#Polynomial regression
set.seed(20)
q<-seq(from=0,to=20,by=0.1)
y<--500+0.4*(q-10)^3
noise<-rnorm(length(q),mean=10,sd=80)
noisy.y<-y+noise
plot(q,noisy.y,col='deepskyblue4',xlab='q',main='Observed data')
lines(q,y,col='firebrick1',lwd=3)
model<-lm(noisy.y~poly(q,3))
summary(model)
confint(model,level=0.95)
plot(fitted(model),residuals(model))
plot(q,noisy.y,col="deepskyblue4",xlab="q",main="Observed data")
lines(q,y,col="firebrick1",lwd=3)
predicted.intervals<-predict(model,data.frame(x=q),interval='confidence',level=0.99)
lines(q,predicted.intervals[,1],col='green',lwd=3)
lines(q,predicted.intervals[,2],col='black',lwd=1)
lines(q,predicted.intervals[,3],col='black',lwd=1)
legend("bottomright",c("Observ.","Signal","Predicted"),col=c("deepskyblue4","red","green"),lwd=3)

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