Splines: knots, degrees of freedom, regularization.
hardAnswer
- Spline = piecewise polynomial with continuity at knots.
- Cubic splines: 3rd-degree pieces, continuous through 2nd derivative.
- Natural spline: linear beyond boundary knots (avoids wild extrapolation).
- Knot placement: at quantiles of X (uniform coverage).
- Regularization: penalized splines add smoothing penalty λ * ∫ dx → tune λ by REML / GCV.
- Standard smoother in GAMs.
Check yourself — multiple choice
- Random
- Piecewise polynomials with continuity at knots; cubic/natural common; knots at X quantiles; penalized splines add ∫ penalty tuned by REML/GCV
- Same as regression
- Not real
Splines: piecewise polynomials with continuity; penalized by ∫.
#regression#glm
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