######################################
#
# Mathematical Operations 
#
######################################

3+5
3*9
27 / 9
3^2
8^(1/3)
3^-2
-4^(1/3)
(-4)^2
(-4)^2.00000000000001
log(10)
exp(1)
log10(6)
log(9,3)
sin(pi/2)
cos(pi/2)
cos(pi/2)==0
sin(pi/2)==1
floor(5.7)
ceiling(5.7)
round(5.77454,3)
round(5.77456,2)

######################################
#
# Vectors and sequences
#
######################################

x<-c(5,7,7,7,9,8)   	#  Dnmioupgeia stnlns me 6 stoixeia
x
x[2]                	# to stoixeio 2 autns tns stnlns    
length(x)			# to mnkos tns stnlns
x[length(x)]		# to teleutaio stoixeio tns stnlns
		# praxeis me diavusmata
2*x
x*x
x^2
sum(x^2)
y<-x+3
y
x*y
t(x)
x%*%t(x)
t(x)%*%x

sort(x)
rev(sort(x))
max(x)
min(x)
x[x>=7]			# ta stoixeia tou x pou eivai >=7
which(x>=7)
sum(x)
sum(x>=7)             # posa stoixeia tou x eivai >=7
sum(x[x>=7])          # to a8poisma autwv

#  poses fopes emfavizetai ka8e stoixeio (movo auta pou emfavizovtai)
table(x)

#######################################################################

x<-c(rep(0,10))		# stnln me 10 mndevika
x 
x<-c(1:10)			# stnln me tous api8mous 1,2,3,...,10
x				
				#   mndevikos pivakas me 2 grammes kai 5 stnles 
x<-matrix(c(rep(0,10)),nrow=2,ncol=5) 
x
x<-matrix(c(1:10),nrow=2,ncol=5) #  1,2,...,10 topo8etnmeva kata stnles  
x
				#   1,2,...,10 topo8etnmeva kata grammes
x<-matrix(c(1:10),nrow=2,ncol=5,byrow=T)
x

######################################
#
# Reading Data
#
######################################

mich.df<-scan()
850
740
900
1070
930
850
950
980
980
880
 
mich.df<-c(mich.df,1000,980,930,650,760,810,1000,1000,960,960)
mich.df
z<-mich.df
summary(z)
summary(z)[1]
summary(z)[5]

####################################################################

kyphosis<-read.table("C:\\kyphosis.txt",header=TRUE)
kyphosis
kyphosis[1,]
kyphosis[,2]
kyphosis$Age

####################################################################

help(InsectSprays)
InsectSprays

help(ToothGrowth)
ToothGrowth

######################################
#
# Statistical functions
#
######################################

mich.df
z<-mich.df
quantile(z,probs=c(.25,.50,.75)) # posostimopia
mean(z)					# deigmatikos mesos
sum((z-mean(z))^2)/(length(z)-1)
var(z)					# diaspora
sqrt(var(z))
sd(z)					# tupikn apoklisn

######################################
#
# Plots
#
######################################

devAskNewPage(ask=TRUE)    # perimevei priv ftia3ei vea grafikn parastasn 
boxplot(z)

par(mfrow=c(2,1))          # duo grafikes parastaseis pavw kai katw
hist(z)				# istogramma suxvotntwv
hist(z,probability=T,col="grey")
par(mfrow=c(1,1))

par(mfrow=c(1,2))
z<-rnorm(5000) 			# tuxaio deigma mege8ous 5000 apo N(0,1)
hist(z,nclass=25,col=4,xlab="x",main="Histogram of N(0,1)",xlim=c(-4,4))
plot(dnorm,xlim=c(-4,4))
par(mfrow=c(1,1))
mean(z)
sd(z)

#################################################################


help(InsectSprays)

InsectSprays

boxplot(count ~ spray, data = InsectSprays)

boxplot(count ~ spray, data = InsectSprays,
            notch = TRUE, col = "blue")

boxplot(count ~ spray, data = InsectSprays,
              add = TRUE, col = "blue")

############################################################################

help(ToothGrowth)

ToothGrowth

boxplot(len ~ dose, data = ToothGrowth,
              boxwex = 0.25, at = 1:3 - 0.2,
              subset = supp == "VC", col = "yellow",
              main = "Guinea Pigs' Tooth Growth",
              xlab = "Vitamin C dose mg",
              ylab = "tooth length",
              xlim = c(0.5, 3.5), ylim = c(0, 35), yaxs = "i")
      boxplot(len ~ dose, data = ToothGrowth, add = TRUE,
              boxwex = 0.25, at = 1:3 + 0.2,
              subset = supp == "OJ", col = "orange")
      legend(2, 9, c("Ascorbic acid", "Orange juice"),
             fill = c("yellow", "orange"))

############################################################################

par(mfrow=c(1,2))
z<-rnorm(5000) 			# tuxaio deigma mege8ous 5000 apo N(0,1)
hist(z,nclass=25,col=4,xlab="x",main="Histogram of N(0,1)",xlim=c(-4,4))
plot(dnorm,xlim=c(-4,4))
par(mfrow=c(1,1))
mean(z)
sd(z)