<p>To estimate physical parameters in a grey-box model with linear regressions, a two-step approach with much reduced computational complexity is developed. First, the parameters of the linear regression model are estimated via the simple linear least square method, before they are fed into a nonlinear optimization problem of a much reduced dimension. It is discovered that the right formulation of the optimization criterion depends on the input-output data, and can be expressed in terms of the singular value decomposition of the data matrix. It is also found that the estimated physical parameters can be fed back to improve the parameters of the linear regression model. This improvement is a consequence of exploiting the structural information of the system contained in the grey-box model, and thus overfitting to the limited training data can be avoided. Numerical examples are presented to demonstrate the effectiveness of the approach.</p>