Ceteris LabInteractive Econometrics

Lesson 11

Interpreting regression output

Big question

Which output numbers matter first, and how should students explain them?

Lesson progress

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Learning objectives

  • Explain interpreting regression output in plain language.
  • Use standard error correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Regression output can look crowded. Start with the coefficient table and R-squared. Interpret the slope in units, check the intercept carefully, use standard errors and t-statistics as uncertainty clues, and avoid causal language unless the design supports it.

Key terms

Standard error
A measure of sampling uncertainty around an estimated coefficient.
t-statistic
A coefficient divided by its standard error.
p-value
A probability-style measure used to judge evidence against a null hypothesis.
Output interpretation
A plain-language explanation of model estimates, fit, uncertainty, and limits.

t-statistic

t=β^1−0se(β^1)t = \frac{\hat{\beta}_1 - 0}{se(\hat{\beta}_1)}

Example

A strong interpretation says: In this sample, one more year of education is associated with about $2.33 higher predicted hourly wage. This is an association from a simple model.

Interactive visual

Regression output explainer

Read the coefficient, standard error, t-statistic, p-value, and R-squared as separate clues.

wage_sample.csv
Output itemValueHow to read it
coef: education2.33One more education year is associated with about $2.33 higher predicted hourly wage.
coef: const-10.10The fitted line's intercept; handle literal interpretation carefully.
std erruncertaintyA smaller standard error means a more precise coefficient estimate.
t and pevidenceUsed to assess evidence against a zero-slope benchmark.
R-squared0.949About 94.9 percent of sample wage variation is explained by education.

Interactive activity

Regression output explainer

Read the output one row at a time, then translate it into plain English.

Output itemExampleMeaning
Coefficient2.33The estimated slope on education.
Standard error0.16A measure of uncertainty around the slope estimate.
t-statistic14.8The coefficient divided by its standard error.
p-value< 0.001Evidence against the zero-slope benchmark in this sample.
R-squared0.949The model explains about 94.9% of wage variation in this small sample.
Observations12The number of rows used in the regression.

A precise coefficient and high R-squared still do not automatically prove causality.

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

Which sentence best interprets the education coefficient of 2.33?

Quick quiz

What is a p-value commonly used for in regression output?

Key takeaway

Regression output becomes manageable when students translate one number at a time into units, uncertainty, and caution.

Download dataDownload resultsDownload interpretation