Calculators/Logistic Regression Calculator

Regression & Correlation

Logistic Regression Calculator

Fit a logistic regression for a yes/no outcome, and see each predictor's coefficient, odds ratio, and whether the whole model beats chance.

Your data

First row: headers, outcome first as 0/1 (e.g. pass,hours). Each row after that: one observation. The model is fit by Newton-Raphson iteration.

logit(p) = -8.357 + 1.8551·hours

Term	Coef.	SE	z	p-value	Odds ratio
Intercept	-8.3569	4.781	-1.748	0.0805	—
hours	1.8551	1.0442	1.777	0.0756	6.3926

McFadden's R²

0.6661

Log-likelihood

-3.46

LR χ²

13.807

LR p-value

0.0002

The likelihood-ratio test (χ² = 13.81 on 1 degrees of freedom, p = 0.0002) compares this model with one that has no predictors at all. Each odds ratio shows the multiplicative change in the odds of pass = 1 for a one-unit increase in that predictor, holding the others fixed, as explained in logistic regression.

How to use this tool

Paste your data as comma-separated values, with the 0/1 outcome in the first column and each predictor in its own column.
The first row must be headers, for example pass,hours.
Read the fitted logit equation and the coefficient table, including each odds ratio.
Check the likelihood-ratio test to see whether the model as a whole explains more than chance.

Formula Reference

Logit model

logit(p) = ln[p / (1 - p)] = b0 + b1*x1 + ...

Predicted probability

p = 1 / (1 + e^(-logit))

Odds ratio

e^(coefficient)

Likelihood-ratio test

2 x (log-likelihood - null log-likelihood)

ArticleLogistic Regression ArticleMultinomial Logistic Regression ArticleOdds vs. Probability ArticleSensitivity, Specificity & ROC Curves CalcMultiple Regression Calculator GlossaryGlossary: Odds Ratio

Frequently Asked Questions

Why use logistic regression instead of ordinary linear regression?+

A 0/1 outcome violates the assumptions behind ordinary regression, and a fitted line can predict probabilities below 0 or above 1. Logistic regression models the log-odds instead, which keeps predicted probabilities between 0 and 1.

What does an odds ratio above 1 mean?+

It means that predictor is associated with higher odds of the outcome being 1, holding the other predictors fixed. An odds ratio of 2 means the odds roughly double for each one-unit increase; an odds ratio below 1 means the odds fall.

What is McFadden's pseudo R-squared?+

It compares the fitted model's log-likelihood with that of a model containing only an intercept. Unlike ordinary R-squared, it has no simple "percent of variance explained" reading; values from about 0.2 to 0.4 are often considered a good fit for this measure.

Why does it say the model could not be fit?+

This usually means perfect separation: some value of a predictor perfectly predicts the outcome, which makes a coefficient tend toward infinity. It can also happen when predictors are too closely related to each other.

Term

Coef.

p-value

Odds ratio

Intercept

-8.3569

4.781

-1.748

0.0805

—

hours

1.8551

1.0442

1.777

0.0756

6.3926

How to use this tool

Paste your data as comma-separated values, with the 0/1 outcome in the first column and each predictor in its own column.

The first row must be headers, for example pass,hours.

Read the fitted logit equation and the coefficient table, including each odds ratio.

Check the likelihood-ratio test to see whether the model as a whole explains more than chance.

Frequently Asked Questions

Why use logistic regression instead of ordinary linear regression?+

What does an odds ratio above 1 mean?+

What is McFadden's pseudo R-squared?+

Why does it say the model could not be fit?+