#set up working directory in R
setwd("C:\\Users\\authorized user\\Dropbox\\STAT445\\week1\\tutorials")
getwd()

#Read data from .csv (comma-separated values) file directly into R
(MLB<-read.csv("Major League Baseball Main Stats.csv"))
 
MLB[,2]=as.numeric(MLB[,2])



#print data set that was imported into R 
MLB

#check if MLB is matrix 
is.matrix(MLB)
#FALSE

#check if MLB is data.frame object
is.data.frame(MLB)
#TRUE

#turn MLB into a matrix object
#MLB=as.matrix(MLB)

#calculate mean vector (mean for each of the columns in MLB respectively)
#round it to the second decimal place
#and print the results
(round(colMeans(MLB[,2:6]),2))


#calculate variance-covariance matrix for the columns of the MLB
#that are of numeric type (columns from 2 to 6)
#and print the results rounded to the second decimal place
(round(cov(MLB[,2:6]),2))


#calculate correlation matrix for the columns of the MLB
#that are of numeric type (columns from 2 to 6)
#and print the results rounded to the second decimal place
(round(cor(MLB[,2:6]),2))


#all pairs of two-variable scatterplots for 
#the numeric variables in the MLB data set
pairs(MLB[,2:6])

#all pairs of two-variable scatterplots for 
#the numeric variables in the MLB data set
#included smoothed line in each of the scatterplots
pairs(MLB[,2:6],panel=panel.smooth)

#function panel.cor
#that will create entries in the lower-left triangle below the diagonal 
#containing estimates of the correlation coefficients
panel.cor <- function(x, y, digits=2, prefix="", cex.cor) 
{
    #graphics setup
    usr <- par("usr"); on.exit(par(usr)) 
    par(usr = c(0, 1, 0, 1)) 
    r <- abs(cor(x, y)) 
    txt <- format(c(r, 0.123456789), digits=digits)[1] 
    txt <- paste(prefix, txt, sep="") 
    if(missing(cex.cor)) cex <- 0.8/strwidth(txt) 
 
    #hypothesis testing with null hypothesis:
    #"true correlation is equal to zero"
    test <- cor.test(x,y) 
    # borrowed from printCoefmat
    #symbolic number coding
    Signif <- symnum(test$p.value, corr = FALSE, na = FALSE, 
                     cutpoints = c(0, 0.001, 0.01, 0.05, 0.1, 1),
                     symbols = c("***", "**", "*", ".", " ")) 
 
    #add the exact correlation coefficients to 
    #the lower-left triangle below the diagonal 
    text(0.5, 0.5, txt, cex = cex * r) 
    text(.8, .8, Signif, cex=cex, col=2) 
}


#all pairs of two-variable scatterplots for 
#the numeric variables in the MLB data set
#with the entries in the lower-left triangle below the diagonal 
#containing estimates of the correlation coefficients
#panel.cor function will be executed for each pair
pairs(MLB[,2:6],panel=panel.smooth,lower.panel=panel.cor)