#regression equation on p. 122.
#first generating ffev1a = ffev1/100.
lung$FFEV1a <- lung$FFEV1/100

coef(lm(FFEV1a ~ FHEIGHT, lung))

#summary stats, middle p. 122.
summary(lung[, c("FAGE", "FHEIGHT", "FFEV1a")])

# regression equation, p. 122.
# we also store the model for use later
coef(m <- lm(FFEV1a ~ FAGE + FHEIGHT, lung))

#covariance matrix, p. 127.
cov(lung[, c("FAGE", "FHEIGHT", "FWEIGHT", "FFEV1a")])
cor(lung[, c("FAGE", "FHEIGHT", "FWEIGHT", "FFEV1a")])

#table 7.2, p. 132.
anova(m)

#table 7.5.
# drop made up FFEV1a variable
lung <- lung[-which(colnames(lung) == "FFEV1a")]
# reshape data from wide to long
# this is a bit complicated because the repeated variables
# were not adjacent in the data frame, instead, we use grep()
# to search for the column numbers matching our search string
lung.long <- reshape(lung, direction = "long", varying = list(
  grep("SEX", colnames(lung)), grep("AGE", colnames(lung)),
  grep("HEIGHT", colnames(lung)), grep("WEIGHT", colnames(lung)),
  grep("FVC", colnames(lung)), grep("FEV", colnames(lung))),
  v.names = c("SEX", "AGE", "HEIGHT", "WEIGHT", "FVC", "FEV"),
  timevar = "Member", idvar = "ID",
  times = c("Father", "Mother", "OldestChild", "MiddleChild", "YoungestChild"))

lung.long$FEV1a <- lung.long$FEV/100

# subset data to fathers and mothers only
lung.sub <- subset(lung.long, Member == "Father" | Member == "Mother")

# to make nice output for the table, we will write a little function
f <- function(x) {
  mu <- sapply(x, mean)
  sigma <- sapply(x, sd)
  m <- lm(FEV1a ~ AGE + HEIGHT, data = x)
  data.frame(Mean = mu, Sx = sigma, coef(summary(m))[, 1:2],
    row.names = c("FFEV1a/Intercept", "AGE", "HEIGHT"))
}

# overall
f(lung.sub[, c("FEV1a", "AGE", "HEIGHT")])
## separate by member (father/mother)
by(lung.sub[, c("FEV1a", "AGE", "HEIGHT")], lung.sub$Member, f)

# Page 147 top of the page
# first we convert member to a factor with Mother as the first level
# and Father as the second, the test the HEIGHT x Member interaction
lung.sub$Member <- factor(lung.sub$Member, levels = c("Mother", "Father"))

coef(summary(lm(FEV1a ~ AGE + HEIGHT * Member, data = lung.sub)))