Multiple Regression
Predict with several variables.
Key idea
Predict with several variables.
In depth
Models y with several predictors: ŷ = b₀ + b₁x₁ + b₂x₂ + ... Each coefficient is the effect of one predictor holding the others constant. Adjusted R² penalises useless predictors.
Worked example
Price = 50 + 120(size) + 15(rooms): each extra room adds 15, for the same size.
Formula
Real-world uses
- Predicting house prices from size, location and age together in property analysis
Common mistake
Adding predictors that are strongly correlated with each other (multicollinearity), making coefficients unstable.
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 Multiple Regression?
Predict with several variables. It is a topic at the expert level in Probability & Statistics.
What is the formula for Multiple Regression?
The key formula is y = b₀ + b₁x₁ + b₂x₂.
Where is Multiple Regression used in real life?
Real-world examples: Predicting house prices from size, location and age together in property analysis.
What should I learn before Multiple Regression?
Make sure you are comfortable with Nonparametric Tests, the previous topic in Probability & Statistics.
What is a common mistake with Multiple Regression?
Adding predictors that are strongly correlated with each other (multicollinearity), making coefficients unstable.
How can I practise Multiple 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 Multiple Regression?
Move on to Logistic Regression 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.