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My Ph.D. training is mostly in applied mathematics. I'm interested in learning materials of linear statistical models, especially their applications in data science or statistical machine learning. Is there a good reference book to start with?

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The Elements of Statistical Learning is probably a very good starting point if you are going to be working in machine learning and/or data science.

Friedman, J., Hastie, T., & Tibshirani, R. (2001). The elements of statistical learning (Vol. 1, No. 10). New York: Springer series in statistics.

This is also available free online, and has many further references.

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