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I am using bootstrapping to estimate the statistics and CIs of coefficients of linear regression.

As far as I understand, bootstrap is used for estimate the statistics of estimates, here the estimates of the coefficients in linear regression.

I have heard that bootstrap is a solution to bad assumptions in linear regression in a slide "One Solution to Bad Assumptions". There are several assumptions in linear regression, such as independence between observations, additivity (no multicollinearity), linearity, normality, homoscedasticity, .... Is bootstrap a solution to some bad assumptions in linear regression, and if yes, how?

Thanks.

Tim
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    Could you post actual quote? The link holds raw HTML that is rather hard to read directly. – Tim May 11 '20 at 17:26
  • To open it in presentation mode, first download it, and then open it in a browser. It says in a way that I understand to be "bootstrap is a solution to bad assumptions in linear regression". I am not sure what it means. It is better to read what it says, in case that I am mistaken. – Tim May 11 '20 at 17:29
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    Please put the relevant information into the body of your question, otherwise you simply risk that people would just ignore the unreadable file and don't bother with downloading it. Moreover, we want this site to be a repository of knowledge and if the link dies, your question would become contextless. – Tim May 11 '20 at 17:39
  • As I mentioned, the slides present the claim in a way which is difficult for me to quote verbally. I have done my best to describe here what it tries to present. – Tim May 11 '20 at 17:42

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Bootstrapping can't really save you from bad data. If your observations aren't independent, then they aren't independent. If they're highly collinear, then they're highly collinear. If the relationship is non-linear and you're estimating it to be linear, then you'll have issues. And so forth. Bootstrapping (at least what I've used it for) is for things like complicated standard error calculation or dealing with small sample size issues (although I tend to be skeptical when used for small sample size). I haven't used it for heteroskedasticity, but it seems like that's an option (see: Is bootstrapping standard errors and confidence intervals appropriate in regressions where homoscedasticity assumption is violated?).

norvia
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