st: rsquare Command

["Carl Mastropaolo" <accuscience@comcast.net>]

I have a perplexing issue with the rsquare command.  This command is used to
return the R^2 value, Mallow's C statistic and other values for all possible
regressions between a single dependent variable and a set of independent
variables.

Following is command line and output for showing rsquare information for the
simple regression of how  y1  as dependent upon  x19.  Note that for the
simple model of  y1  regressed against  x19, the R^2 value is  .0596:

. rsquare y1 x19

Regression models for dependent variable : y1

R-squared  Mallows' C           SEE           MSE      models with 1
variable
0.0596           2.00       3.128e+12    1.422e+11     x19



Following is command line and output for rsquare showing regressions of how
y1  is dependent upon  x18 and x19.  Note, again, that for the simple model
of  y1  regressed against  x19, the R^2 value is  .0596:

. rsquare y1 x18 x19

Regression models for dependent variable : y1

R-squared  Mallows' C           SEE           MSE      models with 1
variable
0.0071           2.28       3.302e+12    1.501e+11     x18
0.0596           1.10       3.128e+12    1.422e+11     x19
R-squared  Mallow's C           SEE           MSE      models with 2
variables
0.0641           3.00       3.113e+12    1.482e+11     x18 x19


Now I add a third indy variable, x17.  Why should the R^2 value for the
simple model  y1  vs  X19 now change to  .0624 from the original value of 
.0596?


. rsquare y1 x17 x18 x19

Regression models for dependent variable : y1

R-squared  Mallows' C           SEE           MSE      models with 1
variable
0.0001           1.42       3.281e+12    1.562e+11     x17
0.0086           1.25       3.253e+12    1.549e+11     x18
0.0624           0.15       3.076e+12    1.465e+11     x19
R-squared  Mallow's C           SEE           MSE      models with 2
variables
0.0088           3.25       3.252e+12    1.626e+11     x17 x18
0.0636           2.13       3.072e+12    1.536e+11     x17 x19
0.0682           2.03       3.057e+12    1.529e+11     x18 x19
R-squared  Mallow's C           SEE           MSE      models with 3
variables
0.0698           4.00       3.052e+12    1.606e+11     x17 x18 x19

Thanx
Carl

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