NOTE: Sometimes a logistic regression attempt will fail. This can be because of insufficient rank in the matrix due to there not being enough observations or due to some of the regressors being “colinear”, that is, being linear combinations of another regressor or regressors and therefore not able to “present new data” to the regression.

However, see 17.14 for other causes of regression failure much more specific to logistic regression.

17.13.1 Residual Spreadsheet

A residual spreadsheet may optionally be produced. This spreadsheet will contain the actual, predicted, and residual values for each sample, as well as the spreadsheet values for each covariate and interaction term. The residual value of a sample is defined as the difference between the sample’s actual value and its predicted value from the regresssion.

NOTE: Strictly speaking, residuals do not make as much sense for logistic regression as they do for linear regression because the distribution of a logistic regression separates into two parts. However, ChemTree shows this spreadsheet anyway to allow seeing a crude gauge of how well the the regression is predicting the dependent variable, as well as seeing the covariates and interaction terms.

17.13.2 Logistic Regression Statistical Output Viewer

As detailed in 16.2.5, a statistical output viewer will be displayed for the regression.

17.13.3 Overall Statistics

The following overall statistics are displayed for both normal and stepwise regression:

• The name of the response variable.
• The regression likelihood.
• The null model likelihood.
• The sample size.
• The regression chi-square statistic.
• The regression p-value.
• The permuted P-Value, if permutation testing has been selected.
• The number of permutations, if permutation testing has been selected.
• The regression degrees of freedom.
• The residual degrees of freedom.
• The total degrees of freedom.

17.13.4 Regressor Statistics

The y-intercept is displayed. Then, the following statistics are displayed for each regressor:

• The regressor (the covariate or interaction term).
• The regression coefficient for this regressor.
• Pr(> ∣t∣). This is the p-value from regressing using the actual full model as its full model, but using the actual full model without this regressor as its reduced model. Thus, this shows how much difference this particular regressor is making in the regression. Pr(> ∣t∣) refers to the probability that the difference made by adding this regressor is accounted for by chance, and thus that this case could be thought of as being in one of the “tails” of the applicable t-distribution.
• The odds ratio for this regression coefficient. The regression odds ratio for the coefficient β is e^β. The interpretation of this is how much (by what ratio) the odds of the dependent being one change if the given regressor changes by one unit.
• Univariate Fit. This is the p-value of simply taking a regression with this regressor, all by itself, against the dependent variable.

17.13.5 Left-Out Regressors

Any potential regressors which have been left out are listed here. This list will include all regressors that were excluded from the final model of a stepwise regression.

17.13.6 Parameters

The parameters used for the regression are shown.