logreg() — Logistic regression

Predicts a probability between 0 and 1 with an S-shaped curve.

logreg(X, y)

Key idea

• It outputs the PROBABILITY (likelihood) of class 1, squashed into the 0-to-1 range by the S-shaped sigmoid curve. (e.g. P(y=1) = 1 / (1 + e^-(b0+b1 x)))
• You usually predict class 1 when that probability passes 0.5. (e.g. p = 0.5 sets the decision boundary)
• Despite the name, it does CLASSIFICATION (sorting into categories), not regression.
• Coefficients are interpretable as log-odds — how much each feature shifts the betting odds.

Definition

$$P(y=1\mid x)=\frac{1}{1+e^{-({\beta }_0+{\beta }_{1}x)}}$$

${\beta }_0$

the intercept

${\beta }_1$

the slope (effect of x)

$e$

about 2.718

$P(y=1\mid x)$

the predicted probability of class 1

In plain words

Instead of a yes/no jump, it draws a smooth ramp from almost certainly no up to almost certainly yes.

Where you'd use it

• Email spam detection: probability an email is spam from its words.
• Medical risk: the chance a patient has a condition given their test values.
• Credit scoring: the probability a loan will default.

Frequently asked questions

What does logistic regression predict?

The probability of a class, via the log-odds. Each coefficient shifts the log-odds; exponentiate it (e^coef) to get an odds ratio.