Heat evolved during setting of 13 cement mixtures of four basic ingredients. Each ingredient percentage appears to be rounded down to a full integer. The sum of the four mixture percentages varies from a maximum of 99% to a minimum of 95%. If all four regressor X-variables always summed to 100%, the centered X-matrix would then be of rank only 3. Thus, the regression of heat on four X-percentages is ill-conditioned, with an approximate rank deficiency of MCAL = 1.
data(Hald)A data frame with 13 observations on the following 5 variables.
X1p3ca: Integer percentage of 3CaO.Al2O3 in the mixture.
X2p3cs: Integer percentage of 3CaO.SiO2 in the mixture.
X3p4caf: Integer percentage of 4CaO.Al2O3.Fe2O3 in the mixture.
X4p2cs: Integer percentage of 2CaO.SiO2 in the mixture.
yhear: Heat (cals/gm) evolved in setting, recorded to nearest tenth.
The (lmridge) Hald data are identical to the (MASS) cement data except for variable names.
Hald, A. (1952). Statistical Theory with Engineering Applications.(page 647.) New York; Wiley.