lmout <- lm(Ozone ~ .,data=airquality[,-(5:6)])

a <- c(1,188,8.8,62)  # prepare for (10.56)
pred <- t(a) %*% coef(lmout)
print(pred)
se <- sqrt(t(a) %*% vcov(lmout) %*% a)
print(c(pred-1.96*se,pred+1.96*se))

aq <- airquality[,-6]
# need to form dummy variables (4 of them, since have 5 months)
month <- aq$Month
aq$D5 <- as.integer(month == 5)
aq$D6 <- as.integer(month == 6)
aq$D7 <- as.integer(month == 7)
aq$D8 <- as.integer(month == 8)
aq$Month <- NULL
lmout <- lm(Ozone ~ .,data=aq)
a <- c(0,0,0,0,1,0,-1,0)
mayjuly <- t(a) %*% coef(lmout)
se <- sqrt(t(a) %*% vcov(lmout) %*% a)
print(c(mayjuly-1.96*se,mayjuly+1.96*se))