This diagnostics workshop was generated by Claude (Anthropic) for the STAT 101 course materials. Every number on it is computed in your browser and recomputed on every drag: the least-squares coefficients, all residuals, s² with the n − P divisor, the standard errors, the t statistic and its two-sided p-value from a real incomplete-beta evaluation, R² two independent ways and cross-checked, every hat value, every studentised residual, the confidence and prediction bands, and the QQ plot's normal scores from a real inverse normal CDF.

Cook's distance is computed twice on purpose. Once by the algebraic shortcut using leverage and the residual, and once by its definition — dropping the point, refitting, and adding up how far every fitted value moved. Comparison 3 prints the difference, so the shortcut is demonstrated rather than asserted. This matters here: the denominator must be the number of parameters (P = 2), and using the number of predictors instead makes it exactly twice too large. The lessons had it the second way and were corrected on all four surfaces on 2026-08-23 (see TODO.md §10). The page prints Σh_ii = P live so you can see where that 2 comes from.

The three flags are conventions, not facts, and are labelled as such at the point of use: leverage > 2P/n ("twice the average"; some texts use 3P/n), Cook's D > 1 (Cook 1977, and generous in practice), and |studentised residual| > 2 (a rough normal cut-off). Every actual number is printed beside its flag so you can disagree with the threshold. Nothing on this page rests on a figure transcribed from a document.

Chosen rather than computed: the six datasets and the noise seed — though the noise is a real seeded Gaussian draw, so its statistics are computed and every preset is reproducible. Known limits, measured and stated rather than hidden: the inverse normal used for the QQ plot is accurate to about 1.8×10⁻⁹, and the normal CDF to about 1.2×10⁻⁷. A Newton-style refinement of the inverse was written and then removed, because measuring it against 15-digit reference quantiles showed it made the answer thirty times worse — it was correcting towards the coarser of the two functions. The checker asserts the accuracy actually achieved. Scope: simple linear regression only — the multiple-regression builder and the logistic half of the syllabus lab are not here.