Montgomery and Peck (1982) illustrated variable selection techniques on the Hald cement data and gave several references to other analysis. The response variable y is the heat evolved in a cement mix. The four explanatory variables are ingredients of the mix, i.e., x1: tricalcium aluminate, x2: tricalcium silicate, x3: tetracalcium alumino ferrite, x4: dicalcium silicate. An important feature of these data is that the variables x1 and x3 are highly correlated (corr(x1,x3)=-0.824), as well as the variables x2 and x4 (with corr(x2,x4)=-0.975). Thus we should expect any subset of (x1,x2,x3,x4) that includes one variable from highly correlated pair to do as any subset that also includes the other member.
data(hald)hald is a matrix with 13 observations (rows) and 5 variables (columns), the first column is the dependent variable. y.hald and x.hald are also availables.