Correlation
Strength of linear relationship from −1 to 1.
Key idea
Strength of linear relationship from −1 to 1.
In depth
The correlation coefficient r (from −1 to 1) measures the strength and direction of a linear relationship. r = 0 means no linear relationship, though a nonlinear one may exist. It is unaffected by units or scale.
Worked example
r = 0.9 indicates a strong positive linear relationship. r = −0.2 is weak and negative.
Formula
Real-world uses
- Measuring how closely advertising spend moves with sales
- Picking features in data science
Common mistake
Treating r = 0 as meaning no relationship at all; y = x² can have r ≈ 0.
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 Correlation?
Strength of linear relationship from −1 to 1. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Correlation?
The key formula is r = Σ(x−x̄)(y−ȳ)/(n sₓ sᵧ).
Where is Correlation used in real life?
Real-world examples: Measuring how closely advertising spend moves with sales; Picking features in data science.
What should I learn before Correlation?
Make sure you are comfortable with Scatter Plots, the previous topic in Probability & Statistics.
What is a common mistake with Correlation?
Treating r = 0 as meaning no relationship at all; y = x² can have r ≈ 0.
How can I practise Correlation?
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 Correlation?
Move on to Linear Regression 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.