  In this paper, we consider the classic measurement error regression scenario
in which our independent, or design, variables are observed with several
sources of additive noise. We will show that our motivating example's
replicated measurements on both the design and dependent variables may be
leveraged to enhance a sparse regression algorithm. Specifically, we estimate
the variance and use it to scale our design variables. We demonstrate the
efficacy of scaling from several points of view and validate it empirically
with a biomass characterization data set using two of the most widely used
sparse algorithms: least angle regression (LARS) and the Dantzig selector (DS).
