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I've read that univariate analysis is a huge part of EDA, pretty much everywhere. What I understand of univariate analysis basically comes down to using Seaborn pairplot and correlation matrices and heatmaps.

However, today I read about "Simpson's Paradox" on a kaggle kernel, then in a Britannica article. It was quite fascinating and seemed to render useless what I believed to be commonly accepted best practices.

I then read that one way to combat this sort of misleading analysis is through partial residual plots:

$$\text{Residuals} + \beta_iX_i \text{ vs } X_i$$

What I can't figure out is how this formula controls for multiple independent variables in an intuitive way. What's the explanation for how this works?

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