Correlation and causation

In short: Correlation means two quantities rise or fall together. Causation means one causes the other. Correlation alone does not imply a cause.

In more detail: The correlation coefficient r lies between −1 and +1. Near +1: same direction, near −1: opposite, near 0: no linear relationship.

In Depth

Third variable (confounder): Ice-cream sales and sunburns correlate because both depend on weather, not because ice cream causes sunburn.
Reverse direction: Do people who exercise a lot get healthier? Or do healthy people exercise more? Both can be true.
Chance: With many comparisons there are always apparent relationships (“spurious correlations”), for example between cheese consumption and accidents with bedsheets.
Non-linear: r captures only linear relationships. A U-shaped relationship can have r ≈ 0.
Testing causation: Controlled experiments with random assignment (randomised trials, A/B tests), temporal order, plausible mechanism, replication.
Everyday tip: For headlines such as “X raises the risk of Y”, check: how big is the effect in absolute numbers? What type of study?
AI: Models learn correlations. Without extra knowledge they confuse them with causes.