Complex regression plot in R

Question

I need to draw a complex graphics for visual data analysis. I have 2 variables and a big number of cases (>1000). For example (number is 100 if to make dispersion less "normal"):

x <- rnorm(100,mean=95,sd=50)
y <- rnorm(100,mean=35,sd=20)
d <- data.frame(x=x,y=y)

1) I need to plot raw data with point size, corresponding the relative frequency of coincidences, so plot(x,y) is not an option - I need point sizes. What should be done to achieve this?

2) On the same plot I need to plot 95% confidence interval ellipse and line representing change of correlation (do not know how to name it correctly) - something like this:

library(corrgram)
corrgram(d, order=TRUE, lower.panel=panel.ellipse, upper.panel=panel.pts)

but with both graphs at one plot.

3) Finally, I need to draw a resulting linar regression model on top of this all:

r<-lm(y~x, data=d)
abline(r,col=2,lwd=2)

but with error range... something like on QQ-plot:

but for fitting errors, if it is possible.

So the question is:

How to achieve all of this at one graph?

Answer 1

Does the picture below look like what you want to achieve?

Here's the updated R code, following your comments:

do.it <- function(df, type="confidence", ...) {
  require(ellipse)
  lm0 <- lm(y ~ x, data=df)
  xc <- with(df, xyTable(x, y))
  df.new <- data.frame(x=seq(min(df$x), max(df$x), 0.1))
  pred.ulb <- predict(lm0, df.new, interval=type)
  pred.lo <- predict(loess(y ~ x, data=df), df.new)
  plot(xc$x, xc$y, cex=xc$number*2/3, xlab="x", ylab="y", ...)
  abline(lm0, col="red")
  lines(df.new$x, pred.lo, col="green", lwd=1.5)
  lines(df.new$x, pred.ulb[,"lwr"], lty=2, col="red")
  lines(df.new$x, pred.ulb[,"upr"], lty=2, col="red")    
  lines(ellipse(cor(df$x, df$y), scale=c(sd(df$x),sd(df$y)), 
        centre=c(mean(df$x),mean(df$y))), lwd=1.5, col="green")
  invisible(lm0)
}

set.seed(101)
n <- 1000
x <- rnorm(n, mean=2)
y <- 1.5 + 0.4*x + rnorm(n)
df <- data.frame(x=x, y=y)

# take a bootstrap sample
df <- df[sample(nrow(df), nrow(df), rep=TRUE),]

do.it(df, pch=19, col=rgb(0,0,.7,.5))

And here is the ggplotized version

produced with the following piece of code:

xc <- with(df, xyTable(x, y))
df2 <- cbind.data.frame(x=xc$x, y=xc$y, n=xc$number)
df.ell <- as.data.frame(with(df, ellipse(cor(x, y), 
                                         scale=c(sd(x),sd(y)), 
                                         centre=c(mean(x),mean(y)))))
library(ggplot2)

ggplot(data=df2, aes(x=x, y=y)) + 
  geom_point(aes(size=n), alpha=.6) + 
  stat_smooth(data=df, method="loess", se=FALSE, color="green") + 
  stat_smooth(data=df, method="lm") +
  geom_path(data=df.ell, colour="green", size=1.2)

It could be customized a little bit more by adding model fit indices, like Cook's distance, with a color shading effect.

Answer 2

For point 1 just use the cex parameter on plot to set the point size.

For instance

x = rnorm(100)
plot(x, pch=20, cex=abs(x))

To have multiple graphs in one plot use par(mfrow=c(numrows, numcols)) to have an evenly spaced layout or layout to make more complex ones.