Correlation

#### Tier: #Foundation #Higher

Description

Correlation describes the relationship between two variables plotted on a scatter graph.

Types of correlation:

• Positive correlation: as one variable increases, so does the other — points slope upward left to right
• Negative correlation: as one variable increases, the other decreases — points slope downward
• No correlation: no visible pattern — points scattered randomly

Strength of correlation:

• Strong: points close to a straight line
• Weak: points loosely scattered around a trend
• Perfect: all points lie exactly on a line (rare in real data)

$$\text{Positive: } r > 0, \quad \text{Negative: } r < 0, \quad \text{No correlation: } r \approx 0$$

Important: correlation does not imply causation — two variables may be correlated due to a third (confounding) variable.

The line of best fit passes through the mean point $(\bar{x}, \bar{y})$ and minimises the overall distance of points from the line.

Common error: confusing correlation with causation, or drawing a line of best fit that does not pass through the mean point.

Links

Gradients and intercepts