# Spline regression Spline regression is a reparameterization of the polynomial regression that are more numerically stable and have better spatial interpretation. A spline regression is specified with the following form: $ E(Y \mid X = x) = \eta_0 + \eta_1 b_1(x) + ... + \eta_d b_d(x) $ $b_1(x),..., b_d(x)$ are a set of piecewise polynomials of order $d$ such that they form a basis for the same space spanned by the polynomials $x, ..., x^d$. ## Choosing number of basis functions - Heuristically, a degree of 3 or 4 is sufficient, but these models require a lot of data - Degree can also be chosen on the basis of predictive ability, if prediction is the main task of the model - Note this gets into problems of overfitting --- # References [[Applied Linear Regression#5. Complex Regressors]]