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Multivariate Lab

Showcase · walkthroughs and screenshots

A guided tour

Three short recordings of the main workflows, each step captioned on screen, followed by screenshots of every feature in light, dark and mobile views. A scripted browser tour made them against this site, so anyone with the repository can re-record them and get the same seeds and the same numbers.

  • 3 walkthroughs
  • captions and transcripts
  • 19 screenshots

Workflow walkthroughs

Watch the main journeys

The videos are silent. Each step is captioned on screen, the player offers the same captions as a text track, and the numbered steps beside each video are its transcript, with the time each step starts.

Walkthrough 1 · 0:55

Eigen playground

Drag the entries of a 2 × 2 matrix and watch the eigen-decomposition, the ellipse and the validity checks follow.

Open Covariance

Steps and transcript

  1. 10:00Problem 1(b): Σ = ΓΛΓᵀ with eigenvalues 5 and 1. The eigenvectors γ₁ and γ₂ are the axes of the density ellipse.
  2. 20:05Drag σ₁₁, the variance of X₁: the ellipse stretches and shrinks along X₁ and γ₁ turns with it.
  3. 30:16Drag the covariance σ₁₂ (kept symmetric): past zero the correlation changes sign and the ellipse tilts the other way.
  4. 40:25Push σ₁₂ past √(σ₁₁σ₂₂): λ₂ turns negative, so Σ is not positive semi-definite and no ellipse exists.
  5. 50:38Unlock symmetry and drag σ₂₁: a non-symmetric matrix is never a covariance, the condition the 2023 answer to 1(a) missed.
  6. 60:48A singular, rank-1 matrix is still a valid covariance: one direction has zero variance.

Walkthrough 2 · 0:56

Seeds PCA

Switch between the covariance, correlation and as-submitted PCA of the wheat data, explore the biplot, then read the bootstrap intervals.

Open Seeds PCA

Steps and transcript

  1. 10:00210 wheat kernels, 7 measurements. PCA of the covariance matrix S, computed in your browser: PC1 keeps 82.9% of the variance.
  2. 20:08Turn on the biplot: area and perimeter, the variables with the largest raw variances, dominate PC1.
  3. 30:14Scaled: the correlation PCA puts every variable on the same footing, and three PCs keep 98.7% of the variance.
  4. 40:25As submitted in 2023: correlation loadings applied to the raw, uncentred data, so the score cloud is shifted.
  5. 50:32Added in 2026: 1,000 bootstrap resamples, seed 90138. PC1 of S keeps 82.9% (95% CI 79.8–85.9%).
  6. 60:39Loadings with 95% bootstrap intervals after sign alignment; grey intervals include zero.
  7. 70:48Correlation PCA: three PCs pass the ψ ≥ 95% rule, but parallel analysis (95th percentile) finds only 1 beyond chance.

Walkthrough 3 · 0:43

North or South?

Flip the random forest's mOOB bug between as submitted and corrected, then compare the classifiers with intervals on identical folds.

Open Rainfall Open Evaluation

Steps and transcript

  1. 10:00North or South? 191 Australian weather stations, 365 days of rainfall each: 150 to train, 41 to test.
  2. 20:05Random forest, 5,000 trees, m tuned by out-of-bag error. Corrected loop: the lowest OOB error, 6.67%, is at m = 57.
  3. 30:11As submitted: if (oob_error <- min_oob_error) assigns instead of comparing, so every m wins and the last, 153, is kept.
  4. 40:16Same verdict either way: 3 of 41 test stations wrong (95% Wilson CI 2.5–19.4%). The bug changed m, not the result.
  5. 50:24Added in 2026: 10 × 5-fold stratified CV on identical folds. Seven pipelines, each with a Wilson 95% interval.
  6. 60:30Paired on the same folds: PCA + logistic leads the forest by 2.4 pp, but the corrected interval (−1.5 to +6.2) includes zero.
  7. 70:35Fixing the mOOB loop: −0.1 pp (−2.4 to +2.2), no change. Fixing the PLS test scaling: +23.6 pp, the one fix that clearly matters.

Screenshots

Every feature at a glance

16 desktop views at 1440 × 900 and 3 on a phone. Select one to open a larger view; the arrow keys move between them.

On a phone (390 px)

How these were made

Reproducible, like the numbers