Optimum exponential regression with one nonlinear term

摘要

A method is suggested for estimating regression parameters for a model E(Y = a + bX + ce-∂t, where observations on Y, X and t are given. This model has been extensively used in economics for relating optimum output of a production process with the available labor and services. This method is optimum in the sense it involves minimizing the error sum of squares for the linear regression of Y on X and e-∂t over the range ∂>0. The limits as ∂ → 0 and ∂ → ∞ are obtained and the computational procedure is discussed.