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I am analyzing an environmental data set containing one response variable (R) and many explanatory variables.

The explanatory variables are either factors (F1, F2, F3) or continuous variables (V1, V2, V3…).

I wanted to conduct a linear regression in the form lm (R~F1+F2+F3+V1+V2+V3+F1*F2+F2*F3…)

The matrix scatterplot did not show any collinearity issue between my explanatory variable, but from previous analysis (ANOVA) I know that the factors are significantly explaining variation in the continuous variables. (i.e. aov (V1~(F1+F2+F3)^3), all factors significant; (V2~(F1+F2+F3)^3), all factors significant….)

The vif in the linear regression model for each explanatory variable is <3.

So my questions are:

1) If an ANOVA analysis points out a relationship between subsets of explanatory variables are these to be considered collinear?

2) Should then I remove all the continuous variables from the analysis?

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    $\begingroup$ (1) "Significant" says relatively little about amount of the effect. Especially if your data are numerous, ANOVA can declare utterly trivial amounts of collinearity to be "significant." (2) Why would you remove all continuous variables? What would the reason be for losing all that information? $\endgroup$
    – whuber
    Mar 25, 2013 at 13:50
  • $\begingroup$ The effect size in some case is quite relevant (partial eta squared < 0.3-0.5), and it really looks like that factors and continuous variable are changing at the same time. $\endgroup$
    – Gaia
    Mar 25, 2013 at 15:34

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