I came here to say that, but in a slightly different way:

True:

> no discussion of how one might interpret this model, what its assumptions are, and how to assess validity or fit?

Quoting OP from the comments in his blog:

> Hey Victor, thanks for reading! You’re absolutely right, I should have taken some time to talk about the assumptions of linear regression. I tried to mention them in passing, but I’ll try to be more explicit next time. I should have brought up the pearson correlation coefficient. I tried to write this from a more machine learning point of view, not as much statistics.

Either way it was a decently written post and would read more in the future (though I would like to see more statistics side of things rather than just me thinking Alex here is waving his hands saying 'you see nothing!' when we look at the mathematical assumptions / 'pure' statistics).

In other thoughts:

I'm currently in the process of writing a blog series on the analytics of Firearm projectiles (What ammo is most accurate from a Ruger American 308 Win.). Seeing other statistical posts like this help me figure out how to make mine better. So thanks Alex!

would you mind sharing the blog post when you're finished? sounds very interesting!

Of course.

My biggest inspiration (other than taking a perfect shot at a whitetail deer and him just dropping dead) was a good PDF about shotGroups over on the CRAN[1]. It is a little dry and statistically heavy (meaning you need to have some statistical background to make sense of it), but well enough detailed for the info that triggered me to pursue this pet project.

I would love to write it at a level where if a person with no statistical background would be able to read through it and be able to understand it "enough". (Which requires a lot of rewriting on my part to make sure I'm also not boring a person with statistics background to death too explaining what Standard Deviation is :P)

[1] https://cran.r-project.org/web/packages/shotGroups/vignettes...

We wrote a couple docs about regression. I'd be curious to get folks' feedback.

Guide itself: http://docs.statwing.com/user-friendly-guide-to-regression/

Perhaps more interestingly to a lot of folks in this crowd, a guide to interpreting residuals: http://docs.statwing.com/interpreting-residual-plots-to-impr...

One valid critique is that the approach we describe is not super rigorous, there's more "add a variable and see if it sticks" and "explore a bunch of bivariate relationships to decide what to include" then you'd want to do if you were publishing a paper on your findings. To our minds, though, this approach is more realistic for the use cases we're more concerned about, like analyzing an ad hoc survey. You can always consider your results to be exploratory and then validate later. (Note that these docs occasionally refer to Statwing, our product, but really could be used for any tool).

Criticism is welcome.

Just as two quick comments, confidence intervals != prediction intervals. One gives a range around a true mean value, the other gives a range around where the variable may actually fall (prediction intervals are bigger).

You may also want to mention adjusted R^2 as a measure of quality of the model. I've never heard of AICR before, the standard metrics for quality of the model are AIC/BIC (and sometimes Mallus Cp).

Edit: fixed sloppy wording about confidence interval.

The prediction interval thing was sloppy, good catch.

The r^2 and AICR comments reflect the fact that these docs were built around Statwing's regression capabilities, which default to m-estimation instead of OLS. There's no adjusted r^2 for that, which I agree is a better measure when available, and it uses AICR, where the R stands for "robust". But still a good catch, since I didn't caveat ahead of time that we were only talking about robust methods (and we don't note it in the docs).

Much appreciated.

OLS is an M-estimator.

AIC depends on residual variation just like R^2, so I guess some people might be inclined to call it AIC_R to make that clear. Also, it's Mallows' C_p :-)

Thanks for the clarification about Mallow's C_p, I always get the name messed up for some reason.

Hey, just FYI, your posts are getting killed for some weird reason. See:

http://imgur.com/FmBkqgo

Thank you, I'm confused as to why this is happening.

Do you have a doc on whether the data are supposed to be Normally Distributed, and if they are then how to measure said Normality? I'd really appreciate such a doc if you do.

Sorry, we don't. My understanding, though, is that the typical statistical measures of normality (e.g., Kolmogorov–Smirnov) aren't really that effective, and the best way to assess normality is a visual inspection of a Q-Q plot. I don't have a specific source for this assertion, it's my memory from having researched this stuff a few years ago.