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+# Purpose: to demonstrate polynomial regression
+#
+#
+# Created by Hui Lan on 19 April 2018
+
+
+### Functions ###
+
+f <- function(x)
+{
+    # the true function
+    # y <- 0.5 + 1.5*x + 0.5*x^2  # also try quadratic function
+    y <- 0.5 + 1.5*x  # y is implicitly returned. don't need a return statement
+}
+
+
+
+### main ###
+sd.err <- 2
+N <- 12
+x1 <- rnorm(N, mean=5, sd=3)  # my data for the the predictor variable X1
+e = rnorm(N, mean=0, sd=sd.err) # error term
+y  <- f(x1) + e   # my data for the response variable Y
+
+
+model <- lm(y~x1) # call linear model fit. use ?lm to get details of this function
+model
+summary(model)
+
+D <- data.frame(Y=y, X1=x1, X2=x1^2, X3=x1^3, X4=x1^4,
+                X5=x1^5, X6=x1^6,X7=x1^7)
+model.polynomial <- lm(Y ~ X1+X2+X3+X4+X5+X6+X7, data=D)
+par(mfrow=c(1,1))
+plot(x1, y, pch='+')
+abline(model, lwd=1, col='green')
+curve(f, from=min(x1), to=max(x1), col='red', add=T)
+num.interval <- 100
+new.x <- seq(min(x1),max(x1),length=num.interval)
+test.x <- data.frame(X1=new.x, X2=new.x^2, X3=new.x^3, X4=new.x^4, X5=new.x^5, X6=new.x^6, X7=new.x^7)
+lines(new.x,predict(model.polynomial, newdata=test.x), col="blue")