Correlation & Regression

This lesson covers correlation and regression at A-Level. These techniques are used to explore and quantify the relationship between two variables. Understanding when and how to apply regression analysis and interpret correlation coefficients is essential for the statistics component of A-Level Mathematics.

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Scatter Diagrams

A scatter diagram plots pairs of data $(x, y)$(x,y) to visualise the relationship between two variables. The explanatory (independent) variable is plotted on the $x$x-axis, and the response (dependent) variable on the $y$y-axis.

Types of Correlation

Type	Description
Positive correlation	As $x$x increases, $y$y tends to increase
Negative correlation	As $x$x increases, $y$y tends to decrease
No correlation	No linear relationship between $x$x and $y$y
Strong correlation	Points lie close to a straight line
Weak correlation	Points are widely scattered but show a general trend

Exam Tip: Correlation does not imply causation. Even if two variables are strongly correlated, one does not necessarily cause the other. Always consider confounding variables and the context.

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The Product Moment Correlation Coefficient (PMCC)