Binary Logistic Regression Calculator

Enter Model Inputs

Use estimated coefficients from a binary logistic model. Then enter predictor values for one observation to calculate probability, odds, class, and related diagnostics.

Intercept (β0)

Classification Threshold

Actual Outcome (Optional)

Coefficient β1

Predictor X1

Coefficient β2

Predictor X2

Coefficient β3

Predictor X3

Coefficient β4

Predictor X4

Coefficient β5

Predictor X5

Reset

Example Data Table

This example shows how entered coefficients and predictors can estimate the probability of a binary event such as churn, default, approval, or disease status.

Case	β0	β1	X1	β2	X2	β3	X3	Probability	Predicted Class
1	-4.20	0.06	45	1.15	1	-0.80	2	12.46%	0
2	-4.20	0.06	58	1.15	1	-0.80	0	40.13%	0
3	-4.20	0.06	68	1.15	1	-0.80	0	55.52%	1
4	-4.20	0.06	50	1.15	0	-0.80	5	1.10%	0

Formula Used

1) Linear Predictor

z = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5

This combines the intercept and each coefficient multiplied by its predictor value.

2) Logistic Probability

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

This transforms the logit into a probability between 0 and 1.

3) Odds

Odds = e^z

Odds show how many times more likely the event is than the non-event.

4) Odds Ratio for Each Predictor

OR = e^βi

An odds ratio above 1 increases event odds. Below 1 decreases event odds.

5) Marginal Effect

ME = p(1 − p)βi

This approximates how a one-unit increase in a predictor changes probability at the current observation.

6) Optional Accuracy Metrics

Residual = y − p

Log Loss = −[y ln(p) + (1 − y) ln(1 − p)]

Brier Score = (y − p)²

These require the actual outcome and help evaluate one prediction.

How to Use This Calculator

Enter the intercept and up to five logistic coefficients from your fitted model.
Enter the corresponding predictor values for the observation you want to score.
Set a classification threshold, such as 0.50 or another policy cutoff.
Optionally provide the true outcome to calculate residual, log loss, Brier score, and deviance contribution.
Click the calculate button to display the result summary above the form.
Review probability, odds, predicted class, coefficient contributions, and marginal effects.
Use the CSV and PDF buttons to export the displayed results.

FAQs

1) What does this calculator do?

It converts logistic regression coefficients and predictor values into a predicted probability, odds, class decision, and several practical diagnostic measures for one observation.

2) Does this tool estimate coefficients from raw data?

No. It evaluates predictions from coefficients you already estimated elsewhere. Enter your fitted intercept and coefficients, then score a new or existing case.

3) What is the difference between probability and odds?

Probability is the chance of the event from 0 to 1. Odds compare event likelihood to non-event likelihood and are calculated as exp(logit).

4) What does the threshold control?

The threshold decides when a probability becomes class 1. A threshold of 0.50 predicts an event only when the probability is at least 50%.

5) Why are odds ratios shown?

Odds ratios help interpret coefficients. A value above 1 increases event odds, while a value below 1 reduces them, holding other predictors constant.

6) What is a marginal effect?

A marginal effect estimates how much the predicted probability changes for a one-unit increase in a predictor at the current observation values.

7) When should I enter the actual outcome?

Enter it when you want prediction error metrics like residual, log loss, Brier score, and whether the chosen threshold classified the case correctly.

8) Can I use fewer than five predictors?

Yes. Leave unused coefficients and predictor values as zero. The calculator will ignore their contribution and still compute the final probability correctly.