Problems of Tutorial 10 1. Consider a data set consisting of 1 response variable (Y) and 4 predictor variables (X1, X2, X3 and X4) with n=40. The following table lists all possible regression models with their corresponding SSE: X’s SSE none 608319 23 231561 1 247407 24 37513 2 234399 34 28804 3 594533 123 98327 4 38863 124 36475 12 106805 134 27554 13 226454 234 28279 14 36685 1234 27524 a). List all the best p-variable models for p=0,1,2,3,4 with their corresponding SSE. b). Compute for all the models in a). c). Consider the Forward Selection Procedure using F-test. If the F-test of a (p+1)-variable model versus a p-variable model is larger than a predetermined F- value Fin , the variable is introduced into the model. We then consider if we can introduce a new variable. If yes, we repeat the process; otherwise, we stop the procedure. Use this procedure to find the best model using Fin=1.2. State each step clearly. d). Test if the best model obtained in c) is adequate to describe the response variable Y, compared to the Full model, using . 2/27/2019 ST3131, Tutorial 10

Download the “Data for Exercise 4. 12-4. 14” from the class website Download the “Data for Exercise 4.12-4.14” from the class website. The data consist of 1 response variable and 6 predictor variables. Use the Forward Selection Procedure to build the best model, using 1 as the cutoff-value for the t-test. Write down each step clearly. Consider the same data set as that of Problem 2. Use the Backward Elimination Procedure to build the best model, using 1 as the cutoff-value for the t-test. Write down each step clearly. Check if the resulting models from Problems 2 and 3 are the same. If not, do your best to explain why, using some graphs if needed. 2/27/2019 ST3131, Tutorial 10