My job is starting to have me delve into categories that require things like regression analyses on data sets, essentially I'm being introduced to "Data Science" type material. Coming from a computer science background however, I'm aware of how easy it is to misapply statistics.

My only course on statistics was over a decade ago and it didn't include any of the theoretical underpinnings that actually explained why the formulas worked, which would help me understand when to use method X vs method Y. I'm dreadfully afraid of creating false findings.

I'm looking for teaching resources that would hopefully bridge the gap from "I can do X, Y, or Z" but would give enough math to help me understand when and where to use what. If there's anything like Roger Penrose's "The Road to Reality" for statistics, that would help. Otherwise any suggestions of what a good course plan for self-study would look like would be welcome.

[EDIT] Clarifications:

Having a comp sci background, I know for example that if the problem before me seems like a graph-theoretic problem, I can reach for my copy of "Graph Theory and its Applications" from Gross/Yellen.

Physics isn't my forte, but when I want to leverage the mathematics I do have, I can reach for "The Road to Reality" by Roger Penrose.

And if it's dealing with Data structures, I can check out "The Art of Computer Programming" from Donald Knuth, and for algorithms--although it's a textbook--there's also Cormen's "Introduction to Algorithms," or even Skeina's book "The Algorithm Design Manual." All of these works provide enough theory and proofs to make it pretty clear why these tools work. I'm fishing for items in this same category for Statistics, but judging by the comments, there isn't quite this level of organization and unity in statistics?

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    $\begingroup$ It's hard to tell exactly what you need, because your question doesn't really say the extent of what you need to be able to do. You just give the one example of doing a regression. Without more info, the answer would basically be to buy a statistics textbook and read it. $\endgroup$
    – user507
    May 18, 2020 at 16:25
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    $\begingroup$ I'm not aware of a clear cut such resource. One of the issues is that different methods and methodologies are used in different disciplines. I've thought before about compiling a big "tree" for my students but at the end of the day I don't think it's helpful. I would suggest All of Statistics or Elements of Statistical Learning as good foundational text, but they both somewhat causally assume a lot of mathematical knowledge. Otherwise, look for books on the type of problem you're working on. But statistics is not "unified" in the way physics is. $\endgroup$
    – Nate Bade
    May 18, 2020 at 17:25
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    $\begingroup$ What specific area are you working in? $\endgroup$
    – Nate Bade
    May 18, 2020 at 17:31
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    $\begingroup$ You give examples of what you think of as canonical references for some topics in CS and physics, but these actually seem pretty idiosyncratic. I'm a physicist, and I certainly wouldn't recommend the Penrose book for this purpose. It's a useless book unless you already know physics, and even if you already know physics it's only useful in a certain patchy, weird way. $\endgroup$
    – user507
    May 18, 2020 at 21:24
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    $\begingroup$ It might be better to ask this question over on Cross Validated. If you choose to do so, you can either delete your question here or at least link between both versions of the question. $\endgroup$
    – J W
    May 19, 2020 at 7:06

1 Answer 1


I am a third-year student pursuing a bachelor of science with a major subject as statistics.

Statistics can be categorized into 2 types:

  1. Descriptive Statistics: It is used for summarizing observations etc.

  2. Inferential Statistics: It is used for interpreting the meaning of the descriptive stats.

Firstly, search out which part of statistics is more useful to you, i.e., descriptive or inferential, and then learn the basics. I suggest learning the basics of statistics as without basics there's no use of other theories. For learning, you have two ways: online and offline. For online learnings, You could simply login to Coursera or Khan academy they have simple and good explanations of the topics. For offline, my suggestions on books are based on materials used by students in our college.

Suggested Textbooks for self-study:

  1. Fundamentals of Mathematical Statistics, Sultan Chand & Sons Pvt. Ltd. New Delhi. https://www.academia.edu/31552250/FUNDAMENTALS_OF_MATHEMATICAL_STATISTICS
  2. Statistics, S. Chand and Company Ltd. New Delhi
  3. Mathematical Statistics with Applications, Pearson Education.

I hope this is helpful.

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    $\begingroup$ There's all kinds of inference going on in regression. What makes you think it's descriptive statistics? $\endgroup$
    – Dave
    Sep 29, 2020 at 18:48

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