11.21 Comparison of prediction intervals. Refer to the previous exercise. Another way to compare these two models is in terms of prediction. The Ohio State University has Admit = 56, GradRate = 59, InCostAid = 12,103, and OutCostAid = 28,603. Use statistical software to construct.

  1. (a) a 95% prediction interval based on the model with all p = 4 predictors.

  2. (b) a 95% prediction interval based on the model using just InCostAid.

  3. (c) Compare the two intervals. Do the two models give similar predictions? Which provides a more narrow prediction interval?