Chemical Reaction Experiment
This data set is used to illustrate the concept of canonical correlations. Here, temperature, concentration, and time have influence on three yield variables, namely outputs, while the percentage of unchanged starting material, the percentage converted to the desired product, and the percentage of unwanted by-product form another set of related variables.
data(chemicaldata)
A data frame with 19 observations on the following 6 variables.
y1the percentage of unchanged starting material
y2the percentage converted to the desired product
y3the percentage of unwanted by-product
x1temperature
x2concentration
x3time
Box, G. E. P., and Youle, P. V. (1955). The Exploration of Response Surfaces: An Example of the Link between the Fitted Surface and the Basic Mechanism of the System. Biometrics, 11, 287-323.
Rencher, A.C. (2002). Methods of Multivariate Analysis, 2e. J. Wiley.
data(chemicaldata)
names(chemicaldata)
chemicaldata$x12 <- chemicaldata$x1*chemicaldata$x2;
chemicaldata$x13 <- chemicaldata$x1*chemicaldata$x3;
chemicaldata$x23 <- chemicaldata$x2*chemicaldata$x3
chemicaldata$x1sq <- chemicaldata$x1^{2}
chemicaldata$x2sq <- chemicaldata$x2^{2}
chemicaldata$x3sq <- chemicaldata$x3^{2}
S_Total <- cov(chemicaldata)
cancor_xy <- sqrt(eigen(solve(S_Total[1:3,1:3])%*%S_Total[1:3,
4:12]%*%solve(S_Total[4:12,4:12])%*%S_Total[4:12,1:3])$values)
cancor_xy
cancor(chemicaldata[,1:3],chemicaldata[,4:12])Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.