chemicaldata {ACSWR}

Chemical Reaction Experiment

Description

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.

Usage

data(chemicaldata)

Format

A data frame with 19 observations on the following 6 variables.

y1

the percentage of unchanged starting material

y2

the percentage converted to the desired product

y3

the percentage of unwanted by-product

x1

temperature

x2

concentration

x3

time

Source

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.

References

Rencher, A.C. (2002). Methods of Multivariate Analysis, 2e. J. Wiley.

Examples

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])