# Linear Regression plot with normal curves for error (sideways)

Linear Regression: Normal Errors

I remember my first encounter to the classical linear regression model with normally distributed errors by Dan Gillen in Stat 120c in spring 2005 at UCI. I mean, I’ve done linear regression in high school science classes: you get a best fit line out of your data. In the stat class, I remember seeing data drawn on the board and a line going through the data. To illustrate the normally distributed errors, he drew sideway normal curves.

I liked this presentation of the classical model. How do convey this in R? I couldn’t find a package for it (searched for an hour I think). I always search for packages because I always think others could do a better job at it than me and because I don’t like to re-invent things, even though it requires less time for me to do it myself in many cases. Well, here it is, written by me in R:

<pre class="src src-R"><span style="color: #87cefa;">sideways.dnorm</span> <span style="color: #7fffd4;">&lt;-</span> <span style="color: #00ffff;">function</span>(where.x, where.y, values=seq(-4,4,.1), magnify=4, ...){


###… consists of mean, sd, and log passed to dnorm function dens <- dnorm(x=values, …) x <- where.x + dens * magnify y <- where.y + values return(cbind(x,y)) }

temp <- sideways.dnorm(where.x=3, where.y=3, values=seq(-2,2,.1)) plot(temp)

##jpeg(“LinearRegressionNormalErrors.jpeg”) pdf(“LinearRegressionNormalErros.pdf”) set.seed(123) n <- 200 x <- runif(n, -8,8) y <- 1 + .5*x + rnorm(n, sd=1) fit <- lm(y~x) plot(x,y, xlim=c(-10,10), ylim=c(-8, 10) , main=“Classical Linear Regression\nwith Gaussian errors” ##, main=expression(paste(“Classical Linear Regression\nwith N(0,”, sigma\^2, “) errors”, sep=”)) , col=“red” ) abline(fit, lwd=3, col=“blue”) where.normal.x <- c(-4,0,4) for(i in 1:length(where.normal.x)){ where.x <- where.normal.x[i] where.y <- predict(fit, newdata=data.frame(x=where.x)) xy <- sideways.dnorm(where.x=where.x, where.y=where.y, magnify=4) lines(xy) abline(h=where.y, lty=2) abline(v=where.x, lty=2) }

dev.off()