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I am having a question about the following problem that I am wondering about for quite some time. Let's assume I am doing a regression with the dependent variable weight. My independent variable would be height and sex. I have normalized the design matrix and the DV to obtain standardized regressors (so my variable coding sex is not 0/1 anymore). In cases of continuous predictors I would check for correlations in the design matrix to assess multicollinearity. In my understanding it does not really make sense to correlate sex with height (because sex can only take two value in my example). However, they are still highly dependent upon one another since males are also likely taller. Does this affect my interpretation of regression weights? If it does, does multicollinearity only tends to make p values greater since variance increases or is it also possible to decrease them?

Any thoughts on that would be appreciated!

Laurie

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  • $\begingroup$ Normalizing and standardizing have distinct meanings. You normalize something to be in a certain range (e.g. from 0 to 1), while you standardize something to have a certain mean and variance. $\endgroup$
    – Frans Rodenburg
    Commented Mar 13, 2020 at 18:24

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Multicollinearity is never a problem; it is just a description of the state of the world. In your case there is multicollinearity, but that is why you added both sex and height to your model. You wanted to compare the weight of comparable men and women, that is, men and women of the same height. Otherwise, part of the difference in weight that you found between the genders is not due to gender but due to a difference in height. So, yes multicolinearity does influence the interpretation of the coefficients, but in a desirable way. It also influences the p-value (makes them larger). We may not like that (who likes to loose information?), but it does accurately represent the amount of information present in your data. So I would not consider that a problem.

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    $\begingroup$ Thanks,that make a lot of sense! However, is my assupmtion correct that including two correlated regressors always increase their p values due to higher variance or is it theoretically possible that one predictor is not significant at all anymore and ( by exlaining noise variance in the DV) decreases the p value of the other, correlated regressor? $\endgroup$
    – Laurie
    Commented Mar 12, 2020 at 11:55

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