Latent-variable chapters: numbers and descriptions that do not match what process-improve computes

[kgdunn]

Found by executing every code block and re-deriving every quoted number against process-improve 1.78.0 (#274). All API names and keywords in these chapters exist; the items below are numbers or descriptions.

Determining the number of components (cross-validation)

• Line 147: the one-standard-error band "is never wider than 0.01". The library's own q2_se for the chapter's call ranges from 0.014 to 0.068 across the eleven components; recomputed across the five repeats it reaches 0.08 at A = 7. The Q2 list itself reproduces element for element.
• Lines 129-136 pass MCUVScaler().fit_transform(ldpe) to PCA.select_n_components(..., cv_scheme="ekf"). The library's guidance (Decide what the library's own tests and docs should pass to select_n_components, now that pre-scaled X warns process-improve#533, #539) is to pass the raw block so each fold derives its own scaling; PLS already warns on pre-scaled input and PCA will. Pass ldpe and re-verify the printed Q2 list.

Interpreting score plots and loading plots

• Line 65: the Density loading is quoted as -0.47; the fit gives -0.4787 (-0.48, as pca-exercises.rst:93 has it).
• Lines 66-67: the hand equation evaluates to -4.14, the block prints -4.171, the prose says -4.2. Three values for one quantity. Same at pca-exercises.rst:96.

PLS exercises

• Line 271: the LDPE bullet list reads K = 54 / K = 14 / K = 5; the third is M = 5 (the five Y variables named at line 277).
• Lines 62 vs 77-78: question 3 asks about PCA on the three X variables, but the verification code fits PCA(n_components=4) on cheese.iloc[:, 1:5], which includes Taste.

Judging and comparing designs

• Lines 693 and 464: G (maximum scaled prediction variance) for the thirteen-run OMARS design is 12.50 under the page's own settings (n_samples=80_000, seed 1), not 12.70. The 12.7 belongs to the twenty-five-run, five-factor OMARS design on the Comparing design families page.
• Lines 86-89: the ilp extra is not needed for this page's four-factor OMARS design (exhaustive branch).

OMARS designs

• Lines 167-172 and 180-187 describe step 4 as "guided by factor heredity" and say analyze_omars() carries out "exactly the stages above". Both heredity options default to "none" in the library; the reader must pass interaction_heredity="strong".

Product development

• Line 312: "the SPE value is 10.4" is the sum of squared residuals; the 95% limit printed at line 399 (1.38) is on the square-root scale the library uses. The comparable value is 3.22.

Mixed-level profile case study

• Lines 907-911 describe the PLS spe_ as "the part of the ten-point curve the three components do not reconstruct ... on the absorbance scale". It is the X-block residual over the 24 scaled model-matrix columns.
• Lines 214-243: the G-efficiency and FDS-max columns of the design-quality table differ from a fresh run (51.8 / 19.6 / 63.0 / 27.1 vs 48.4 / 17.6 / 66.3 / 26.8; 1.29 / 4.26 / 1.06 / 3.07 vs 1.38 / 4.74 / 1.01 / 3.11); both are sampled worst-case statistics. D, I and FDS-median reproduce exactly, as does the whole augmentation table later.
• Line 974 / 1129: the goal's SPE is 2.43 under cell-means coding, outside "between about 1 and 2". Lines 1735-1737: compound B's relaxed solution has SPE 2.05, not at the 6.5 limit.

Everything else in these chapters, including all 60-plus numbers in PLS model inversion and the orthogonal space, reproduced.