Identify the explanatory and response variables

Explanatory and response variables

The explanatory variable is used to explain or predict; the response variable is the quantity predicted. The wording fixes the roles, not the order in which the variable names appear

1. Find the predicted quantity The quantity being predicted is the response variable \(\displaystyle \text{predict test score from practice time}\Rightarrow\text{test score}=\text{RV}\)
2. Choose the predictor The quantity used to predict the response is the explanatory variable \(\displaystyle \text{practice time}=\text{EV}\Rightarrow\text{test score}=\text{RV}\)
3. Keep the roles fixed The order of names in a table or sentence does not decide the roles \(\displaystyle \text{question wording}\Rightarrow\text{EV}\longrightarrow\text{RV}\)
4. Check paired numerical data A scatterplot needs two numerical variables with both values recorded for each case \(\displaystyle \text{numerical EV}+\text{numerical RV}+\text{paired cases}\Rightarrow\text{scatterplot suitable}\)

Worked example

A school records three pairs of practice hours and performance scores. The question asks whether the score can be predicted from practice hours. Identify the explanatory and response variables

1. \(\displaystyle \text{predicted quantity}=\text{performance score}\)The response variable is the quantity being predicted
2. \(\displaystyle \text{predictor}=\text{practice hours}\)The explanatory variable is the quantity used to predict the response
3. \(\displaystyle \text{EV}=\text{practice hours},\quad\text{RV}=\text{performance score}\)The role assignment follows the direction of the question

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