explorations with correlation

correlation.R

# negative correlation                                                                                                                                                                                      x = seq(0,10,0.5)
fX = function(x) { return(x) }
fY = function(x) { return(-x) }
df = data.frame(x=x, fX=fX(x), fY=fY(x))
ggplot(df, aes(x=x)) + geom_line(aes(y=fX), color="green") + geom_line(aes(y=fY), color="blue")
cov(df$fX, df$fY)
cor(df$fX, df$fY)


fX = function(x) { return(x - 5) }
fY = function(x) { return(-x + 5) }
df = data.frame(x=x, fX=fX(x), fY=fY(x))ggplot(df, aes(x=x)) + geom_line(aes(y=fX), color="green") + geom_line(aes(y=fY), color="blue")
cov(df$fX, df$fY)
cov(df$fX, df$fY)/(sd(df$fX)*sd(df$fY)) # == cor(x,y)
cor(df$fX, df$fY)

# how do we generate a plot with a cor 1 > x > -1? 
x = seq(0,100,5)[0:20]
df = data.frame(x=x, fX=rnorm(20,50,25), fY=rnorm(20,50,12))
ggplot(df, aes(x=x)) + geom_point(aes(y=fX), color="green") + geom_point(aes(y=fY), color="blue")cov(df$fX, df$fY)cov(df$fX, df$fY)/(sd(df$fX)*sd(df$fY)) # == cor(x,y)cor(df$fX, df$fY)

df <- data.frame(x = 1:20 + rnorm(20,sd=3), y = 1:20 + rnorm(20,sd=3))
ggplot(df, aes(x=x,y=y)) + geom_point(color="blue") + geom_smooth(method=lm, se=F)
cor(df$x,df$y)