Siotani et al. (1985) describe a study of Japanese rice wine (sake)
used to investigate the relationship between two subjective ratings
smell) and a number of physical measurements
on 30 brands of sake.
These data provide one example of a case where a multivariate regression doesn't benefit from having multiple outcome measures, using the standard tests. Barrett (2003) uses this data to illustrate influence measures for multivariate regression models.
A data frame with 30 observations on the following 10 variables.
mean taste rating
mean smell rating
one measure of acidity
another measure of acidity
direct reducing sugar content
total sugar content
smell values are the mean ratings of 10 experts
on some unknown scale.
Siotani, M. Hayakawa, T. & Fujikoshi, Y. (1985). Modern Multivariate Statistical Analysis: A Graduate Course and Handbook. American Sciences Press, p. 217.
Barrett, B. E. (2003). Understanding Influence in Multivariate Regression. Communications in Statistics - Theory and Methods 32 (3), 667-680.
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data(Sake) # quick look at the data boxplot(scale(Sake)) Sake.mod <- lm(cbind(taste,smell) ~ ., data=Sake) library(car) Anova(Sake.mod) predictors <- colnames(Sake)[-(1:2)] # overall multivariate regression test linearHypothesis(Sake.mod, predictors) heplot(Sake.mod, hypotheses=list("Regr" = predictors))
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