Which statistics textbooks would explain why linear least squares regression fails when data is heteroskedastic I have recently interviewed for a statistical analysis job and was asked a question about why linear least squares regression fails when the data is heteroskedastic. The correct answer to this question, according to the interviewers, is that heteroskedastic data means that the equation of the regression line produced by least squares regression is an unbiased estimator of the true relationship, but that it is NOT efficient, essentially because the part of the dataset where the variance is smaller than average is effectively underweighted. 
My question is which textbooks could I use to find more detail about this topic, and other similar topics at this level, e.g. 


*

*the relationship between data being normally distributed and least-squares linear regression being the maximum likelihood estimator for the straight line fit 


[I have a degree in mathematics but with minimal statistics background & understand general probability concepts such as the central limit theorem, random variables, etc, and I know high school level statistics up to the British A-level S4 statistics, however I lack a certain level of statistics knowledge and don't know what I don't know or where to find out more... ]
 A: Seber and Lee's seminal linear regression modeling text goes over calculation of errors. You simply have to go through the derivation of the estimator and specify a non-constant conditional variance for the Ys. You show two critical things: 1) when the model is correctly specified, point estimates are not biased 2) standard error estimates for parameters can be either conservative, anticonservative, or coincidentally correct with hetereoscedasticity. 
A: Rencher's Linear Models in Statistics is pretty easy to find book and has fairly straight-forward proofs (and this is coming from a non-math major).
Since you are coming from a math background, you might appreciate the extensive use of matrices to explain everything instead of statistics notation, which you might get in some statistics texts.
Also, the Gauss-Markov Theorem starts on the bottom of page 146.
A: Greene's 7th edition is the standard reference in US. Look up chapter 9, particularly section 9.1. It also has a chapter on Gauss-Markov theorem earlier in the book.
Some people find Judge et al easier to read, if you're one of them then Chapter 11 will have heteroscedasticity discussion
