Source | DF | Adj Dev | Adj Mean | Chi-Square | P-Value |
---|---|---|---|---|---|
Regression | 1 | 22.7052 | 22.7052 | 22.71 | 0.000 |
Dose (mg) | 1 | 22.7052 | 22.7052 | 22.71 | 0.000 |
Error | 4 | 0.9373 | 0.2343 | ||
Total | 5 | 23.6425 |
In these results, the p-value for dose is 0.000, which is less than the significance level of 0.05. These results indicate that the association between the dose and the presence of bacteria at the end of treatment is statistically significant.
Use the odds ratio to understand the effect of a predictor. Minitab calculates odds ratios when the model uses the logit link function.
Odds ratios that are greater than 1 indicate that the event 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.
Unit of Change | Odds Ratio | 95% CI | |
---|---|---|---|
Dose (mg) | 0.5 | 6.1279 | (1.7218, 21.8087) |
In these results, the model uses the dosage level of a medicine to predict the presence or absence of bacteria in adults. Each pill contains a 0.5 mg dose, so the researchers use a unit change of 0.5 mg. The odds ratio is approximately 6. For each additional pill that an adult takes, the odds that a patient does not have the bacteria increase by about 6 times.
Use the fitted line plot to examine the relationship between the response variable and the predictor variable.
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 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} is always between 0% and 100%.
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. The deviance R^{2} is usually higher for data in Event/Trial format. 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.
Deviance R-Sq | Deviance R-Sq(adj) | AIC | AICc | BIC | Area Under ROC Curve |
---|---|---|---|---|---|
96.04% | 91.81% | 10.63 | 14.63 | 10.22 | 0.9398 |
In these results, the model explains 96.04% of the deviance in the response variable. 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 other values to compare how well the models fit the data.
Use the residual plots to help you determine whether the model is adequate and meets the assumptions of the analysis. If the assumptions are not met, the model may not fit the data well and you should use caution when you interpret the results.
For more information on how to handle patterns in the residual plots, go to Graphs for Binary Fitted Line Plot and click the name of the residual plot in the list at the top of the page.
Use the residuals versus fits plot to verify the assumption that the residuals are randomly distributed. Ideally, the points should fall randomly on both sides of 0, with no recognizable patterns in the points.
The residuals versus fits plot is only available when the data are in Event/Trial format.
Pattern | What the pattern may indicate |
---|---|
Fanning or uneven spreading of residuals across fitted values | An inappropriate link function |
Curvilinear | A missing higher-order term or an inappropriate link function |
A point that is far away from zero | An outlier |
A point that is far away from the other points in the x-direction | An influential point |