Correlation & Regression Modelling

This lesson covers correlation and regression in depth — the tools used to quantify and model the relationship between two variables. These techniques are central to the A-Level Mathematics statistics specification and are frequently tested using data from the large data set.

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Correlation

Correlation measures the strength and direction of the linear relationship between two variables. It does not imply causation.

Product Moment Correlation Coefficient (PMCC)

The PMCC, denoted $r$r, quantifies the linear correlation between variables $x$x and $y$y:

$r = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}}$r=Sxx​Syy​​Sxy​​

where:

$S_{xx} = \sum x^2 - \frac{(\sum x)^2}{n}, \quad S_{yy} = \sum y^2 - \frac{(\sum y)^2}{n}, \quad S_{xy} = \sum xy - \frac{(\sum x)(\sum y)}{n}$Sxx​=∑x2−n(∑x)2​,Syy​=∑y2−n(∑y)2​,Sxy​=∑xy−n(∑x)(∑y)​

Interpreting $r$r