# Final Part I

data autompg;
  infile 'C:\Users\sungkyu\Dropbox\Teaching\1301-StatisticalPackages\Exams\auto-mpg.data';
  input mpg cylinders displacement hp weight acc;
run;

proc sgscatter data = autompg;
   matrix mpg--acc;
run;

  proc reg data =autompg;
   model mpg = cylinders--acc / vif;
run;
ods graphics on;

proc reg data=autompg;
    model mpg = cylinders--acc / selection = stepwise;
run;

data autompg;
 set autompg;
   lmpg = log10(mpg);
run;

proc reg data=autompg;
    model lmpg = cylinders--acc / selection = stepwise;
 output out = autompgfit 
         predicted = yhat
		 residual = resid
		 student = rstandard
		 rstudent = rstudent
		 h = leverage
		 cookd = cooksd;
run; 
proc print data = autompgfit; 
run;
data autompgfit2;
set autompgfit; 
   if leverage > 0.08 then delete;
run;

proc reg data=autompgfit2;
    model lmpg = weight hp cylinders /vif;
run;













# Final Part II
# 1
data(sleep)
str(sleep)
help(sleep)
t.test(extra~group, data = sleep,paired = TRUE) # Do not use two-sample t-test
attach(sleep)
paired.difference = extra[group==1]-extra[group==2]
qqnorm(paired.difference);qqline(paired.difference)
hist(paired.difference)
wilcox.test(extra~group, data = sleep, paired = TRUE)
wilcox.test(paired.difference)
detach(sleep)

#2
getwd()
col=read.table("college.txt",header = T, sep = "\t")
dim(col)
attach(col)
sum(Alumni.giving > 50, na.rm = T)
sum(is.na(Alumni.giving))
hist(Alumni.giving, breaks = 50)
a<-School[Alumni.giving > 45]
a[!is.na(a)]

#3 
boxplot(Full.time~ Tier, data =col)
tapply(Full.time, Tier, mean, na.rm = T)
tapply(Full.time, Tier, sd, na.rm = T)
bartlett.test(Full.time~Tier, data = col)
anova(lm(Full.time ~ Tier)) # not good 
oneway.test(Full.time ~ Tier)
pairwise.t.test(Full.time, Tier)

#4
bp<-read.table("hypertension.dat", header = F)
drug = rep(rep(c("x","y","z"),c(12,12,12)),2)
biofeed = rep(c("P","A"),c(36,36))
diet = rep(rep(c("No","Yes"),c(6,6)),6)
bp = as.vector(t(bp))
hypertension <- data.frame(bp, drug, biofeed, diet)
str(hypertension)
head(hypertension)

combined.factors <- factor(paste(diet,drug,biofeed))
boxplot(bp ~ combined.factors)

anova(lm(bp~ ., data = hypertension))

#5 
power.t.test(power = 0.9, delta = 0.6, sd = 1, sig.level = 0.05)

#6 
sign.test.pvalue <- function(x) { 
w <- sum(x > 0)
p <- pbinom(w,length(x),0.5)
return(p)
}
sign.test.pvalue(x)
attach(sleep)
paired.difference = extra[group==1]-extra[group==2]
sign.test.pvalue(paired.difference)