Linear Regression
Best-fit line through data.
Key idea
Best-fit line through data.
In depth
The least-squares line ŷ = a + bx minimises the sum of squared vertical errors. Slope b = r·(sᵧ/sₓ), and the line passes through (x̄, ȳ). It predicts y within the range of data.
Worked example
If b = 2.5, each extra hour studied is associated with 2.5 more points on average.
Formula
Real-world uses
- Predicting house prices from size
- Forecasting sales from marketing budgets
Common mistake
Extrapolating far beyond the data range.
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 Linear Regression?
Best-fit line through data. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Linear Regression?
The key formula is ŷ = a + bx.
Where is Linear Regression used in real life?
Real-world examples: Predicting house prices from size; Forecasting sales from marketing budgets.
What should I learn before Linear Regression?
Make sure you are comfortable with Correlation, the previous topic in Probability & Statistics.
What is a common mistake with Linear Regression?
Extrapolating far beyond the data range.
How can I practise Linear 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 Linear Regression?
Move on to Residuals and R² next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.