# Measuring the degree to which two variables co-vary: Correlation
# covariance examples
# all online:
# (x,y); (1,1), (2,2), (3,3), (4,4) 
x<- c(1, 2, 3, 4)
y <- c(1, 2, 3, 4)
cov(x,y)
# ex 2
# (x,y); (1,4), (2,3), (3,2), (4,1)
x<- c(1, 2, 3, 4)
y <- c(4, 3, 2, 1)
cov(x,y)

########### equivalent to cos()
# in R cos() function Angles are in radians, 
# not degrees (i.e., a right angle is pi/2)
# cos 90 degrees
cos(pi/2)
# cos 0 degrees
cos(0)
#############
# from url
 mydataframe <- read.delim("http://www.robin-beaumont.co.uk/virtualclassroom/book2data/correlation_vo2max.dat",header=TRUE)
# local file ignore:
# mydataframe <- read.delim(file.choose(), header=TRUE)
# mydataframe <- read.delim("D:\\web_sites_mine\\HIcourseweb 
# new\\book2data\\correlation_vo2max.dat", header=TRUE)

names(mydataframe)
# vo2max scatter matrix
# vo2max data correlation_vo2max.dat in book2data folder
# to find one correlation + p value + ci
cor.test(mydataframe$mftvomax, mydataframe$weight)


# adapted from rdmr option
library(car)
scatterplotMatrix(~abdcurln+height+mftvomax+weight, reg.line=lm, 
  smooth=FALSE, spread=FALSE, span=0.5, id.n=0, diagonal = 'histogram', 
  data=mydataframe)
####
# Using result from:
# cor.test(mydataframe$mftvomax, mydataframe$weight)
res <- .3345			 
N<- 20			 
	adj_r <- sqrt(1-((1-res^2)*(N-1))/(N-2))
adj_r

# alternative
model1 <-lm(mydataframe$mftvomax ~ mydataframe$weight, data=mydataframe)
# r
summary(model1)$r.squared
sqrt(summary(model1)$r.squared)
# adjusted r
summary(model1)$adj.r.squared
sqrt(summary(model1)$adj.r.square)


# rank order
# method is "kendall" or "spearman", 
kendallres<- cor.test(mydataframe$mftvomax, mydataframe$weight, method="kendall")
kendallres
str(kendallres)
spearres<- cor.test(mydataframe$mftvomax, mydataframe$weight, method="spearman")
str(spearres)

### examples
# url:
mydataframe <- read.delim("http://www.robin-beaumont.co.uk/virtualclassroom/book2data/regression1.dat")

# local file ignore:
# mydataframe <- read.delim("D:\\web_sites_mine\\HIcourseweb new\\book2data\\regression1.dat", 
# header=TRUE)

names(mydataframe)
rcorr.adjust(mydataframe[,c("fastingBG","HBA1C")], type="pearson", use="complete")
  
cor.test(mydataframe$fastingBG, mydataframe$HBA1C, alternative="two.sided", method="pearson")


######################  correlation panel
# url:
mydataframe <- read.delim("http://www.robin-beaumont.co.uk/virtualclassroom/book2data/ais_daag.dat", header=TRUE)

# local file ignore:
#mydataframe <- read.delim("D:\\web_sites_mine\\HIcourseweb new\\book2data\\ais_daag.dat",
# header=TRUE)

names(mydataframe)
attach(mydataframe)
library(psych)
pairs.panels(mydataframe)
pairs.panels(mydataframe[1:11])


cor.plot(cor(mydataframe[1:11]), color=FALSE)