# Solved – A good book for regression analysis for pure mathematicians

I am looking for a good book for regression that is mainly focused on mathematical stuff instead of applied parts. Basically, I want a book that contains all the proofs and mathematical descriptions related to regression analysis in a purely mathematical way.
I looked for recommendations given for other related quarries but I couldn't find any good book dedicated to regression in a pure mathematical way, I mean contains all the proofs and mathematical relations between different concepts.

These are some topics I am mainly interested in :

• Simple Linear Regression (Review estimation)
• Test of the parameters
• Validation of the model and its assumptions ($$R^2$$ value, test of the model,
residual analysis)
• Multivariate Normal and related results
• Multiple Linear Regression
• Estimation of the parameters
• Projection revisited
• Tests for the parameters
• Validation of the model and its assumptions ($$R^2$$, adjusted-$$R^2$$, test of the
model, residual analysis)
• Variable selection (forward, backward, AIC)
• Multicollinearity (Ridge-regression)

Note: I know it might be possible that a single book does not cover all topics in detail but I am fine with reading a different book for different topics.

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