Correlation and Regression

Correlation and regression are tools for exploring and modelling the relationship between two (or more) quantitative variables. Correlation measures the strength and direction of a linear relationship, while regression provides a predictive equation.

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Correlation

Scatter Plots

The first step in studying the relationship between two variables is to create a scatter plot. Each point represents one observation plotted as (x, y).

Patterns to look for:

• Direction — positive (upward trend), negative (downward), or no trend
• Form — linear, curved, or no clear pattern
• Strength — how tightly points cluster around a line or curve
• Outliers — points that deviate markedly from the pattern

Pearson Correlation Coefficient (r)

The Pearson correlation coefficient measures the strength and direction of a linear relationship:

r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √[Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²]