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##
##  Intro STATS : Normal Distributions
##  JDRS
##  http://www.reuningscherer.net/stat10x/r/
##
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#NOTE - need the car package for some of the functions below
library(car)

#Get WB Data

WB <- read.csv("http://reuningscherer.net/stat10x/data/WorldBank2013.csv")

#see variables available
names(WB)

#draw a quick normal density curve

plot(seq(-4,4,by=.01), dnorm(seq(-4,4,by=.01)), type="l", lwd=3, col='blue', ylab="Normal Density Height", main="Standard Normal Density Curve",
     xlab="z-score")

###########################################################################################
##  Normal Density Probabilities (Prob of getting value less than or equal to specified value)
##  See example on Page 82 of notes - mean=6.6, sd=1.4, what is prob of 8 or less?

pnorm(8,6.6,1.4)
#prob of 5 or less
pnorm(5,6.6,1.4)


##################################################################
##   Normal Quantile Plots
##
##   NOTE - both plots below have data on VERTICAL axis (opposite of MINITAB)

#Quantile plot for Life Expectancy
qqnorm(WB$Fertility, pch=19, col='blue')
qqline(WB$Fertility, col='red', lwd=2)

#Quantile plot function with bounds - from car package
qqPlot(WB$Fertility, dist="norm", pch=19, col='blue', ylab="Fertility Rate Data", main="Normal Quantile plot of Fertility Rates")

#Quantile plot of Percent Urban
qqPlot(WB$Rural, dist="norm", pch=19, col='blue', ylab="Rural Rate Data", main="Normal Quantile plot of Rural Pct")

#Do random data for sample sizes, 5, 50, 500
qqPlot(rnorm(5), dist="norm", pch=19, col='blue', ylab="Rural Rate Data", main="Normal Quantile Plot, 5 Rand Normal Obs")
qqPlot(rnorm(50), dist="norm", pch=19, col='blue', ylab="Rural Rate Data", main="Normal Quantile Plot, 50 Rand Normal Obs")
qqPlot(rnorm(500), dist="norm", pch=19, col='blue', ylab="Rural Rate Data", main="Normal Quantile Plot, 500 Rand Normal Obs")