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

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

2^c(1,2,3,4)     #powers of two
0:10             #sequence from 0 to 10
3:-7             #sequence from 3 down to -7
seq(-3,3,by=0.5) #sequence by specified increment

#scripts & functions for STAT 221
 source("http://www.uvm.edu/~rsingle/stat221/data/scripts-221.R")

murder 
illit                        
states  
mean(murder)     
median(murder)   
                         
murder > 12                #logical operator
murder / illit             #murders per 1000 illiterate 
abs(murder - mean(murder)) #abs difference from the mean

###________ Section 2: Extracting Data; Subscripts ________###

murder[1:3]           #1st 3 elements of murder
murder[murder > 12]   #elements of murder where murder>12 is TRUE  
states[murder > 12]   #elements of states where murder>12 is TRUE
illit[states == "CA"] #illiteracy rate for CA
murder     
murder[-1]            #murder without 1st element
murder[-7] 

###________ Section 3:  Plotting ________###

data(state)
ls()
state.x77
murder <- state.x77[,5] 
illit  <- state.x77[,3]  
states <- state.abb     
plot(illit,murder)      
abline(2.4, 4.3)                                   
identify(illit, murder, states, col = 2) #interactive function 
#NOTE: click "finish" in the upper right of the plot window when done 

plot(illit,murder, type="n")    #type="n" means nothing plotted
text(illit,murder,states,col=2)  

#-----  

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 )         

#----- A fancy plot 

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(-77,31, c("VHIGH","HIGH","LOW","VLOW"),pch="*",col=1:4,cex=.5)
    
title(main = "Quartiles of murder rates by state", col = 6)

###________ Section 4: CLT demo & loops ________###

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

xbar <- vector(length=500)
for(i in 1:500)
{
  tmp <- sample(x,64,replace=T) 
  xbar[i] <- mean(tmp)
}
xbar
hist(xbar)

mean(x)
mean(xbar)

sd(x)
sd(xbar)
sd(x)/sqrt(64)

###________ Section 5: Writing Functions ________###

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

###________ Section 6: 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