Regression Analysis

Fitting a Regression Line

plot(Y ~ X, pch = 20, col = "red") #1 lines(lowess(X, Y), lwd = 2, col = "blue") #2 abline(lm(Y ~ X), lty = 2) #3

Bivariarte Regression Analysis

ls <- lm(Y ~ X) #1 summary(ls) #2 stem(residuals(ls), scale = 2) #3 plot(X, Y, pch = 20) #4 title("Ordinary least-squares regression, X vs. Y") #5 abline(ls) #6 segments(X, Y, X, fitted(ls), lty = 2) #7

Compare Fitted and Observed

ls <- lm(Y ~ X) #1 plot(fitted(ls), Y, pch = 20, xlab = "Fitted", ylab = "Observed", xlim = c(0, 1), ylim = c(0, 1), main ="Observed vs. Fitted") #2 abline(0, 1) #3 segments(fitted(ls), Y, fitted(ls), fitted(ls)) #4

Make a Normal Quantile-quantile (Q-Q) Plot of The Regression Residuals

ls <- lm(Y ~ X) #1 qqnorm(residuals(ls)) #2 qqline(residuals(ls)) #3