Residuals and R²
Error of a fit and proportion of variance explained.
Key idea
Error of a fit and proportion of variance explained.
In depth
A residual is observed minus predicted value. A good model has residuals scattered randomly around zero. R² = r² gives the fraction of variation in y explained by x.
Worked example
R² = 0.64 means 64% of the variation in y is accounted for by the linear relationship.
Real-world uses
- Judging how well a fitted model explains sales data
- Checking that errors look random
Common mistake
Thinking a high R² proves the model is right; check residual patterns.
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 Residuals and R²?
Error of a fit and proportion of variance explained. It is a topic at the expert level in Probability & Statistics.
Where is Residuals and R² used in real life?
Real-world examples: Judging how well a fitted model explains sales data; Checking that errors look random.
What should I learn before Residuals and R²?
Make sure you are comfortable with Linear Regression, the previous topic in Probability & Statistics.
What is a common mistake with Residuals and R²?
Thinking a high R² proves the model is right; check residual patterns.
How can I practise Residuals and R²?
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 Residuals and R²?
Move on to Correlation vs Causation next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- 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.
- Linearity of Expectation – Expectation of sums is sum of expectations.