The increasing power and decreasing price of smalI computers, especialIy "personal" computers, has made them increasingly popular in statistical analysis. The day may not be too far off when every statistician has on his or her desktop computing power on a par with the large mainframe computers of 15 or 20 years ago. These same factors make it relatively easy to acquire and manipulate large quantities of data, and statisticians can expect a corresponding increase in the size of the datasets that they must analyze. Unfortunately, because of constraints imposed by architecture, size or price, these smalI computers do not possess the main memory of their large cousins. Thus, there is a growing need for algorithms that are sufficiently economical of space to permit statistical analysis on smalI computers. One area of analysis where there is a need for algorithms that are economical of space is in the fitting of linear models.