For a fixed set of x-values, samples of y are drawn one at a time from the true model y = β₀ + β₁x + ε, ε ~ N(0, σ²), shown against the gray dashed true line. Each sample's OLS fit (red) contributes one value to the accumulating β̂₀ and β̂₁ histograms below, which are compared against the theoretical sampling distribution (also in red). Once all 1000 samples have been drawn, a confidence interval panel appears beneath the histograms.
The x-values are held fixed throughout — only y is resampled each time, matching the classical assumption behind these formulas. "Restart" replays the animation with the same x-values; "New x-values" draws a different fixed set of x-values (changing x̄ and the spread of x) and also restarts.
True model: y = 2.00 + 1.30x + ε, σ = 2.0 | sample 0 of 1000
This sample: β̂₀ = –, β̂₁ = –
Plotting all 1000 intervals would be unreadably dense, so only samples 1–100 (in the order they were drawn) are shown below — since every sample is drawn independently the same way, this is just as representative as any other 100 would be. The coverage rate underneath, however, is computed across all 1000 samples, not just the 100 plotted, for a more precise estimate.
Click any interval below, or use "Show a missed example," to load that specific sample's data and fitted line into the "Current sample" panel above — a concrete look at what an unlucky sample actually looks like.
coverage across all samples = –, nominal target = –