Since many functions which express physical relationships are of a disjointed or disassociated nature, spline regression procedures are often carried out on data with random components. However, the problem of determining the number of knots and their locations has not been satisfactorily solved. Estimators using the usual least squares approach are not theoretically tractable. Furthermore, Jupp'slethargyproperty which is intrinsic to free knot spline problems affects the stable, and effective, computation of optimal knots. A new approach using the Laplace transform is suggested. The data can be used to estimate the Laplace Transform of the regression function, and then several methods are available to estimate the number of knots and their locations. An approach which leads to an explicit expression for the position of the knot in a two-phase linear regression is presented. No assumptions about the error structure are needed to apply this new procedure. However, in the case of normally distributed erro...