Statistics Foundation · Lesson 5.5
Logistic regression foundations.
Logistic regression explains how regression ideas change when the outcome is binary. This lesson develops probability, odds, log-odds, the logistic curve, odds ratios, prediction thresholds, calibration, discrimination and responsible interpretation.
Lesson route
Move from linear regression to probability modelling.
Linear regression predicts a continuous mean. Logistic regression predicts the probability of an event. This requires changing the scale from probability to odds to log-odds.
0–20 min
Why linear regression is not enough
Understand why binary outcomes require a model that produces probabilities between 0 and 1.
20–45 min
Probabilities, odds and log-odds
Build the conceptual bridge from probability to odds to log-odds.
45–75 min
The logistic curve
Study how the logistic function converts any real number into a valid probability.
75–105 min
The logistic regression equation
Learn the model logit(p) = β₀ + β₁X and interpret coefficients carefully.
105–135 min
Odds ratios
Understand why exponentiating a logistic coefficient gives an odds ratio.
135–170 min
Prediction and classification
Separate predicted probabilities from classification decisions and understand threshold trade-offs.
170–200 min
Model interpretation and limits
Study non-collapsibility, confounding, calibration, discrimination and responsible reporting.
Mastery checklist
Students should understand probabilities, odds and decisions.
Explain why binary outcomes need probability models.
Convert between probability and odds.
Define log-odds and the logit transformation.
Write the logistic regression equation.
Convert a linear predictor into probability.
Interpret logistic coefficients as log-odds changes.
Interpret odds ratios correctly.
Separate probability prediction from classification.
Explain threshold trade-offs.
Distinguish calibration from discrimination.