Outliers in regression

In this section we return to a problem already discussed in Chapter 3, the occurrence of outliers in our data. These anomalous results inevitably arise in calibration experiments, just as they occur in replicate measurements, but it is rather harder to deal with them in regression statistics. One difficulty is that, although the individual yj-values in a calibration experiment are assumed to be independent of one another, the residuals (y - pj) are not independent of one another, as their sum is always zero. It is therefore not normally permissible to take the residuals as if they were a conventional set of replicate measurements, and apply (for example) a Q-test to identify any outliers. (If the number of y-values is large, a condition not generally met in analytical work, this prohibition can be relaxed.) 

Finally we note that, just as in the treatment of outliers in replicate measurements, non-parametric and robust methods can be very effective in handling outliers in regression robust regression methods have proved particularly popular in recent years. These topics are covered in the next chapter. 

Analytical Methods Committee. 2002. Fitting a Linear Functional Relationship to Data with Error on Both Variables, Royal Society of Chemistry, Cambridge. (This Technical Brief provided by the Society s Analytical Methods Committee is one of a series obtainable at www.rsc.org/lap/rsccom/amc/amc index.htm. The same site provides links to the downloadable software.) 

Draper, N. R. and Smith, H. 1998. Applied Regression Analysis, 3rd edn, Wiley, New York. (An established work with comprehensive coverage of many aspects of regression and correlation problems.) 

Edwards, A. L. 1984. An Introduction to Linear Regression and Correlation, 2nd edn, W. H. Freeman, New York. (Clearly written treatment, with a good introduction to matrix algebra.) 

---

The problems caused by possible outliers in regression calculations have been outlined in Sections 5.13 and 6.9, where rejection using a specified criterion and non-parametric approaches respectively have been discussed. It is clear that robust approaches will be of value in regression statistics as well as in the statistics of repeated measurements, and there has indeed been a rapid growth of interest in robust regression methods amongst analytical scientists. A summary of two of the many approaches developed must suffice. 

---