  We use location model methodology to guide the least squares analysis of the
Lasso problem of variable selection and inference. The nuisance parameter is
taken to be an indicator for the selection of explanatory variables and the
interest parameter is the response variable itself. Recent theory eliminates
the nuisance parameter by marginalization on the data space and then uses the
resulting distribution for inference concerning the interest parameter. We
develop this approach and find: that primary inference is essentially
one-dimensional rather than $n$-dimensional; that inference focuses on the
response variable itself rather than the least squares estimate (as variables
are removed); that first order probabilities are available; that computation is
relatively easy; that a scalar marginal model is available; and that
ineffective variables can be removed by distributional tilt or shift.
