Matrices

Least squares fitting and the QR decomposition

The function lsfit() returns a list giving results of a least squares fitting procedure. An assignment such as 

> ans <- lsfit(X, y)

gives the results of a least squares fit where y is the vector of observations and X is the design matrix. See the help facility for more details, and also for the follow-up function ls.diag() for, among other things, regression diagnostics. Note that a grand mean term is automatically included and need not be included explicitly as a column of X. Further note that you almost always will prefer using lm(.)

Another closely related function is qr() and its allies. Consider the following assignments 

> Xplus <- qr(X)
> b <- qr.coef(Xplus, y)
> fit <- qr.fitted(Xplus, y)
> res <- qr.resid(Xplus, y)

These compute the orthogonal projection of y onto the range of X in fit, the projection onto the orthogonal complement in res and the coefficient vector for the projection in b, that is, b is essentially the result of the MATLAB 'backslash' operator.

It is not assumed that X has full column rank. Redundancies will be discovered and removed as they are found.

This alternative is the older, low-level way to perform least squares calculations. Although still useful in some contexts, it would now generally be replaced by the statistical models features.