Logistic Regression
Model probabilities of binary outcomes.
Key idea
Model probabilities of binary outcomes.
In depth
Models a probability of a yes/no outcome: log(p/(1 − p)) = b₀ + b₁x. The S-shaped curve keeps predictions between 0 and 1. Coefficients change the log-odds.
Worked example
If b₁ = 0.7, each unit increase in x multiplies the odds by e^0.7 ≈ 2.0.
Formula
Real-world uses
- Estimating the chance a customer will churn or that a loan will default
Common mistake
Interpreting coefficients as changes in probability instead of log-odds.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Logistic Regression?
Model probabilities of binary outcomes. It is a topic at the expert level in Probability & Statistics.
What is the formula for Logistic Regression?
The key formula is p = 1/(1+e^(−z)).
Where is Logistic Regression used in real life?
Real-world examples: Estimating the chance a customer will churn or that a loan will default.
What should I learn before Logistic Regression?
Make sure you are comfortable with Multiple Regression, the previous topic in Probability & Statistics.
What is a common mistake with Logistic Regression?
Interpreting coefficients as changes in probability instead of log-odds.
How can I practise Logistic Regression?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Logistic Regression?
Move on to Maximum Likelihood Estimation next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.