Using R:

What is the best polynomial order (1-20) modeling the structure of the following dataset (`x` vs `y`)?

Your answer should include a numerical approach (e.g. MSE estimates) along with a convincing set of visuals supporting your answer.

```{r} set.seed(4) n <- 1000 x <- runif(n, -4, 4) mu <- ifelse(x > 0, cos(4*x), 1-sin(x)) y <- mu + rnorm(n) data <- data.frame(x=x, y=y) plot(x, y, col="black", pch=21, bg="steelblue", ylab = "y") lines(x[order(x)], mu[order(x)], col="red", lwd=3, type="l") legend("bottomleft", legend=c("E[Y|X=x], truth", "Data"), cex=.8, lty=c(1, NA), col=c("red","steelblue"), pch=c(NA, 21), pt.bg=c(NA, "steelblue")) ```