Polynomial regression provides interpolation by approximating the source data points using a best fit global polynomial expression. The surfaces are typically simple polynomial functions of order 1, 2 or 3, fitted to the point set by ordinary least squares (see examples in Figure 6‑38, below). With linear regression the fitted surface has 3 constants, and is of the form:

whilst the bi-cubic model requires estimation of 10 constants and is of the form:

Typically global polynomial surface fitting is not used as a means of interpolation, but rather as a form of trend analysis, with further analysis being carried out on the residuals obtained when the fitted surface values are subtracted from those of the source.

Figure 6‑38 Regression fitting to test dataset OS NT04

A. Linear regression |
B. Bicubic polynomial regression |