Cubic splines

Cubic splines are frequently used for interpolation. Run cubic splines in Excel using the XLSTAT add-on statistical software.

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.