##### SCA-42b
##### 
##### Correlation and Regression
##### 

### This gives a single example of using regression to answer a
### question of interest.



### Preamble

source("http://rfs.kvasaheim.com/stat200.R")



### The Topic: Unfairness in Ruritanian election

# Is there are relationship between the invalidation rate and the candidate
# support rate in the 2017 Ruritanian presidential election?

dt = read.csv("http://rfs.kvasaheim.com/data/xr2017pres.csv")
attach(dt)
summary(dt)



# create the proportion variables

VALID = TOTAL-INVALID
pInv = INVALID/TOTAL
pKuz = KUZNECOV/VALID

mod1 = lm(pInv~pKuz) 
summary(mod1)
# or #
cor.test(pInv,pKuz)

# There is a statistically significant relationship between the invalidation rate and
# the support level for Kuznecov in the 2017 Ruritanian presidential election (p-value = 
# 0.03). A 95% confidence interval for that correlation is from -0.039 to -0.624, with
# a point estimate of -0.367. 
#
# Electoral divisions with higher support for Kuznecov also had a lower invalidation rate.
# This is consistent with ballot box stuffing and differential invalidation in favor
# of Kuznecov.



## Graphic

plot(pKuz,pInv)

# better

plot(pKuz,pInv, xlim=c(0,1), ylim=c(0,0.1), xlab="Kuznecov Support Level", ylab="Rejection Rate")

# even better

plot(pKuz,pInv, xlim=c(0,1), ylim=c(0,0.1), xlab="Kuznecov Support Level", ylab="Rejection Rate")
abline(mod1)

# pretty graphic

par(mar=c(3,3,0,0)+1)
par(las=1)
par(family="serif")
par(xaxs="i", yaxs="i")
par(cex.lab=1.2, cex.font=2)

plot.new()
plot.window( xlim=c(0,1), ylim=c(0,0.06) )

axis(1, at=0:10/10)
axis(2, at=0:6/100)

title(xlab="Kuznecov Support Level", line=2.5)
title(ylab="Rejection Rate", line=3)

abline(mod1, col="grey")

points(pKuz,pInv, pch=21, bg="honeydew2")