Heat evolved during setting of 13 cement mixtures of four (or five) ingredients. The first four ingredient percentages appear to be "rounded down" to a full integer. The fifth integer percentage of "other" material assures that the five percentages sum to exactly 100%. However, the "centered" X-matrix resulting from inclusion of all five ingredients would then be Singular (rank=4). In other words, regressing any y-Outcome on only the first four X-variables yields an "ill-conditioned" model that, while having numerical "full rank"=4, actually suffers a effective "rank deficiency" of at least mcal = 1.
data(haldport)A data frame with 13 observations on the following 6 variables.
p3caPositive Integer percentage of 3CaO.Al2O3 [tricalcium aluminate] in the mixture.
p3csPositive Integer percentage of 3CaO.SiO2 [tricalcium silicate] in the mixture.
p4cafPositive Integer percentage of 4CaO.Al2O3.Fe2O3 [tetracalcium aluminoferrite] in the mixture.
p2csPositive Integer percentage of 2CaO.SiO2 [dicalcium silicate] in the mixture.
otherPositive Integer percentage of other ingredients in the mixture.
heatHeat (cals/gm) evolved in setting, recorded to nearest tenth.
The (RXshrink) haldport data are identical to the (MASS) cement data except for variable names and inclusion of the "other" X-variable.
Hald A. Statistical Theory with Engineering Applications. 1952 (page 647.) New York; Wiley.
Obenchain RL. (2022) Efficient Generalized Ridge Regression. Open Statistics 3: 1-18. tools:::Rd_expr_doi("10.1515/stat-2022-0108")