library(MASS)

set.seed(123123)
train <- c(rep(0, 40), rep(1, 40))
knowledge <- round(30 + 20*train + rnorm(80, 0, 10))
motivation <- round(30 + 20*train + rnorm(80, 0, 10))
performance <- round(30 + 0.5*(motivation - mean(motivation)) + 0.5*(knowledge - mean(knowledge)) + rnorm(80, 0, 10))
performance <- performance - min(performance)

dat <- data.frame(train, knowledge, motivation, performance)

summary(lm(performance ~ train))
summary(lm(knowledge ~ train))
summary(lm(performance ~ knowledge + train))

# c = 24.625
# a = 20.950
# b = 0.4166
# c' = 15.8983

write.table(dat, file="example.csv", sep=",", row.names=FALSE, col.names=TRUE)

set.seed(123123)
conflict <- round(rnorm(262, 15, 2))
selfstress <- round(0.799 + 0.173*conflict + rnorm(262, 0, 0.94))
pcouplestress <- round(rnorm(262, 3, 1))
lifesat <- round(-1.447 + (0.077 * conflict) + (-0.769 * selfstress) + rnorm(262, 0, 1.34)) + 9

dat2 <- data.frame(conflict, selfstress, pcouplestress, lifesat)

summary(lm(lifesat ~ conflict))
summary(lm(selfstress ~ conflict))
summary(lm(lifesat ~ selfstress + conflict))

# c = 24.625
# a = 20.950
# b = 0.4166
# c' = 15.8983

write.table(dat2, file="conflict.csv", sep=",", row.names=FALSE, col.names=TRUE)

library(boot)
ab.fun <- function(d, i) 
{    
	newdat <- d[i,]
	a <- coef(lm(performance ~ train, data = newdat))[2]
	b <- coef(lm(performance ~ knowledge + train, data = newdat))[2]
	a * b
}
ab.boot <- boot(dat, ab.fun, R = 5000)
boot.ci(ab.boot, type = c("norm", "basic", "perc", "stud"))