A NOTE ON AN INPUT CONTROL MODEL OF A PREDICTIVE REGRESSION INTERVAL

A well-known problem of prediction in linear regression models is to f ind a confidence interval for the random value of the dependent variab le when the values of the independent variables are given. Such a situ ation may arise in economic quality control models when the independen t variables are costly inputs and the dependent variable is some measu re of quality or production. In such a circumstance, an important cont rol objective may be to find values for the inputs that will maximize the lower limit of the prediction confidence interval for a fixed budg et, or alternatively, to minimize the cost of the inputs for a fixed l ower limit of the confidence interval. In this paper, we shall show th at global optima can be found using known algorithms. The special case of simple linear regression is discussed and an illustrative example is provided.