# Chapter 19, Exercises 8 and 9
# Input lowbwt data
lowbwt <- read.table("lowbwt.txt",header=T, sep="\t",quote="", skip=1,
         row.names=NULL)
#######################
sbp <- lowbwt[[1]]
sex <- lowbwt[[2]]
gestage <- lowbwt[[5]]
apgar5 <- lowbwt[[6]]

#Exercise 8
##################################
#(a) Scatter plot

plot(gestage, sbp, xlab="Gestational age", ylab="SBP")
plot(apgar5, sbp)

#(b)
out1 <- lm(sbp ~ gestage)
summary(out1)
out2 <- lm(sbp ~ gestage+apgar5)
summary(out2)

#(c) The fitted model is

 y.hat = 9.8034 + 1.1848 * gestage + 0.4875 * apgar5

# For the population of infants with gestage=31 and apgar5=7, the estimated
mean systolic blood pressure is

y.hat = 9.8034 + 1.1848 * 31 + 0.4875 * 7 = 49.945 mmHg       

#(d) Confidence interval for the mean sbp of infants whose 
#    gestage=31 and apgar5=7 
  
new <- data.frame(gestage = 31, apgar5=7)
predict(lm(sbp ~ gestage+apgar5), newdata=new, int="confidence", se.fit=T )

#Prediction interval for an infant with gestage=31 and apgar5=7

new <- data.frame(gestage = 31, apgar5=7)
predict(lm(sbp ~ gestage+apgar5), newdata=new, interval="prediction", se.fit=T)

#(g)  Model evaluation 
res  <- out2$residuals 
fitted <- out$fitted.values
plot(fitted, res)
plot(gestage, res)






#######################################################################
#Exercise 9

out3 <- lm(sbp ~ gestage+sex)
summary(out3)

out4 <- lm(sbp ~ gestage+sex+sex*gestage)
summary(out4)