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I want to be self taught data scientist. After watching a lot of YouTube, I found out that learning statistics at the very beginning is the best approach (although debatable). I wanted to know what are the best free resources to learn statistics i.e. books, courses, etc. Also, how long does it take to learn all the skill necessary to be an employable data scientist if I take the self-study approach?
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As a start, I suggest learning the following:
  

  
Statistics:
  
\- probability (distributions, basic manipulations)
  
\- statistical summaries (univariate and bivariate)
  
\- hypothesis testing / confidence intervals
  
\- linear regression
  

  
Linear Algebra:
  
\- basic understanding of arranging data in vectors and matrices
  
\- operators (matrix multiplication, ...)
  

  
Calculus:
  
\- limits
  
\- basic differentiation and integration (at least of polynomials)
  

  
Information Theory (Discrete):
  
\- entropy, joint entropy, conditional entropy, mutual information
  

  

  
For statistics, I highly recommend:
  

  
"Practice of Business Statistics"
  
by David S. Moore, George P. McCabe, William M. Duckworth and Stanley L. Sclove
  
ISBN-13: 978-0716757238
  

  

  
To learn about machine learning, I recommend both of these:
  

  
"Computer Systems That Learn"
  
by Weiss and Kulikowski
  
ISBN-13: 978-1558600652
  

  
"Data Mining: Practical Machine Learning Tools and Techniques"
  
by Ian H. Witten, Eibe Frank, Mark A. Hall and Christopher J. Pal
  
The 4th edition (2016) has ISBN-13: 978-0128042915, though older editions are fine and likely less expensive.
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Doing a Bachelor's and Master's in Statistics or data science often takes around 5 years, a PhD even longer.

So I would assume some years if you study alone and part time.
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Laerd statistics is a brilliant website that goes through many common statistical tests and how to do them on spss. There is a pay wall to access some content but last time I did it it was only 7 quid a month. Saved me during my masters.
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I'd agree, you have to know some math to do data science. BUT... If you want to get a job, you have to be able to program effectively and have some experience building projects.

You don't have to know everything there is to know to be employed. Focus on the CORE skills
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Go for udemy course,which will come with a good roadmap and no need to worry of an external resources that might lead to distractions sometimes
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I think Dataquest is great!
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>Also, how long does it take to learn all the skill necessary to be an employable data scientist if I take the self-study approach?

There's no easy answer to this, because every position emphasizes statistics to a different extent. I went back to school for a masters in stats a few years after getting a masters in psych, and have interviewed for some positions where I could've gotten away with using what I learned in the pysch research methods classes (it was a two-class sequence). And others that asked theory questions my stats program did not cover.

If I were you, I'd start with the low hanging fruit. Work through a textbook like Statistics for the Social Sciences to get a working knowledge of how statistics are *used,* maybe an intro book on data mining, then focus on connecting what you're learning to DS tools. After that, circle back around for a more mathematical treatment of statistics, to get a better sense of *how* the things you're using actually work. This is where you're going to start needing calculus and (maybe) linear algebra. Most universities offer a "introduction to statistics with calculus" type class, so I'd look for some syllabi for direction and reference material. If you want to dig deeper into the *why*, you're entering the territory where people take calc, linear algebra, and analysis prereqs and go to grad for stats. I personally think that learning stats theory in a non-formal context would be a nightmare.

Start sending out applications to DS/DA related positions as you learn. You're going to be underqualified for many positions, but you just need to get your foot in door somewhere so that you can start working with data as you learn. Having tangible experience on your resume is going to be critical given that your stats background will be a work in progress for a looooong time.
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Many people are giving a theory-first answer. f you are more interested in applying statistical analysis, then an alternative approach would be the following:  

- understand sampling theory. What the goal of statistical inference is
- learn how to fit linear models, common errors, and model diagnostics. Its relationship to t-tests etc.
- how to interpret main effects, perform post hoc tests, design contrasts, learn about interactions
- learn about generalized linear models
- learn about the bootstrap
- learn about some of the most commonly used rank statistics like mann-whiteney etc.
- learn how to fit and diagnose ARIMA models
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