1. 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

2. Download the “Data for Exercise 4. 12-4. 14” from the class website
Download the “Data for Exercise ” 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