## Lab Exercise for R: Linear Regression

### Exercise 1: Characterize a linear relationship

If two independent samples are obtained, then we can ask whether they may have been drawn from two different underlying distributions.

 First generate a Data set n = 50 x = sample(40:70,n,rep=T) y = .7*x+rnorm(n,sd=5) Now plot the data and a horizontal line at the mean plot(x,y) ybar = mean(y) abline(a=ybar,b=0,col="black") Calculate the best fit model line and draw in the line fit.lm = lm(y~x) abline(fit.lm,col="red") points(x,fitted(fit.lm),col='red',pch=20) Predict y-hats and construct confidence intervals for the slope newx = seq(min(x),max(x)) prd = predict(fit.lm,data.frame(x=newx),interval="confidence",level=0.95,type="response") lines(newx,prd[,2],col="red",lty=2) lines(newx,prd[,3],col="red",lty=2) Get a plot of the results, for residuals vs fitted values, residuals vs independent values, a Q-Q plot for residuals, etc ... plot(fitted(fit.lm), resid(fit.lm)) plot(x,resid(fit.lm)) qqnorm(resid(fit.lm)) qqline(resid(fit.lm),col="red")