1. Problems of Tutorial 9
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. 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.