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November 3rd, 2014, 06:21 AM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 582 Thanks: 81  Is This Correlation Possible?
I made a regression equation with three independent variables and one dependent variable. Two of the independent variables had a positive coefficient (positive correlation) with the dependent variable and one independent variable had a negative coefficient. Then when I made a regression equation with that independent variable as the only independent variable, it had a positive coefficient with the same dependent variable. Is it possible for two variables to have a positive correlation on their own but appear to have a negative correlation when more independent variables are added in?

November 3rd, 2014, 07:53 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,151 Thanks: 2390 Math Focus: Mainly analysis and algebra 
I'm reasonably sure that the answer is 'yes'. I think you might be talking about Simpson's paradox.
Last edited by v8archie; November 3rd, 2014 at 07:57 AM. 
November 3rd, 2014, 01:08 PM  #3  
Senior Member Joined: Oct 2013 From: New York, USA Posts: 582 Thanks: 81  Quote:
Equation 1 used every variable and: a and x had a positive correlation b and x had a negative correlation c and x had a positive correlation Equation 2 had only b and x and in that case b and x had a positive correlation. Is that possible?  
November 3rd, 2014, 02:15 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,151 Thanks: 2390 Math Focus: Mainly analysis and algebra 
Maybe the same amount of variables each time, butthe different environments equate to other variables having differing values, perhaps uncontrolled, or perhaps controlled unintentionally.

June 9th, 2017, 06:20 PM  #5  
Senior Member Joined: Oct 2013 From: New York, USA Posts: 582 Thanks: 81  Quote:
 

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