In crosses between inbred lines, linear regression can be used to estimate
the correlation of markers with a trait of interest; these marker effects t
hen allow marker assisted selection (MAS) for quantitative traits. Usually
a subset of markers to include in the model must be selected: no completely
satisfactory method of doing this exists. We show that replacing this sele
ction of markers by ridge regression can improve the mean response to selec
tion and reduce the variability of selection response.