Logistic Regression Calculator
This free logistic regression calculator fits a logistic model to your data, returns the coefficients, odds ratio, accuracy and decision boundary, and plots the fitted S-curve — so you can see exactly how the probability of a yes/no outcome changes with your predictor.
How to use the logistic regression calculator
- Enter your predictor ($x$) values — any numeric variable such as hours studied, age, or dose.
- Enter the outcome ($y$) as
0or1(fail/pass, no/yes), one label per $x$ value. - Press “Fit logistic model” to estimate the coefficients and draw the probability curve.
- Type any $x$ in the predict box to get the probability and predicted class for a new case.
What the logistic regression calculator computes
Logistic regression models the probability of the outcome with the sigmoid function:
$$p = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x)}}$$The calculator estimates $\beta_0$ and $\beta_1$ by maximum likelihood (using gradient descent), then reports:
| Output | Meaning |
|---|---|
| Intercept $\beta_0$ | Log-odds of the outcome when $x = 0$. |
| Coefficient $\beta_1$ | Change in log-odds per one-unit increase in $x$. |
| Odds ratio $e^{\beta_1}$ | How the odds multiply for each one-unit rise in $x$. |
| Accuracy | Share of points classified correctly at the 0.5 threshold. |
| Pseudo $R^2$ | McFadden’s fit measure — higher means a better fit. |
| Decision boundary | The $x$ where $p = 0.5$ (the model flips its prediction). |
Worked example: hours studied vs passing
The built-in example is the classic study-hours dataset: 20 students, their hours of study ($x$), and whether they passed ($y = 1$) or failed ($y = 0$). Fitting it gives roughly $\beta_0 \approx -4.08$ and $\beta_1 \approx 1.50$, so each extra hour multiplies the odds of passing by about $e^{1.5} \approx 4.5$, and the 50% decision boundary lands near 2.7 hours. Study less and you are more likely to fail; study more and the curve climbs toward a near-certain pass.
🤖 Why logistic regression matters in ML
Logistic regression is the simplest classification model and the building block of neural networks — a single neuron with a sigmoid activation. It is supervised learning; see supervised vs unsupervised vs reinforcement learning. To understand how it differs from fitting a straight line, read logistic regression vs linear regression, or fit continuous data with the linear regression calculator.
Assumptions to keep in mind
- The outcome is binary (exactly two classes).
- The log-odds are linearly related to the predictor.
- Observations are independent.
- There is enough data in both classes — this tool needs at least one 0 and one 1.
Frequently asked questions
What does a logistic regression calculator do?
What data do I need?
How is the coefficient interpreted?
What is the decision boundary?
Is this multiple or simple logistic regression?
Key takeaways
A logistic regression calculator turns raw 0/1 data into a fitted probability curve, coefficients and an odds ratio in one click. Use it to model any yes/no outcome, read the decision boundary, and predict the probability for new inputs. Pair it with the logistic vs linear regression guide or the formal reference on Wikipedia.