That’s really a useful package, thanks for writing it!
Regarding the rendering, the Julian approach is to implement various show methods for your RegressionTable type, one for each backend (plain text, LaTeX, Markdown, HTML, CSV…). That way you don’t need to define your own render method, nor require the user to explicitly pass the expected type of output via an argument (except of course when s/he wants to): it’s automatically chosen depending on the current interface, so it will look good in the REPL, IJulia, Atom, etc. For example, asciiOutput would be replaced with MIME"text/plain" and so on. Julia is much more powerful than R in that regard. See the manual for details.