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This article does not capture what is actually wrong with the regression. First, it's not necessarily wrong to fit a linear regression to data that might not b
by spekcular 6y ago
This article does not capture what is actually wrong with the regression.
First, it's not necessarily wrong to fit a linear regression to data that might not be from a linear model, or that you know to be nonlinear. The data could be linear enough in the region of interest for the line to nonetheless be useful, for example. Sure, you need an underlying linear process if you want certain theorems and guarantees to apply. But with any data set, linear or not, regression still gives the best linear approximation to the conditional expectation function.
Second, the following paragraph seems to imply that small correlations are the same as no correlation, and the reason the regression is problematic is that the correlation is small:
> How does that fit look to you? I don’t have access to the original dataset, so I can’t check it, but I’m guessing that the correlation there is somewhere around 0.1 or 0.2 – also known as “no correlation”.
But small correlations, if they actually exist, can sometimes be of great practical relevance. So that's not it either.
The actual problem is that the correlation isn't statistically significant – there isn't enough evidence to conclude that the observed (small) correlation actually exists, as opposed to being the result of random noise in the data. And indeed, as some other comments here point out, you can get similar graphs by fitting lines to randomly simulated fake data.
(If you prefer a Bayesian gloss: the data isn't informative enough to move you off any reasonable prior with most of its mass around zero. Same principle.)
- fractionalhare 6y ago> First, it's not necessarily wrong to fit a linear regression to data that might not be from a linear model, or that you know to be nonlinear. The data could be linear enough in the region of interest for the line to nonetheless be useful, for example. Yes, very good point! Likewise regression is not robust to log transformations, but we still use log transformations (depending on the data) because we may be able to tolerate some loss of information. If the nonlinear correlation is bounded below some tolerable amount it's okay to use the linear relationship on its own.
- gbrown 6y agoWhat do you mean it’s not robust to log transformations? A log transformation changes the inference to be about the conditional geometric mean, certainly (the log of an average of x is not equal to the average of a log(x)), but this is often quite sensible.
- khr 6y agoAgreed. I was curious enough to run the model myself so I used a tool to extract the data. The slope estimate (b=17.24) is not significantly different from zero, p=.437. The data are here: https://pastebin.com/HhWTKZRb https://pastebin.com/HhWTKZRb
- SubiculumCode 6y agoThe problem is that the author is essentially claiming that running the regression for data not passing his eyeball test is, in itself, a misuse of regression...which is nonsense.
- gleenn 6y agoI'm not sure I understand your point. Did you actually look at the regression line through the data? It looks crazy off. I'm not a statistician but that line looks like it doesn't represent that data very well at all. People area also saying nuanced comments above but the underlying fact seems to be that this is not a good use of linear regression, and there is no strong correlation between the two axes.
- SubiculumCode 6y agoWithout access to the residuals, I'd still venture to guess that the assumptions of the regression are not severely violated in this data set. When this regression is conducted, the null hypothesis is not rejected (regression slope not significantly different than zero). If someone is somehow arguing this regression rejects the null hypothesis, then they would be incorrect. But there is nothing wrong with using regression here. Its kind of the whole point. This is basic regression statistics 101. Error bands on the regression slope would help people understand the uncertainty of the apparent slope.
- deleted 6y ago[deleted]
- gowld 6y ago
- gweinberg 6y agoThe way I'd say it is that the uncertainty of the value is large compared to the value itself. Just thinking about the causal mechanisms, drinking (binge or not) with other people could put you at risk if any of the other drunks are infected. But drinking alone might help protect you from covid, since it is a way to avoid other people.
- s1artibartfast 6y agoFurthermore, even if the fit is statistically significant, that doesn't mean is it causal.