2. Why Logistic Regression?
⢠Used for binary classification problems
⢠Predicts probability of outcome between 0
and 1
⢠Unlike linear regression, output is bounded
⢠Common in medical diagnosis, spam
detection, fraud detection
3. Sigmoid Function
⢠Maps any real value to (0, 1)
⢠Formula: Ď(z) = 1 / (1 + e^(-z))
⢠S-shaped curve for probability mapping
4. Mathematical Form
⢠Linear predictor: z = β0 + β1x1 + β2x2 + ... +
βnxn
⢠Probability: p = Ď(z)
⢠Logit form: log(p/(1-p)) = β0 + β1x1 + ... + βnxn
5. Odds and Log-Odds
⢠Odds: p / (1-p)
⢠Log-Odds (logit): log(p/(1-p))
⢠Coefficients represent change in log-odds per
unit change in predictor
6. Example
⢠Predicting disease based on age and BMI
⢠Model outputs probability of disease
⢠Threshold (e.g., 0.5) used for classification
7. Decision Boundary
⢠Separates classes in feature space
⢠Probability threshold defines boundary
⢠Can be visualized in 2D for two features
8. Key Assumptions
⢠Binary dependent variable
⢠Linearity of independent variables and log-
odds
⢠No or little multicollinearity
⢠Independent observations
9. Summary
⢠Logistic regression models probability
⢠Uses sigmoid to bound predictions
⢠Interpretable through odds ratios
⢠Widely used for classification tasks
