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If I smooth a data vector with a smoothing cubic spline my understanding is that each ‘segment’ between knots should be representable as a cubic polynomial.

Is it possible to infer the equation of each segment from the spline coefficients after e.g fitting by the smooth.spline function in R?

This is straightforward for an interpolating spine as the array of polynomial coefficients is generated explicitly. However, I’ve not been able to find an answer as to whether this is possible with a smoothing spline or regression spline?

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