Standard Edition

Logistic regression with odds ratios and inverse prediction Binary logistic regression with continuous and categorical predictors — odds ratios, Wald and likelihood ratio tests, and inverse prediction with confidence intervals.

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Model binary outcomes with the same iterative workflow

Excel’s LINEST function and the chart trendline fit a straight line and stop. Fitted to a yes/no outcome — survived or not, responded or not, defective or not — the line predicts probabilities below zero and above one. It gives no odds ratio, no confidence interval and no test of whether a predictor matters. A table of coefficients is not what clinicians or stakeholders act on. Clinicians need odds ratios they can interpret and confidence intervals they can report.

Which predictors change the odds of the outcome, and by how much? Does the model as a whole beat the null model? Does adding a term improve the fit enough to justify keeping it? At what dose do half of the subjects respond?

Binary logistic regression with continuous and categorical predictors

Real outcomes depend on a mix of measurements and categories, not on one variable. Binary logistic regression takes continuous and categorical predictors in the same model, with simple, crossed, polynomial and factorial terms. The dummy variables for each categorical predictor are coded automatically. The model-building workflow is the same as linear regression: add or drop a term in the task pane, Recalculate and see how the fit changes. A scatter plot shows the data.

Binary logistic regression
Probit regression with the same model terms and outputs new in v5.50
Continuous and categorical predictors
Simple, crossed, polynomial and factorial terms
Automatic dummy variable coding
Scatter plot

Microsoft Excel showing the ICU survival logistic regression report from the top: the report title, N 200, and the odds ratio table for 17 predictors with reference levels for each categorical predictor, and the Fit Model task pane open on Fit listing the response STA and the 17 model terms. Handwritten notes: The logit equation, one term per predictor; Terms: 17 predictors, continuous and categorical; Each categorical term against its reference level.

The ICU survival model: 17 predictors listed in the Fit Model task pane, and the odds ratio table with each categorical predictor against its reference level.

Odds ratios with Wald confidence intervals and parameter estimates

An odds ratio is the number a clinician can act on. Each predictor is reported as an odds ratio with a confidence interval. The odds ratio is directly interpretable as the change in odds per unit increase, or against the reference level of a categorical predictor. The underlying coefficients come as parameter estimates with standard errors and Wald Z statistics, with the covariance of estimates matrix and the model equation for documentation.

Odds ratios with confidence intervals
Odds ratios for all pairs or against a reference level, including models with interactions new in v6.01
Parameter estimates with standard errors and Wald Z statistics
Covariance of estimates matrix
Model equation

Likelihood ratio and Wald χ² tests for the model and each term

A predictor that does not contribute should be dropped, and the evidence for each one is in the analysis. The effect of model test shows whether the predictors collectively improve on the null model. The effect of terms test shows whether each term contributes or can be dropped, by likelihood ratio or Wald χ² test. Log-likelihood, AIC, BIC and deviance compare nested models — add a term and see whether the fit improves enough to justify the complexity.

Effect of model: likelihood ratio or Wald χ² test
Effect of terms: likelihood ratio or Wald χ² test for each term
Log-likelihood, AIC, BIC and deviance

Microsoft Excel showing the Effect of Model and Effect of Terms sections of the ICU survival logistic regression report: the likelihood ratio chi-squared test of the model against the null model, and the likelihood ratio test for each of the 17 terms with the significant p-values flagged, and the Fit Model task pane open on Effect of Terms. Handwritten notes: Likelihood ratio test of the whole model against the null; Likelihood ratio test for each term; Test: likelihood ratio or Wald.

Effect of Model and Effect of Terms for ICU survival: likelihood ratio χ² for the whole model, then for each of the 17 terms, five of them significant.

Inverse prediction: X at a specified probability, with confidence interval

Often the question is not the probability at a given X but the X at which the outcome reaches a given probability. Inverse prediction gives that value with a confidence interval. For a dose-response study, that is the dose at which 50% of subjects respond. For a diagnostic assay, it is the concentration at which detection probability reaches 95%.

Inverse prediction: X for a given probability, with confidence interval new in v5.65
Multiple inverse predictions at once new in v5.60

Example analyses

See logistic regression results in detail — odds ratios, model tests and the likelihood ratio test for each term.

2 pages Binary logistic regression
Intensive care unit survival, 17 predictors. 200 observations. Odds ratios with Wald 95% CIs and likelihood ratio tests for the model and for each term. Age, cancer, CPR, systolic blood pressure and admission type are significant at 5%.

Part of the Standard edition

Logistic regression is one part of a complete statistical analysis toolkit. The Standard edition also includes simple and multiple regression, ANOVA and ANCOVA, PCA and factor analysis, descriptive statistics, hypothesis testing, correlation and categorical data analysis. See everything in the Standard edition →

New to the model? Read logistic regression and odds ratios explained, including why a constant odds ratio does not mean a constant change in probability.

Software you can trust

Validated calculations Every statistic tested against the NIST Statistical Reference Datasets, published datasets and thousands of internal test cases. No reliance on Excel’s built-in functions. How Analyse-it is developed and validated →

Data stays on your PC No cloud processing, no uploads, no third-party access. Your data never leaves your computer — essential when working with sensitive, confidential or patient-identifiable data.

Standard Excel workbooks Analyses are ordinary Excel workbooks that you can share with colleagues, archive for audit and open on any machine with Excel — no Analyse-it licence required.

No formulas to break Results contain no formulas, so there is nothing to overwrite and no cell reference to break. The results you reported will be exactly what you find when you reopen the workbook.

Free trial and pricing

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Standard Edition Logistic regression with odds ratios and inverse prediction Binary logistic regression with continuous and categorical predictors — odds ratios, Wald and likelihood ratio tests, and inverse prediction with confidence intervals.