Ceteris LabInteractive Econometrics

Lesson 1

What is regression?

Big question

How can one line summarize a relationship between two economic variables?

Lesson progress

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Learning objectives

  • Explain what is regression? in plain language.
  • Use regression correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Regression is a way to summarize how an outcome changes as an explanatory variable changes. In simple regression, the model uses one explanatory variable and fits a straight line through the cloud of data points.

Key terms

Regression
A statistical method for estimating the relationship between an outcome and one or more explanatory variables.
Simple regression
A regression model with one dependent variable and one explanatory variable.
Fitted line
The line chosen by the regression method to summarize the sample relationship.
Association
A pattern showing that two variables tend to move together.

Simple regression idea

y=β0+β1x+uy = \beta_0 + \beta_1 x + u

The model connects outcome y to explanatory variable x plus other influences collected in u.

Example

If students plot wage against education, the dots usually do not fall on one perfect line. Regression asks which straight line best summarizes the average pattern.

Interactive visual

Scatter plot plus fitted line

The dots are workers in the wage sample. The fitted line summarizes the average wage-education pattern.

wage_sample.csv
12141618201824303612 years education, $18.50 wage16 years education, $24.20 wage18 years education, $31.80 wage14 years education, $21.10 wage16 years education, $28.40 wage13 years education, $19.70 wage20 years education, $35.60 wage15 years education, $26.90 wage14 years education, $22.30 wage17 years education, $30.10 wage12 years education, $17.90 wage18 years education, $33.40 wageEducationWage

Fitted equation

wage-hat = -10.10 + 2.33 education

Slope

$2.33 per year

R-squared

0.949

The line summarizes the sample pattern. It is not, by itself, proof that education causes wages to change.

Interactive activity

Education and wage

Each dot is one observation. The fitted line summarizes the relationship between Education and Wage.

EducationWage
Slope: 2.33
Intercept: -10.10
R-squared: 0.949

Graph reading activity

Read the wage and education scatter plot.

0/3 graph-reading checks correct

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

What is the main job of simple regression?

Quick quiz

In a wage-and-education regression, what does the fitted line represent?

Key takeaway

Regression turns a cloud of points into an estimated relationship that students can inspect and interpret.

Download dataDownload resultsDownload interpretation