For ANCOVA, many textbooks and other resources require, among other assumptions, that covariates be linearly related to the dependent variable, which makes sense. However, many of the same sources require that pairs of covariates should also be linearly related, while saying in a different section that covariates should not be too strongly correlated with one another (e.g., |r|<0.90), otherwise there can be problems with multicollinearity and singularity. Unless I have misunderstood, |r|>0.90 denotes a strong linear relationship. So my question is: Do pairs of covariates need to be linearly related, and if so, what is the implication for the assumption of no multicollinearity and singularity?
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That sounds like a strange assumptions. Can you give a reference/citation? – kjetil b halvorsen Feb 02 '16 at 17:23