###________ Section 1: Arithmetic and Assignment ________###

3*(2 + 1)          
g <- 4931          
g                  
g*1000             
h <- c(15.1,11.3,10.0) 
h*2.7                  
length(h)
ls()
rm(g,h)
ls()

exp(1)
log(10)
log(10, base=10)

###________ Section 2: Descriptive Statistics ________###

data(state)
ls()
state.x77
class(state.x77)
x77.df <- as.data.frame(state.x77)
class(x77.df)

states <- state.abb     
murder <- x77.df[,5] #column 5 of the dataframe 
illit  <- x77.df[,3] #same as state.x77[,3]

rownames(x77.df)
colnames(x77.df)
names(x77.df)

names(murder)
names(murder) <- rownames(x77.df)
murder
names(murder) <- NULL #remove names

murder <- x77.df$Murder     #rate per 100,000
illit  <- x77.df$Illiteracy #percent

mean(murder)     
median(murder)

###________ Section 3: Comparison Operators ________###

murder / illit             
abs(murder - mean(murder)) 
2^c(5,8,3,1) 
0:10         
3:-7         
murder > 12
which(murder == max(murder)) #index of the maximum value

###________ Section 4: Extracting Data; Subscripts ________###

murder[1:3] 
murder[c(1,3,5)] # 1st, 3rd, and 5th values
murder[murder > 12]    
states[murder > 12]    
illit[states == "CA"]  
murder     
murder[-1] 
murder[-7] 

###________ Section 5:  Basic Graphics ________###

plot(illit,murder)      
abline(2.4, 4.3)                                   
identify(illit, murder, states, col = 2)           

#-----  

plot(illit,murder,type="n")   
text(illit,murder,states,col=2)  

#-----  

boxplot(x77.df$Population)
hist(x77.df$Population)

#-----  

summary(murder)
vhigh <- murder >= 10.68                  
high  <- murder >= 6.85 & murder < 10.68   
low   <- murder >= 4.35 & murder < 6.85     
vlow  <- murder <  4.35                     

plot(illit,murder,type = "n")  

points( illit[vhigh],murder[vhigh],pch="H", col=1 )  
points( illit[high], murder[high], pch="h", col=2 )
  text( illit[low],  murder[low],  "l",     col=3 )
  text( illit[vlow], murder[vlow], "L",     col=4 )         

#-----  

state.x <- state.center$x   
state.y <- state.center$y   

plot(state.x,state.y,type="n")

text( state.x[vhigh],state.y[vhigh],state.abb[vhigh],col=1)
text( state.x[high], state.y[high], state.abb[high], col=2)
text( state.x[low],  state.y[low],  state.abb[low],  col=3)
text( state.x[vlow], state.y[vlow], state.abb[vlow], col=4)

legend(-75,33, c("VHIGH","HIGH","LOW","VLOW"),pch=19,col=1:4,cex=.5)
    
title(main = "Quartiles of murder rates by state", col = 6)

###________ Section 7: Matrices ________###

y <- matrix(data=1, nr=3, nc=2)
y
y[,1]         # column 1 of y
y[2,]         #    row 2 of y
t(y)          # transpose of y
t(y) %*% y    # matrix multiplication
  y  %*% t(y)
  y  %*% y

z <- matrix(nr=3, nc=2)
z
z <- matrix(data=1:6, nr=3, nc=2)
z

###________ Section 8: Writing Functions ________###

stdev <- function(x){ return(sqrt(var(x)))}   
stdev(murder)  

###________ Section 9: CLT demonstration ________###

x <- rchisq(2000,3)
hist(x)

y <- matrix(nr=64,nc=500)
z <- vector(length=500)

for(i in 1:500) y[,i] <- sample(x,64,replace=T)
for(i in 1:500)  z[i] <- mean( y[,i] )
z
hist(z)

mean(x)
mean(z)

sd(x)
sd(z)
sd(x)/sqrt(64)