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Restricted (Natural) cubic spline - wrong equation?

  1. Apr 30, 2015 #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)
     

    Attached Files:

  2. jcsd
  3. May 1, 2015 #2
    Q: Is my problem unclear? Or - is anyone aware of a better forum for my question? Thank you.
     
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