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I understand this is a broad question, but I have been looking all over and can't seem to find a straight answer.

Linear regression is based on a few assumptions, and you should always check to see if they are satisfied, but what if they aren't? Does that automatically mean that any results are invalid? Furthermore, some assumptions aren't necessarily yes or no questions. For example multicollinearity - it seems like it is okay if there is a little bit, but how much is too much? Especially in a business setting, what would you do if an assumption is not true or cannot be verified?

Hunter Swag
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Each assumption has different ways of being addressed.

Multicollinearity in real data is essentially a numerical issue : numbers become to small and your matrix inverse can't be computed - until you increase precision enough or take stock that two variables you are using are essentially the same and you either discard one or average between them.

Heteroskedasticity is address with an appropriate estimator or a separate model for variance.

Correlation in the residuals is usually the most problematic as it points to miss specification of your model - which means you'll have to go out there and get some more data or figure out an instrument to run IV.

Three Diag
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  • So if any of the assumptions are not true are results of the model automatically dismissed? – Hunter Swag Oct 27 '20 at 20:27
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    Most assumptions are never true. What you need to be concerned about instead are the consequences of potential (or apparent) departures from those assumptions. – whuber Oct 27 '20 at 20:30
  • @whuber can you point me to any resources or articles that address this type of thing? – Hunter Swag Oct 27 '20 at 20:35
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    This goes under the rubric of [regression diagnostics](https://stats.stackexchange.com/questions/32600). Any regression textbook written in the last 40 years will have extensive material about it. – whuber Oct 27 '20 at 20:38