In this example, we are assuming that we have a collection of 2-dimensional independent data for which the 1-dimensional dependent data has some error component or is known to be noisy. The presence of noise implies that whatever surface this data represents does not necessarily pass through the given dependent data points. In this case, a surface is approximated by numerically smoothing the data using the lowess algorithm. For any given point to be plotted a window of close enough, surrounding data points will be used to compute a local, weighted, low order fit.

The new command ScatterPlot3D, from the Statistics package, provides a smoothed plot of the 2-D noisy data.

The independent data does not need to be regularly spaced, and is supplied as an n-by-3 Array or Matrix. Each of the n rows represents an individual point. The columns are the  x-, y-, and z-values.

Here is an example. First, we'll look down upon the projection of the data points onto the x-y plane, and thus visualize the layout and spacing of the 2-D dependent data values.

Here is another example, which reads in the n-by3 data from a file.

The default options for the ScatterPlot3D command are to use an order 2 fitting quadratic form, and to use a window of width 1/3 of the original domain in each of the x- and y-directions.

On the right below is the smoothed surface, while on the left is a slightly transparent view of the same surface overlaid with a point-plot of the original data points.