The use of least squares regression and curve fitting is well established in the applied sciences. It is discussed in detail in the monograph Least Squares Analysis and Curve Fitting. Most analyses of this type, however, are done with only one independent variable (the classic linear fit is a good example of this.)
For some problems it is necessary to consider two or more independent variables (a recent example is here.) A way to perform regression on such data is to use the LINEST function, which can be used for linear/planar types of correlations. It can be found in most of the current spreadsheet packages. It is tricky to use; about the only way to illustrate its use is through a video, and one from Dr. Todd Grande is featured here.