4/28/2009
Chapter 11: Remedial Measures
· What if we have Unequal Error Variances
(Heteroskedasticity)? --> Weighted Least
Squares
o
Model
o
Weighted
least squares criterion
o
Process:
1.
Fit
regression model; analyze residuals
2.
Estimate
variance function or standard deviation function
3.
Use
fitted values from estimated variance/SD function to obtain weights, 
4.
Estimate
regression coefficients using these weights: 
o
Caution:
R^2 no longer has clear-cut meaning!
o
Example:
BP-Ch11.sas
· What if we have Multicollinearity?
--> Ridge Regression
o
Biased
estimation: Allow estimators to be biased; pick the estimator that minimizes
mean squared error.
o
Example:
bodyfat-Ch11.sas
· What if we have Influential Cases?
--> Robust Regression
o
LAD
regression
o
LMS
regression
o
IRLS
regression
1.
WLS
with weight functions that dampen the influence of outliers
2.
Process:
1.
Choose
weight function
2.
Obtain
starting weights
3.
Use
starting weights with WLS and obtain residuals
4.
Use
these residuals to obtain revised weights
5.
Iterate
until covergence
3.
Example:
mathprof-Ch11.sas