x<-c(9,3,5,5,1,7)
x*2
x-3
sort(x)
mean(x)
median(x)
mode(x)   #note: this doesn't work



# ----------------------------------------------------------------------------
fuel.frame<-read.table("c:/fuel-frame.txt", header=T, sep=",") 
names(fuel.frame)[1] "row.names" "Weight"    "Disp."     "Mileage"   "Fuel"      "Type" 
attach(fuel.frame) 
hist(Mileage)
boxplot(Weight ~Type) 
title("Weight by Vehicle Types") 
h

# ----------------------------------------------------------------------------
#chi squared: evenly distributed?
x = c(10, 9, 5, 3, 12, 13, 7, 6, 14, 20)
chisq.test(x)

#males and females admitted to Berkely
admit = c(22, 24)
reject = c(351, 317)
chisq.test(rbind(admit, reject))


# ----------------------------------------------------------------------------
#one way ANOVA (analysis of variance: what variables affect the results? 
# How do the variables affect each other?))

# Aircraft primer paints are applied to aluminum surfaces by two methods;
# dipping and spraying. A factorial experiment was performed to investigate 
#the effect of paint primer type and application method on paint adhesion. 
# Adhesion force was measured, with three different primers and two 
# application methods.

paint <- data.frame(adhf = c(4.0,4.5,4.3,5.6,4.9,5.4,3.8,3.7,4.0,5.4,4.9,5.6,5.8,6.1,6.3,5.5,5.0,5.0),
primer = factor(rep(rep(1:3,rep(3,3)),2)),applic = factor(rep(c("D","S"),c(9,9))))

# This is a one-way anova for primer, ignoring application method; 
# lm() fits the linear model and anova() displayes the results in an 
# anova table.

anova(lm(adhf~primer, data=paint))

# This is a one-way anova for application method, ignoring primer.

anova(lm(adhf~applic, data=paint))

# This is a two-way anova for application method, primer and their 
# interaction. Note that the sums of square for primer and for applic 
# are the same as computed in the respective one-way analyses.

anova(lm(adhf~primer*applic, data=paint))

# The interaction is not significant (P = 0.27) so we can test the main 
# effects, both of which are highly significant. We conclude that both the 
# choice of primer and the choice of application method affect the adhesive 
# force of the paint, and the differences between the three primers are the 
# same with both application methods, and the difference between the two 
# application methods is the same with each primer.




# ----------------------------------------------------------------------------
Hypothesis testing (Student's T test)
x<-c(-1, -2, 1, -1, 3, 4, -3, 6, 7,8,9,0,-8,-7,-3,1,2,3,4,5,7,4,2,7,-1,-2)
t.test(x, alternative="greater", mu=0.0, conf.level=0.99)

x = c(0, 1, -1, 2, -2, 3, 3, 2, -2, 0, -1, 5, 2, 1, -2, -1)
t.test(x, alternative="two.sided", mu=0.0, conf.level=0.99)

# ----------------------------------------------------------------------------