Cubic splines

What is a cubic spline?

A cubic spline is defined as a piecewise function of polynomials of degree 3. Cubic splines are used in interpolation problems where they are preferred to usual polynomial interpolation methods. The reason being that they allow a compromise between the smoothness of the curve and the degree of the polynomial.

Use of the cubic splines in XLSTAT

Cubic splines are defined from a set of nodes. In XLSTAT, three options are offered:

• Use data as nodes

• Define a number of nodes equally distributed.

• Choose a set of nodes

Results for the cubic splines in XLSTAT

• Coefficients of the polynomials: This table displays the coefficients of polynomials of degree 3 of the cubic spline.

• Prédictions and residuals: For each observation, the value of the dependent variable, the predictions, the residuals and the standardized residuals are displayed.

• Spline curve: The cubic spline and the selected nodes are displayed.