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Identify the explanatory and response variables

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A maker uses the length of each clay sample to predict its mass. Which variable is the response?

Year 12, VCE Units 3 & 4, Chapter 3, 4 difficulty levels, No calculatorBuild a worksheet

Variables and paired data

Choose roles from the investigation question. A scatterplot displays two numerical measurements recorded for the same cases

\[(x,y)\]
  1. Explanatory The predictor is normally plotted horizontally as x
  2. Response The predicted quantity is normally plotted vertically as y
  3. Pairing Keep each case’s two measurements together. Do not sort columns independently
  4. Suitability Check that both variables measure quantities. A numerical identifier is still a category

Worked example

A maker predicts sample mass from sample length. The measurements are stated with mass first. Sample A has mass 18 g and length 2 cm. State the roles and the plotting coordinate

\[(x,y)=(2,18)\]
  1. \(\displaystyle x=2\)Length is explanatory because it is the predictor; use centimetres horizontally
  2. \(\displaystyle y=18\)Mass is the response; use grams vertically
  3. \(\displaystyle (2,18)\)The original column order does not reverse the required coordinates

Common mistakes

First column decides the role
✕\(\displaystyle x=\text{first column}\)✓\(\displaystyle x=\text{predictor}\)
Read the question before assigning axes
Sorting separately
✕\(\displaystyle \text{sort each column}\)✓\(\displaystyle \text{keep pairs linked}\)
The values must describe the same case

Difficulty levels

introIdentify the roles in a question with an explicit prediction direction
standardIdentify roles when the variable names are presented in either order and the pair is symmetric
challengeCompare a numerical paired investigation with a categorical or unlinked data set
examSelect the explanatory variable in a compact numerical modelling question or select suitable paired numerical data

Questions about this topic

Can the roles be reversed?+

Yes, if the question changes which quantity is predicted. State the new roles and labels clearly

Does explanatory mean causal?+

No. An explanatory variable is used to predict or explain statistical variation. An observational association does not establish causation

What if neither variable is a natural predictor?+

State which variable you put on each axis and investigate the association without forcing a causal interpretation

Do equal-length lists make paired data?+

No. You need a reliable case-by-case link, not merely the same number of values

Can I use a calculator?+

No. This topic is practised without a calculator

Which year level and chapter is this?+

Year 12, VCE Units 3 & 4, General Mathematics, chapter 3: Linear regression

In this chapter

Identify the explanatory and response variablesDescribe an association from a scatterplotProperties and assumptions of Pearson's rResiduals and what least squares minimisesCompute the least squares line from summary statisticsCompute r and the least-squares line from dataCalculate and interpret the coefficient of determinationInterpret the intercept and slope of a fitted modelPredict from a fitted model: interpolation and extrapolation3C Regression models and prediction: Construct and interpret a residual plot3D Residual plots and linearity: Construct and interpret a residual plotA full bivariate investigation