Restricted (Natural) cubic spline - wrong equation?

  • #1
My Restricted (Natural) Cubic Spline Equation is Wrong ?

I am trying to fit a restricted cubic spline (natural cubic spline) to toy data, attempting to follow
Hastie, Tibshirani, Friedman 2nd ed. 5.2.1 p.144-146, Eqs 5.4 and 5.5.
Data: Is basically a transposed ‘S’ shape. R-code is:
n <© 100
x <- (1:n)/n
true <- ((exp(1.2*x)+1.5*sin(7*x))-1)/3
noise <- rnorm(n, 0, 0.15)
y <- true + noise
plot(x,y)

I set knots at: {.2, .4, .6, .8} and am fitting using the non-linear NLS() function in R, but I can’t get the S-shape of the data no matter what I try.

My equations is wrong ? Or I am completely off-base in my approach? Any suggestions?
(Book-excerpt, my equation, and data-plot posted below)
 

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Answers and Replies

  • #2
Q: Is my problem unclear? Or - is anyone aware of a better forum for my question? Thank you.
 

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