Regression for overdetermined systems: A fisheries example

In trying to establish the relationship between a yearly fisheries recruitment series and meteorological or oceanographic variables such as air pressure or sea surface temperature, we are often faced with the situation where the number of regressors exceeds the number of observations. In this paper we use the techniques of penalized least squares and principal-components regression to determine whether air pressure over the North Atlantic can be used to predict two North Atlantic cod recruitment series. The results suggest that penalized least squares can be very effective in these situations.