I watched several videos on linear regression, mainly from Khan Academy.
As I have no background in statistics, I thought this was a good way to get an idea of the topic. However I'm currently writing a bachelor thesis on Structural Equation Modeling and I want to get a deeper understanding of Regression Analysis.
The Book should roughly include these topics:
- linear least squares regression
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variance, covariance
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regression coefficient
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coefficient of determination
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residual analysis (esp. leverage effect)
- multiple regression
I especially enjoyed the videos on khan academy, of the proof of minimizing the squared error to the regression line or illustrations like this one from Wikipedia:
I don't like it when books only present a formula and some common rules etc. without any further explanation of these.
F.e. Residuals should be normally distributed.
However I'm also not comfortable with strictly mathematical books, so I'm searching for something in between. A plus would be example code in R, but definitely not a must have.
Best Answer
I suggest John Fox's "Applied Regression Analysis and Generalized Linear Models" and its companion text "An R Companion to Applied Regression" for one text on regression. James and Hastie's text is introducing regression to develop ideas for statistical learning. Faraway's text has many insights, but is terse. Gelman's book is also nice, but not my suggestion for an introduction to regression. I suggest Fox's text because it is relatively clear, introductory but covers many topics in depth, and has an R companion.