Moving Beyond Linearity
Keep least squares and change what you regress on: fixed basis functions buy curvature, constraints buy smoothness, and a penalty buys a curve that chooses its own flexibility.
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Basis Functions and Piecewise Polynomials
25 min · 100 XPOne idea covers polynomial and step-function regression, and extends to anything else you can write down: transform the predictor, then fit a linear model in the transformed columns.
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Regression Splines and the Truncated Power Basis
30 min · 120 XPOne extra column per knot turns a constrained fitting problem back into plain least squares, and a boundary constraint fixes the tails that ruin polynomials.
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Smoothing Splines, Local Regression and Additive Models
30 min · 120 XPStop choosing knots and penalise roughness instead, fit a separate weighted regression at every point, and carry the whole idea into many predictors at once.
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