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?