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I employed a multiple regression model by applying a backwards selection method of model selection to examine the influence of three explanatory variables their interactions in determining oxygen consumption by fish and determine best equation for that. However, I had multicollinearity problem. I centered my values but the problem is still there. I am not sure that if I have to remove one or more independent variables to cope with this issue or not, if backwards selection method do it automatically because I see that this method remove some variable and introduce one model at the end!! (I am not sure if I have to completely remove those variables and run regression again or not! instead backwards method removes them per se)

One of my indepedent variables has been excluded from the model!! X3 for example. But its interaction with other variables are still there for example backwards method gave me this model: X1+X2+X1X3+X2X3

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  • $\begingroup$ I am not sure if I have to completely remove those variables and run regression again or not! instead backwards method removes them per se $\endgroup$ – Non Apr 2 '17 at 22:06
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    $\begingroup$ Make sure your final model did not include a cross product variable without having included the two main effects. That can happen sometimes in stepwise but is not readily interpretable. $\endgroup$ – David Lane Apr 2 '17 at 22:08
  • $\begingroup$ one of my indepedent variables has been excluded from the model!! X3 fro exmple. But its interaction with other variables are still there for example backwards method gave me this model: X1+X2+X1X3+X2X3 $\endgroup$ – Non Apr 2 '17 at 22:17
  • $\begingroup$ You should add X3 even if it is not significant. X1X3 is not the interaction, it is a combination of main effects and interaction. It is only the interaction when both X1 and X3 are partialled out. $\endgroup$ – David Lane Apr 2 '17 at 23:06
  • $\begingroup$ Sorry but I did not get it! How should I add X3 when collinearity exist. $\endgroup$ – Non Apr 2 '17 at 23:40

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