schooldata: School Data
In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

Description Usage Format Details Source Examples

School Data, from Charnes et al. (1981). The aim is to explain scores on 3 different tests, reading, mathematics and selfesteem from 70 school sites by means of 5 explanatory variables.

1	data(schooldata)

A data frame with 70 observations on the following 8 variables.

education: education level of mother as measured in terms of percentage of high school graduates among female parents
occupation: highest occupation of a family member according to a pre-arranged rating scale
visit: parental visits index representing the number of visits to the school site
counseling: parent counseling index calculated from data on time spent with child on school-related topics such as reading together, etc.
teacher: number of teachers at a given site
reading: total reading score as measured by the Metropolitan Achievement Test
mathematics: total mathematics score as measured by the Metropolitan Achievement Test
selfesteem: Coopersmith Self-Esteem Inventory, intended as a measure of self-esteem

This dataset was shamelessly borrowed from the FRB package.

The relationships among these variables are unusual, a fact only revealed by plotting.

A. Charnes, W.W. Cooper and E. Rhodes (1981). Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through. Management Science, 27, 668-697.

data(schooldata)
# initial screening
plot(schooldata)

# better plot
library(corrgram)
corrgram(schooldata, lower.panel=panel.ellipse, upper.panel=panel.pts)

#fit the MMreg model
school.mod <- lm(cbind(reading, mathematics, selfesteem) ~ 
		education + occupation + visit + counseling + teacher, data=schooldata)
# shorthand
school.mod <- lm(cbind(reading, mathematics, selfesteem) ~ ., data=schooldata)
Anova(school.mod)

heplot(school.mod)
heplot3d(school.mod)

# robust model, using robmlm()
school.rmod <- robmlm(cbind(reading, mathematics, selfesteem) ~ ., data=schooldata)
# note that counseling is now significant
Anova(school.rmod)

# compare classical HEplot with robust
heplot(school.mod, cex=1.4, lty=1, fill=TRUE, fill.alpha=0.1)
heplot(school.rmod, add=TRUE, error.ellipse=TRUE, lwd=c(2,2), lty=c(2,2), 
	term.labels=FALSE, err.label="", fill=TRUE)