#Board question: fit curves ----
x = c(1,2,4)
y = c(3,1,4)
degs = c(1,2)  #the degrees of the polynomials to fit

n = length(x)
# Set the plot limits and plot
xlim = c(0,5)
ylim = c(0,5)
plot(x, y, col = "magenta", pch = 16, cex=1.2,xlim=xlim, ylim=ylim)

###fitting models to the data
xplot = seq(xlim[1],xlim[2],length.out = 1000)
for(j in 1:length(degs)){
  #Sys.sleep(1)
  deg = degs[j]
  fit = lm(y ~ poly(x, deg, raw = TRUE))
  print(summary(fit))
  print(paste("R squared: ", summary(fit)$r.squared))
  lines(xplot, predict(fit, newdata=data.frame(x=xplot)), col=j, lwd=3)
}
legend(4,2,degs,col=1:length(degs), lty=1,lwd=3)