I've got a function, I've added noise to it, then smoothed it to get a regression line. How can I find the MSE between the original function and the regression line at 30 equally spaced points?
Or, how can I give R an x value and get the y value on a regression line?
This is a scaled down version of my problem:
> test<- function(m) {3*m^2+7*m+2}
> r=rnorm(10)
> m=1:10/10
> plot(test(m)+r)
> lines(smooth.spline(1:10,test(m)+r),col="red")
So I've got the true function values at the 10 equally spaced points i.e. test(m). I just need a way to extract the smooth.spline values at those 10 points, then I should be able to calculate MSE.
Answer
How about:
y <- test(m)+r
y.pred <- predict(smooth.spline(1:10,y))$y
mean((y-y.pred)^2) ## variance (could mult by n/(n-r) for an unbiased estimate)
mean((test(m)-y.pred)^2) ## MSE