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?