In order to combine prior and sample information in the estimation of regression coefficients, when the prior knowledge about the parameter space exists in the form of inequality constraints, the regression model is respecified as a quadratic programming problem. The sampling properties of the general restricted estimator are discussed and the inequality restricted formulation is extended to cover a set of regression equations. As an example of the applicability of the specification, the estimation procedure is applied to the problem of obtaining estimates of the transitional probabilities of a finite Markov Process from aggregated outcome data.