#  The code can be commented using #


# assignment operators

x = 5
y <- 6
7 -> z
x
y
z

#  reading data in data frame object
#  need to change the directory appropriately

fish.df = read.table("c:\\orie476\\fish.dat", header=T)
attach(fish.df)

# to list objects
ls()

# to remove a particular object
rm(x)

# now x was removed
ls()

# to remove all objects, go to Misc menu and select the appropriate option

# creating arrays of data
# concatenation
x = c(1,2,3,4)
y = 6:9

# sequence command
z = seq(0,1,.2)

x
y
z

# replicate command
a = rep(1:3, 3)
b = rep(4:6, 1:3)
a
b

x+y
log(x+y)

# arithmetic operations (componentwise multiplication)
x*y

# two ways to raise the components of y to the power specified by x
y**x
y^x

# logical values
weight = seq(100, 219, 17)
weight
weight[1] == 100
weight[1] != weight[2]
weight < 170

A = matrix(1:9, ncol=3)

# note the order in which the entries of A are filled in
A
matrix(1:9, ncol=3, byrow=T)

# use of index (square) brackets 
A[1:2, 2:3]

B = matrix(seq(0,1,.2), ncol=2)

# attaching rows/columns to a matrix (rbind/cbind commands, respectively)
cbind(A, 11:13)
rbind(A, 17:19)

# matrix multiplication
A%*%B

# transposition of vectors/matrices
t(x)


# computing inverses
solve(A) 
A[1,1] = 17
solve(A)
A%*%solve(A)

# two ways to compute inner product of x and y
sum(x*y)
t(x)%*%y

# generating an i.i.d. sample of size from the standard normal distribution
z = rnorm(200)

# various ways to summarize data
hist(z)
boxplot(z)

mean(z)
sd(z)

# generating an i.i.d. sample of size 50 from the binomial distr with n=100, p = 0.2
w = rbinom(50, 100, .2)
stem(w)

# basic regression

fishFit1 = lm(count~area, fish.df)
summary(fishFit1)

fishFit2 = lm(count~area, subset(fish.df, area < 10^5))
summary(fishFit2)

# extracting coefficients from fits
fishFit1$coef
fishFit2$coef

# plotting commands (scatterplot)
plot(area[area<10^5], count[area<10^5])

# adding lines to the plot
abline(fishFit1$coef[1], fishFit1$coef[2])
abline(fishFit2$coef[1], fishFit2$coef[2])

# alternatively, use abline(fishFit1)

# extracting coefficients (alternative way); residuals and fitted values
coefficients(fishFit1)
plot(fitted.values(fishFit1), residuals(fishFit1))

predict(fishFit2, data.frame(area=10^(1:5)))

# pnorm(quantile); qnorm(prob);
pnorm(1.64)
qnorm(.95)
qnorm(pnorm(1.96))
pnorm(qnorm(.95))

# similar functions are defined for Student's t and Snedecor's F distribution
# pf(q, df1, df2); qf(p, df1, df2)
# pt(q, df); qt(p, df)

cauchyp.normp <- data.frame(quantiles=(1:20)/10, cauchy.p=pt( (1:20)/10, 1), norm.p=pnorm((1:20)/10))