Y = β0 + (β1 + β2)X1 + and we may get a good estimate of Y estimating 2 parameters instead of 3. Our estimate will be a bit biased but we may lower our variance considerably creating an estimate with smaller expected prediciton error than the least squares estimate. We won’t be able to interpret the estimated parameter, but our prediction may be good. In subset selection regression we select a ...

In this note, we present two results on the scaled total least squares problem. First, we discuss the relation between the scaled total least squares and the least squares problems. We derive an upper bound for the difference between the scaled total least squares solution and the least squares solution and establish a quantitative relation between the scaled total least squares residual and th...

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the data to make the corrected system compatible. In ordinary least squares (LS) the correction is restricted to the right hand side b, while in scaled total least squares (Scaled TLS) [10; 7] corrections to both b and A are allowed, and their relative sizes are determined by a real positive...

This technical note presents a numerical corrective technique that allows control of nonlinearity in a mass-spring system (MSS) independent of its spring constants or system topology. The governing equations of MSS in the form of ordinary differential equations or a regular function accompanied by any boundary or initial condition as known constraints, are employed to modify the results. A leas...