Lesson 2
Dependent variable and explanatory variable
Big question
Which variable are we explaining, and which variable are we using to explain it?
Lesson progress
Complete checkpoints as you learn
Learning objectives
- Explain dependent variable and explanatory variable in plain language.
- Use dependent variable correctly in an interpretation.
- Connect the lesson idea to a formula, graph, Python result, or real example.
Simple explanation
Every simple regression starts with a clear role assignment. The dependent variable is the outcome. The explanatory variable is the measured factor used to describe or predict that outcome.
Key terms
- Dependent variable
- The outcome the model tries to explain or predict.
- Explanatory variable
- The variable used to describe changes in the dependent variable.
- Outcome
- The measured result or behavior being studied.
- Predictor
- Another name for an explanatory variable, especially when the goal is prediction.
Roles in the model
Example
If the question is 'Do workers with more education earn more?', wage is y and education is x. If the question changes, the variable roles may change too.
Interactive visual
Variable roles
The same data can answer different questions only after the y and x roles are chosen.
y variable
wage
The dependent variable. It is the outcome students want to explain.
x variable
education
The explanatory variable. It is used to describe changes in wage.
Interactive activity
Variable classifier
Classify each part of a regression model.
Try it yourself
Write one plain-English sentence explaining the main idea from this lesson.
Common mistakes
Check these before you move on.
A regression coefficient describes a pattern unless the assumptions or research design support a causal interpretation.
Quick quiz
In wage = beta0 + beta1 education + u, what role does wage play?
Quick quiz
Why should students define y and x before estimating a regression?
Key takeaway
Regression interpretation begins with the variable roles: y is explained, and x does the explaining.