Edexcel IAL - Statistics 1- 4.2 Explanatory and Response Variables- Study notes  - New syllabus

Explanatory and Response Variables

In statistical modelling, relationships between two variables are described using an explanatory variable and a response variable. These ideas are fundamental when interpreting scatter diagrams and regression lines.

Explanatory (Independent) Variable

The explanatory variable is the variable that is believed to influence or explain changes in another variable. 

It is usually plotted on the horizontal axis

It is often controlled or selected

Common notation includes \( x \), but other symbols may be used.

Response (Dependent) Variable

The response variable is the variable whose value is observed or measured as a result of changes in the explanatory variable.

It is usually plotted on the vertical axis

Its value depends on the explanatory variable

Common notation includes \( y \), but other symbols may be used.

Applications and Interpretation

When a regression line is used:

• The explanatory variable is used to predict the response variable
• The relationship describes association, not causation

Interpretation must always be given in the context of the data.

Predictions and Extrapolation

Regression equations should only be used to make predictions:

Within the range of the observed explanatory variable values

Using a regression line outside this range is called extrapolation and can be unreliable.

• The relationship may not continue beyond the observed data
• Predictions may be misleading

Linear Change of Variable

In some situations, variables other than \( x \) and \( y \) are used, or a linear change of variable is required.

A linear change of variable has the form

\( u = a + bx \)

This does not change the strength or direction of the linear relationship, only the scale and units.