Constrained inference in linear regression

Regression analysis is probably one of the most used statistical techniques. We consider the case when the regression function is monotonically changing with some or all of the predictors in a region of interest. Restricted confidence interval for the mean of the regression function is constructed when two predictors are present. Earlier analyses would allow an investigator either to ignore monotonicity altogether or to consider only one predictor at a time but not both simultaneously. The methodologies developed are applied on a real data set to study the effects of patients age and infection risk on their length of stay in US hospitals.