Explain logistic regression.

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Logistic Regression is a statistical and machine learning algorithm used for classification problems, not regression, despite its name. It predicts the probability of an outcome belonging to a particular class, typically binary (e.g., spam/not spam, yes/no).

Instead of fitting a straight line like linear regression, it uses the logistic (sigmoid) function:

$P(y=1|x) = \frac{1}{1 + e^{-(b_0 + b_1x_1 + ... + b_nx_n)}}$

This function outputs values between 0 and 1, representing probabilities.

Decision rule:

If probability ≥ 0.5 → Class 1
If probability < 0.5 → Class 0

Key Points:

Works for binary, multinomial, and ordinal classification.
Coefficients are estimated using Maximum Likelihood Estimation (MLE).
Can include regularization (L1, L2) to prevent overfitting.

Example uses: Email spam detection, disease prediction, customer churn analysis.

In short, logistic regression maps input features to probabilities and uses a threshold to make classification decisions.

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