Date:         Wed, 21 Jul 2010 10:42:38 -0700
Reply-To:     Jon Matthews <jmatthews7101@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Jon Matthews <jmatthews7101@YAHOO.COM>
Subject:      Weighted Least Squares Question in SAS
Content-Type: text/plain; charset=iso-8859-1

Hi, 
 
I am using SAS to create a weighted least squares regression, and I've run into 
a question about the coefficient of determination when using weighted least 
squares regression.
Here is some code I wrote:
data work.temp;
input x y w;
cards;
1 1 1
2 2 1
3 4 1
;
run;
proc reg data=work.temp;
weight w;
model y=x;
run;
quit;
 
Since the weights are all 1, this is the same as unweighted regression and this 
gives me an R-squared of .9643.  Note that in my data, the first two 
observations are perfectly correlated while the third is not.  Now, if I 
re-weight the last observation to place less weight on it since it's not 
perfectly corrected with the others and rerun the weighted least squares 
regression, I get a lower R-squared:
 
 
input x y w;
cards;
1 1 1
2 2 1
3 4 .1
;
run;
proc reg data=work.temp;
weight w;
model y=x;
run;
quit;
 
R-squared now equals .9391.
 
This does not seem intuitive.  Since I'm now underweighting the only 
non-perfectly correlated observation, shouldn't R-squared improve or am I 
missing something?
 
Thanks for any insight.