Logistic Regression Calculator

Work out logistic regression instantly with clear inputs, formula shown and shareable results.

About Logistic Regression Calculator

Logistic regression models the log odds as a linear function, so the probability is the logistic transform 1/(1 + e^(−logit)). Each unit increase in x multiplies the odds by e^(b₁), which is why coefficients are reported as odds ratios.

Formulas

Logistic model

logit = b₀ + b₁x, p = 1 / (1 + e^(−logit))

Odds ratio

OR = e^(b₁) per unit increase in x

Worked example

With the default values below, Logistic Regression Calculator returns Predicted probability of 0.62245933. Change any input above and every figure here is recalculated in your browser.

Inputs used

Intercept b₀: -4
Coefficient b₁: 1.5
Predictor value x: 3

Results

Predicted probability: 0.62245933
Logit b₀ + b₁x: 0.50000000
Odds p/(1 − p): 1.64872127
Odds ratio per unit of x: 4.48168907

Step by step

1Values used
2Logistic model
3Odds ratio
4Predicted probability= 0.62245933
5Logit b₀ + b₁x= 0.50000000
6Odds p/(1 − p)= 1.64872127
7Odds ratio per unit of x= 4.48168907

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

With b₀ = −4, b₁ = 1.5 at x = 3?

The logit is 0.5, so the probability is 0.6224593 and the odds are about 1.6487.

Why not use ordinary linear regression?

A straight line can predict probabilities below 0 or above 1; the logistic curve is bounded to the valid range.