What to explore
Change parameters and watch the model adjust.
- True intercept, true slope, noise scale, and sample size
- The native diagram and full notebook use the same four controls but separate deterministic random draws
Upper-undergraduate econometrics
Simple OLS Regression
An immediate native simulation for simple linear regression compares observed outcomes, the true conditional mean, and the fitted OLS line; the retained notebook adds sample and residual diagnostics.
Focus
Fitted line, residuals, precision, and known truth
Adjust the true intercept, slope, noise, and sample size to relate realised estimates to fit, slope estimation error, and an approximate 95% slope interval.Interactive diagram
Simple OLS
How to read this
Each dot is one observed pair of an explanatory variable x and outcome y. The solid line is the true conditional mean used to generate the data; the dashed line is the OLS estimate from the observations currently in the sample.
Move the true intercept or slope to change the underlying relationship. Noise spreads outcomes around that relationship, so the realised fitted line does not generally equal the truth even though OLS targets the average linear relationship.
Increase the sample size to append observations from the same deterministic latent bank. Compare the slope estimation error and the approximate interval: more data usually improves precision, but a single realised estimate need not move monotonically towards the truth.
Econometrics and causal inference
Step 1 of 5
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 tends to weaken fit, while larger samples usually improve coefficient precision.
- 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 behaviour 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
Open the full interactive notebook (Python · loads on demand)
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