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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)

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)