This preview shows pages 1–2. Sign up to view the full content.
EXST 7015  Statistical Inference II, Fall 2011
Lab 6: Multiple Linear Regression_Variable diagnostics
OBJECTIVES
In multiple regression however, a number of variables can be involved and regressed on one
another (model: Y =
β
0
+
β
1
X1+
β
2
X2+ · · · +
β
p
XP +
ε
) .The overall test of hypothesis of
multiple linear regression is H
0
:
β
1
=
β
2
= · · ·=
β
p
=0 v.s. H
1
: at least one
β
≠
0.
Rejection of H
0
implies that at least one of the regressors, X1, X2, . . . , Xp, contributes significantly to the model.
In the lab5, the problem of multicollinearity caused by highly correlated variables was
introduced by indentify the diagnostic statistics of sequential parameter estimates, simple
correlation, variance inflation factor (VIF) and condition index. In this lab, an extreme case of
muticolinearlity will be presented to help you fully understand those statistics.
Since there are more than one independent variables in the model of multiple linear regression,
many of you have raised the question that which variables are more important than the others. By
using partial SS Ftest (Type II, III, IV) and ttest of regression coefficients, the larger the F
value or tvalue (the smaller the Pvalue), the more significant of the variable to the model as you
might be aware in lab5. In addition, standardized regression coefficients and partial R^2 will be
discussed to help you evaluate the relative importance of individual variables in the model in this
lab.
Some of you might realize that the absolute value of regression coefficient is not a good
predictor of relative importance of the variables. Why it happens is that, most often, the variables
are not on the same scale or are of arbitrary scale, which leads to unmeaningful slope (Y units
per X units). In such cases, the variables could be standardized with a mean=0 and variance=1.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.
 Fall '08
 Wang,J

Click to edit the document details