I'm reading Statistical Rethinking by Richard Mclreath and I am bit confused about the subjects in chapter 5. The book itself is about bayesian analysis. This chapter specifically point out to pitfalls of bayesian regression models.

One of the exercises in this chapter is creating two bi-variate regression models and one multi-variate regression. The models are meant to be an example of masked relationships. There isn't any strong relationship between the predictor and the predicted variable in the bi-variate models, but their relationships with the dependent variable are actually stronger on the multivariate model (Seen by holding one predictor to its mean and plotting the other one against the dependent var). Could someone dumb it down for me? How is that possible?

Now about spurious relationships, If I understand correctly then it is when two predictors are correlated with the dependent variable independently , but when creating a multivariate model, one of the predictors correlation with dependent variable greatly reduced. Does it mean that it must be a case of multicollinearity ? Also, he warned to be aware of multicollinearity in some models but then he claims the models with multicollinearity actually produce predictions as good (if not better) as the non-multicollinearity model. So my question is why should I care to check about multicollinearity at all?

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    $\begingroup$ For the first issue, what does the author say are the conditions under which this "masking" occurs ? For the 2nd, spurious associations can occur in many different ways. What you've described sounds like suppression, not spurious associations, so again you will need to be specific. $\endgroup$ – Robert Long Aug 8 '20 at 4:30
  • $\begingroup$ Hi Robert! It'll be too long for a reply so if its not too much to ask, see here: rpubs.com/jmgirard/sr5 , Questions 5H1, 5H2 . At the end there's an explanation : but these effects get cancelled out in the bivariate regressions because territory area and group size are positively related. Which I can't seem to grasp.. $\endgroup$ – Yarden Gur Aug 8 '20 at 9:04
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    $\begingroup$ Please don't send links. Please put the necessary info into your question by editing it. $\endgroup$ – Robert Long Aug 8 '20 at 9:32

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