Robust Regression (Waterflow Measurements of Kootenay River)
The original data set is the waterflow in January of the Kootenay river, measured at two locations, namely, Libby (Montana, downstream) and Newgate (British Columbia, upstream) for 13 consecutive years, 1931-1943.
For didactical reasons we can modify the original measurements \(P(77.6, 44.9)\) of the year 1934:
Waterflow at Libby in the year 1934
Waterflow at Newgate in the year 1934
In addition the least-squares (ls) estimate of the straight line is added. It is obvious that one single outlier is enough to obtain a bad fit. We want to test the regression M-estimator on the contaminated data. The regression MM-estimator does a very good job and can cope with the leverage point \(P\). It performs equally well as the least-squares estimator without \(P\).