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A regression spline fits a regression function in a finite-dimensional spline approximation space with selected knots. Evaluating its basis at predictor values gives a design matrix, reducing fitting to regression on basis coefficients.

A spline is a piecewise polynomial function whose polynomial pieces obey specified smoothness conditions at their joins, called spline knots. For example, a cubic spline is cubic on each interval and commonly has two continuous derivatives across interior knots. Spline approximation and spline interpolation use these finite-dimensional function spaces to represent data or approximate functions.