage level of a medicine to predict the presence or absence of bacteria in adults. The odds ratio indicates that for every 1 mg increase in the dosage level, the likelihood that no bacteria is present increases by approximately 38 times.

In these results, the response indicates whether a consumer bought a cereal and the categorical predictor indicates whether the consumer saw an advertisement about that cereal. The odds ratio is 3. To determine how well the model fits your data, examine the statistics in the Model Summary table. For binary logistic regression, the data format affects the deviance R 2 statistics but not the AIC.

For more information, go to For more information, go to How data formats affect goodness-of-fit in binary logistic regression. The higher the deviance R 2 , the better the model fits your data. Deviance R 2 always increases when you add additional predictors to a model. For example, the best 5-predictor model will always have an R 2 that is at least as high as the best 4-predictor model. Therefore, deviance R 2 is most useful when you compare models of the same size.

For binary logistic regression, the format of the data affects the deviance R 2 value. Deviance R 2 values are comparable only between models that use the same data format.

Deviance R 2 is just one measure of how well the model fits the data. Even when a model has a high R 2 , you should check the residual plots to assess how well the model fits the data. Use adjusted deviance R 2 to compare models that have different numbers of predictors. Deviance R 2 always increases when you add a predictor to the model. The adjusted deviance R 2 value incorporates the number of predictors in the model to help you choose the correct model.

In these results, the model explains For these data, the Deviance R 2 value indicates the model provides a good fit to the data. If additional models are fit with different predictors, use the adjusted Deviance R 2 value and the AIC value to compare how well the models fit the data. If the deviation is statistically significant, you can try a different link function or change the terms in the model. In these results, the goodness-of-fit tests are all greater than the significance level of 0.

Complete the following steps to interpret a regression analysis. Key output includes the p-value, the odds ratio, R 2 , and the goodness-of-fit tests. In This Topic Step 1: Determine whether the association between the response and the term is statistically significant Step 2: Understand the effects of the predictors Step 3: Determine how well the model fits your data Step 4: Determine whether the model does not fit the data.

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 the term's coefficient is equal to zero, which indicates that there is no association between the term and the response.

A significance level of 0. 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. 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 must 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 does not equal zero. If a categorical predictor is significant, you can conclude that not all the level means are equal. Understand the effects of the predictors Use the odds ratio to understand the effect of a predictor. Odds Ratios for Continuous Predictors Odds ratios that are greater than 1 indicate that the even is more likely to occur as the predictor increases.

Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases. Odds Ratios for Continuous Predictor. Determine how well the model fits your data To determine how well the model fits your data, examine the statistics in the Model Summary table.

Deviance R-sq The higher the deviance R 2 , the better the model fits your data. Deviance R-sq adj Use adjusted deviance R 2 to compare models that have different numbers of predictors. The smaller the AIC, the better the model fits the data. However, the model with the smallest AIC does not necessarily fit the data well. Also use the residual plots to assess how well the model fits the data. Model Summary Deviance R-sq. Determine whether the model does not fit the data Use the goodness-of-fit tests to determine whether the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict.

If the p-value for the goodness-of-fit test is lower than your chosen significance level, the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict.

This list provides common reasons for the deviation: Incorrect link function Omitted higher-order term for variables in the model Omitted predictor that is not in the model Overdispersion. For binary logistic regression, the format of the data affects the p-value because it changes the number of trials per row.

The approximation to the chi-square distribution that the Pearson test uses is inaccurate when the expected number of events per row in the data is small. The Hosmer-Lemeshow test does not depend on the number of trials per row in the data as the other goodness-of-fit tests do.

When the data have few trials per row, the Hosmer-Lemeshow test is a more trustworthy indicator of how well the model fits the data. By using this site you agree to the use of cookies for analytics and personalized content.