# Smoothing spline

Two columns must be selected (x and y values). The data are fitted to a smoothing spline, which is a sequence of third-order polynomials continuous up to the second derivative. A typical application is the construction of a smooth curve going through a noisy data set. The algorithm follows de Boor (2001). Sharp jumps in your data can give rise to oscillations in the curve, and you can also get large excursions in regions with few data points. Multiple data points at the same x value are collapsed to a single point by weighted averaging and calculation of a combined standard deviation.

An optional third columns specifies standard deviations on the data points. These are used for weighting the data. If unspecified, they are all set to 10% of the standard deviation of the y values.

The smoothing value set by the user is a normalized version of the smoothing factor of de Boor (default 1). Larger values give smoother curves. A value of 0 will start a spline segment at every point. Clicking "Optimize smoothing" will calculate an "optimal" smoothing by a crossvalidation procedure.

"View given points" gives a table of the given data points xy and stdev(y), the corresponding y values on the spline curve (ys) and the residuals. The chi-squared test for each point may be used to identify outliers. The final column suggests an stdev(y) value to use if forcing the p value to 0.5.

An optional fourth input column (if used then the third column must also be filled with stdev values) may contain a different number of values from the previous columns. It contains x values to be used for interpolation between the data points. Optional columns 5-7 contain lower and upper limits for x values (rectangular distribution) and standard deviation for y values (normal distribution), to be used by bootstrapping (Monte Carlo) simulation providing error bars for the interpolated values. These functions are included mainly for computing boundary ages for the geological time scale.

#### Reference

de Boor, Carl. 2001. A practical guide to splines. Springer.

Published Aug. 31, 2020 9:49 PM - Last modified Aug. 31, 2020 9:50 PM