What to explore
Change parameters and watch the model adjust.
- True intercept, true slope, noise level, and sample size
- A deterministic random seed keeps the notebook stable across exports
Upper-undergraduate econometrics
Simple OLS Regression
A deterministic simulated-data notebook for simple linear regression, coefficient interpretation, residuals, and the role of noise and sample size.
Focus
Fitted line, residuals, precision, and known truth
Adjust the data-generating process and watch the fitted line, coefficient estimates, and residual behavior move with noise, slope, and sample size.Core ideas
Interpret the mechanics before you chase the graphs.
- OLS recovers the average linear relationship in the sample, not each noisy point.
- More noise weakens fit, while larger samples stabilize the estimate.
- Residual plots are useful because they expose what the fitted line leaves unexplained.
Learning goals
What this model should help students internalize.
- Interpret the slope and intercept in a simple linear regression with simulated data.
- See how noise and sample size affect fit and coefficient precision.
- Connect residual behavior to the gap between the fitted line and the true data-generating process.
Prerequisites
Concepts to review before diving in.
- Basic algebra and scatterplot reading
- Comfort with the idea of a conditional mean relationship
Next models to study
Keep moving through the track.
Upper-undergraduate econometrics
Omitted Variable Bias
Change confounding strength and the omitted variable's effect to compare the true coefficient, the naive regression, and the fully controlled benchmark.
Upper-undergraduate econometrics
Difference-in-Differences
Adjust treatment effects, group gaps, noise, and trend violations to see exactly when the DiD estimate matches the truth and when it drifts.