Regression analyses constitutes an important part of the statistical inference and has great applications in many areas. In some applications, we strongly believe that the regression function changes monotonically with some or all of the predictor variables in a region of interest. Deriving analyses under such constraints will be an enormous task. In this work, the restricted prediction interval for the mean of the regression function is constructed when two predictors are present. I use a modified likelihood ratio test (LRT) to construct prediction intervals.