How can I prove that the cubic regression spline y_i = α + K+4∑k=2 β_kh_k(x_i) + e_i is continuous in the first and second derivative at the knots? I understand how to prove the property by expanding the equation for f(x)=β0+β1x+β2x2+β3x3+β4(x−ξ)3+ which is explained here:https://rstudio-pubs-static.s3.amazonaws.com/65563_d6411480e07b4aaaad9b484b66210497.html, but how can I extend the proof to K knots?
prove continuity of cubic regression spline
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