What is function of 'tolerance criterion' in regression computation

[ssuave]

Hi folks,
Lets say, I am computing regression of some independent variables (say 12) against one dependent variable, to see which of these 12 variables are actually the main predictors and which can be removed from the model.
I use 'Backward Elimination' Method. I see the 'tolerance criterion' involved in there, described here also:
http://publib.boulder.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Flinear_regression_methods.htm

I tried to read about it and found it that its something related the problem of Multicollinearity. Okay, but how?
What if two independent variables are linear to each other-that means its hard to find which one of those is actually responsible for predicting the dependent variable and it is problem of multicoll.?
Then how this tolerance crierion gets in and becomes reason of removal of some variables/predictors?
Plz explain.

Regards!

[David Marso]

Scroll to the REGRESSION algorithms and review Sweep operations and "Methods for Variable Entry and Removal" .  Ponder the tragic consequences of division by zero and how that might relate to multicollinearity.
ftp://public.dhe.ibm.com/software/analytics/spss/documentation/statistics/20.0/en/client/Manuals/IBM_SPSS_Statistics_Algorithms.pdf

ssuave wrote

Hi folks,
Lets say, I am computing regression of some independent variables (say 12) against one dependent variable, to see which of these 12 variables are actually the main predictors and which can be removed from the model.
I use 'Backward Elimination' Method. I see the 'tolerance criterion' involved in there, described here also:
http://publib.boulder.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Flinear_regression_methods.htm

I tried to read about it and found it that its something related the problem of Multicollinearity. Okay, but how?
What if two independent variables are linear to each other-that means its hard to find which one of those is actually responsible for predicting the dependent variable and it is problem of multicoll.?
Then how this tolerance crierion gets in and becomes reason of removal of some variables/predictors?
Plz explain.

Regards!