Lesson 6
What is the error term?
Big question
Why does regression include a term for what the model does not explain?
Lesson progress
Complete checkpoints as you learn
Learning objectives
- Explain what is the error term? in plain language.
- Use error term correctly in an interpretation.
- Connect the lesson idea to a formula, graph, Python result, or real example.
Simple explanation
The error term represents all influences on the outcome that are not included as explanatory variables. It is not a mistake; it is a recognition that simple models are incomplete.
Key terms
- Error term
- The unobserved part of y not explained by the included explanatory variable.
- Unobserved factor
- A relevant influence that is not measured or not included in the model.
- Omitted variable
- A variable left out of the model that may matter for the outcome.
- Causality warning
- A reminder that association is not automatically cause and effect.
Model with unexplained part
Example
Two workers may have the same education but different wages because of experience, occupation, region, negotiation, or measurement error.
Interactive visual
What lives inside u?
The error term collects relevant influences that are outside the one-variable model.
Model sentence
Observed wage = fitted wage + unexplained part
The error term is where the one-variable model places relevant influences that are not in x.
Possible contents of u
Interactive activity
Education and wage
Each dot is one observation. The fitted line summarizes the relationship between Education and Wage.
Causality decision
A wage regression has a positive education coefficient. Can we interpret it as causal?
Try it yourself
Write one plain-English sentence explaining the main idea from this lesson.
Common mistakes
Check these before you move on.
The error term is part of the model. It represents unobserved influences, not a Python mistake.
Quick quiz
Why is the error term included in a regression model?
Quick quiz
Which item could be part of the wage equation's error term when education is the only x?
Key takeaway
The error term is the honest part of the model: it admits that x alone does not explain everything.