Correlation and Regression

This lesson covers correlation and regression as required by the Edexcel A-Level Mathematics specification (9MA0), Paper 3 Section A -- Statistics. You must be able to draw and interpret scatter diagrams, understand the product moment correlation coefficient (PMCC), calculate and use regression lines, and understand the difference between interpolation and extrapolation.

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Scatter Diagrams

A scatter diagram (or scatter plot) is a graph that shows the relationship between two variables. Each data point is plotted as a point with coordinates (x, y).

The explanatory and response variables

• The explanatory variable (independent variable) is plotted on the x-axis. This is the variable you think might influence the other.
• The response variable (dependent variable) is plotted on the y-axis. This is the variable that may be affected.

Example

If you are investigating whether the number of hours of study affects exam score:

• Hours of study = explanatory variable (x-axis)
• Exam score = response variable (y-axis)

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Types of Correlation

Correlation describes the strength and direction of the linear relationship between two variables.