Data show two measured properties, brilliance and vorticity, of 81 girandoles composed of different mixtures of five ingredients: a -- e. Of these ingredients, a and b are the primary light-producting, c is principal propellant, and d and e are binding agents for c.
data(Firework)The data consist of 81 cases and 7 variables: ingredients a, b, c, d, and e, and the two measured properties brilliance and vorticity. The 81 different mixtures form a special experiment design. First the 81 possible quadruples formed from the three values -1, 0, 1 were arranged in ascending order. Then for each such quadruple z, the corresponding mixture x(z)=(a,b,c,d,e)=alrInv(z) is computed. Thus the No. 4 girandole corresponds to z=(-1,-1,0,-1) and so is composed of a mixture x=(.12,.12,.32,.12,.32) of the five ingredients. All 5-part mixtures sum up to one.
Aitchison: The Statistical Analysis of Compositional Data, 1986, Data 13, pp17.