Module 2

Simple Regression

Estimate and interpret one-variable regression models with fitted lines, residuals, R-squared, Python output, and practice projects.

12 lessons4 to 6 hoursBeginner

Prerequisites

Module 0Module 1

Skills

Identify dependent and explanatory variablesWrite a simple regression modelInterpret beta0 and beta1Explain the error termCalculate fitted values and residualsUnderstand OLS intuitionInterpret R-squaredRun simple regression in PythonInterpret statsmodels output
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Module resources

0 quiz checks0 datasets4 notebooks

Lessons

1What is regression?How can one line summarize a relationship between two economic variables?Open lesson2Dependent variable and explanatory variableWhich variable are we explaining, and which variable are we using to explain it?Open lesson3The simple regression equationHow do we read the simple regression equation in plain language?Open lesson4What does beta0 mean?Why does a regression line need an intercept, and when should we be careful with it?Open lesson5What does beta1 mean?How do we turn the slope coefficient into an economic sentence?Open lesson6What is the error term?Why does regression include a term for what the model does not explain?Open lesson7Fitted values and residualsHow do we compare what the model predicts with what actually happened?Open lesson8Ordinary Least Squares intuitionHow does OLS choose the fitted line?Open lesson9R-squaredHow much of the outcome's variation does the regression explain?Open lesson10Regression in PythonHow do we estimate a simple regression with pandas and statsmodels?Open lesson11Interpreting regression outputWhich output numbers matter first, and how should students explain them?Open lesson12Practice regression projectHow can students complete a small regression analysis from question to interpretation?Open lesson

Notebook labs

Scored review quiz

Module 2 review

These questions sample ideas from across the module. Answer all questions, submit once, then review the explanations and score.

0/15 answered

What is regression?

1. A scatter plot of wage and education shows an upward cloud of points. What does simple regression add to the graph?

Dependent and explanatory variables

2. A student estimates voteA on shareA. Which interpretation of the variable roles is correct?

The simple regression equation

3. In y = beta0 + beta1x + u, which part captures influences on y that are not included in x?

What does beta0 mean?

4. Why can an intercept be useful even when x = 0 is not realistic in the sample?

What does beta1 mean?

5. In the teaching wage sample, the education slope is about 2.33. Which sentence is best?

What is the error term?

6. Why can a simple wage-on-education regression be descriptive but not automatically causal?

Fitted values and residuals

7. A worker's actual wage is 26.90 and the fitted wage is 24.85. What is the residual?

Ordinary Least Squares intuition

8. Which line does Ordinary Least Squares choose?

R-squared

9. If a regression has R-squared = 0.72, what is the best interpretation?

Regression in Python

10. In statsmodels, why do we usually add a constant column before estimating a simple regression?

Interpreting regression output

11. Which output-reading sequence is strongest for a beginner?

Practice regression project

12. A student uses SLEEP75 to regress sleep on totwrk. What is a careful final claim?

Datasets

13. Which dataset-question pair is well matched for simple regression practice?

Formula review

14. What does y-hat represent in the fitted equation y-hat = beta0-hat + beta1-hat x?

Interpretation review

15. What makes a regression interpretation high quality?

Choices are shuffled each time the review starts.