I've recently been working with the Python toolset in this space -- pandas, numpy, matplotlib -- and run smack dab into my rusty regression analysis. In particular I need to better understand the distribution assumptions underlying the error distributions and the variances around the coefficient and intercept values.
Any suggestions for some deeper study / refresher?
For more "intuition about working with data, especially if you're a visual person," Howard Wainer's books are wonderful; one example is "Graphic Discovery: A Trout in the Milk and Other Visual Adventures." They're non-technical, short chapters, discussions of different data sets.
Bill Cleveland's "Visualizing Data" and "Elements of Graphing Data" cover the same material -- graphing data -- at a more technical level. I don't know Cleveland's books would help with the issues you asked about, but... they are amazing books and if you're interested in the subject at all I can't recommend them highly enough.
I don't have any free recommendations, unfortunately.
It's not an easy book, but if you've gone through to at least third year level in statistics it's approachable and you will understand it to a deep level.
Take a look at Dudley's Statistics for Applications from MIT's Open Courseware - http://ocw.mit.edu/courses/mathematics/18-443-statistics-for... - is supposed to be very thorough and easy to follow, but warning, it's based on an expensive textbook.