SigmaCalc

Logistic Regression Calculator

Plug in fitted coefficients and an input value to see the predicted probability the sigmoid function produces.

Intercept (b₀)

Coefficient (b₁)

Input value (x)

Predicted probability

0.599

p = 1 ÷ (1 + e^−(b₀ + b₁x))

What you entered

Intercept (b₀): -4Coefficient (b₁): 0.08Input value (x): 55

1
Linear combination (log-odds)
-4 + 0.08 × 55= 0.4
2
Apply the logistic (sigmoid) function
1 ÷ (1 + e^(−0.4))= 0.5987

Result

Predicted probability: 0.599

With these coefficients, an input of 55 maps to a predicted probability of 59.87% — logistic regression squashes any linear combination into a valid 0–1 probability.

Logistic regression predicted probability

The model computes a linear score from the intercept and coefficient, then squashes it through the logistic function into a probability between 0 and 1.

Intercept	Coefficient	x	Linear score	Predicted probability
-2	0.5	2	-1.000	0.2689
-2	0.5	4	0.000	0.5000
-2	0.5	6	1.000	0.7311
0	1	0	0.000	0.5000
0	1	2	2.000	0.8808
1	-0.5	3	-0.500	0.3775

A linear score of 0 always maps to a probability of exactly 0.5, which is the decision boundary - rows two and four show it arriving from different parameter sets. The relationship is not linear in x: moving the score from 0 to 1 raises the probability by 23 points, but from 2 to 3 raises it by only about 7, because the curve flattens towards the extremes. That is the point of the logistic function - it keeps predictions inside 0 and 1 no matter how large the inputs get. A negative coefficient, as in the last row, means the probability falls as x rises.

This calculates from coefficients, not to them

Fitting a logistic regression model (finding the best b₀ and b₁ from training data) requires iterative optimization beyond what a single-formula calculator can do — this tool evaluates a model you already have, converting coefficients and an input into a predicted probability.

Why probabilities, not straight lines

A plain linear model can predict nonsensical probabilities like 1.4 or −0.2. The sigmoid function used here squashes any input into the valid 0-to-1 range, which is exactly why logistic regression is the standard tool for binary outcomes.

Frequently asked questions

How is logistic regression different from linear regression?

Linear regression predicts a continuous value (house price, temperature). Logistic regression predicts the probability of a yes/no outcome (will the customer buy? will the patient recover?). Linear uses a straight line; logistic uses an S-shaped sigmoid curve that stays between 0 and 1.

What does the sigmoid function do?

The sigmoid σ(z) = 1/(1+e⁻ᶻ) maps any input to a probability between 0 and 1. When z = 0, output = 0.5. Large positive z → output near 1. Large negative z → output near 0. It creates the characteristic S-curve of logistic regression.

What are the coefficients b₀ and b₁?

b₀ (intercept) sets the baseline probability when x = 0. b₁ (slope) determines how much each unit increase in x shifts the log-odds. Positive b₁ = higher x increases probability. Negative b₁ = higher x decreases probability. This calculator evaluates a model you already have — it doesn't fit the coefficients from raw data.