
Practical and professional, Wooldridge's INTRODUCTORY ECONOMETRICS: A MODERN APPROACH, 4e bridges the gap between how undergraduate econometrics has traditionally been taught and how empirical researchers actually think about and apply econometric methods. The text's unique approach reflects how econometric instruction has evolved from simply describing a set of abstract recipes to showing how econometrics can be used to empirically study questions across a variety of disciplines. The systematic approach, where assumptions are introduced only as they are needed to obtain a certain result, makes the material easier for students, and leads to better econometric practice. Unlike traditional texts, INTRODUCTORY ECONOMETRICS is organized around the type of data being analyzed -- an approach that simplifies the exposition and allows a more careful discussion of assumptions. Packed with relevant applications and a wealth of interesting data sets, the text emphasizes examples that have implications for policy or provide evidence for or against economic theories. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
I don't do statistics in my day job, but having a solid foundation in the math and the theory and the proofs really had a profound impact on how I approach problem solving generally and root cause analysis specifically (just thinking about e.g. model specification and how you do it is a good exercise). It's still on my bookshelf and I'll pull it out and do a problem set from time to time just to stay sharp - even though, again, I don't do this for my job. Maybe, one day, I'll get a job with a baseball team or something. Understanding heteroskedasticity for example is one of those things where once you "get it", it really opens your eyes to a lot of things and you can't "unsee" it.
PS there are packages in R nowadays but back in the day we used STATA.
PPS if people don't like Wooldridge, what else would you recommend?
Edit: I know you said "Your choices needn't be only math books" but this is a statistics textbook, so it probably doesn't count as "math".
Or are you really curious about how undergraduates are taught, despite the distinction between the undergraduate curriculum and the professional researcher's view? My introductory economics course used Mankiw's textbook. If I remember correctly, it didn't even use calculus. Imagine a university physics course doing that. I think of that more like high school level. Come to think of it, AP Economics probably would have let me skip that class.
Looking over at my bookshelf, I see Wooldridge's "Introductory Econometrics". That's a pretty good one, with plenty of empirical work. I can't spot my macroeconomics textbook, but I remember it evaluating each model by how consistent its predictions were with observed behavior.
... it occurs to me that someone ought to update Wooldridge's exercises for R-language or Python ...
Varian, 'Intermediate Microeconomics' Luenberger, 'Investment Science' Wooldridge, 'Introductory Econometrics'
for the undergraduate background and then at the graduate level Jehle and Renyi for microeconomics, Duffie for asset pricing theory, Tirole for corporate finance and Campbell, Lo and Macinlay for econometrics.
https://www.amazon.com/Introductory-Econometrics-Modern-Appr...
For more "intuition about working with data, especially if you're a visual person," Howard Wainer's books are wonderful; one example is "Graphic Discovery: A Trout in the Milk and Other Visual Adventures." They're non-technical, short chapters, discussions of different data sets.
Bill Cleveland's "Visualizing Data" and "Elements of Graphing Data" cover the same material -- graphing data -- at a more technical level. I don't know Cleveland's books would help with the issues you asked about, but... they are amazing books and if you're interested in the subject at all I can't recommend them highly enough.
I don't have any free recommendations, unfortunately.
Introductory Econometrics by Woolridge is a pretty readable econometrics text you should also check out, since it'll be especially applicable for social science: http://www.amazon.com/Introductory-Econometrics-Approach-App...