Lecture 11: Confidence intervals and model comparison for linear regression; analysis of variance

Just as there was a close connection between hypothesis testing with the one-sample t-test and a confidence interval for the mean of a sample, there is a close connection between hypothesis testing and confidence intervals for the parameters of a linear model. We’ll start by explaining the confidence interval as the fundamental idea, and see how this leads to hypothesis tests. ellipse() from the ellipse package #Sample mean dat <rnorm(100,0,1) hist(dat,breaks=20,prob=T, ylim=c(0,1),xlab="Observed data",main="",cex=2) arrows(t.test(dat)$conf.int[1],0.9,t.test(dat)$conf.int[2],0.9, code=3,angle=90,lwd=3,col=2) points(mean(dat),0.9,pch=19,cex=2) arrows(-0.3,0.5,-0.05,0.85,lwd=2,col=3) text(-0.9,0.7,"PROC",cex=2,col=3)