Please choose a project and a form of interop that appeals to you and your background.
Choose a script from your own work. Modify it so that way it requires and input, and spits out a sensible output. Use Julia's interop functionalities to call this script and retrieve the answer.
Use Julia's interop capabilities to solve the least squares problem using your language of choice and retreve the answer back to Julia.
These are mature interop libraries provided by Julia:
The documentation page for
ccall is: http://docs.julialang.org/en/release-0.4/manual/calling-c-and-fortran-code/. Since I found that slightly opaque on my first read, I wrote a tutorial for using ccall to call compile your C-code for usage with
ccall and writing the wrapper code: http://www.stochasticlifestyle.com/using-julias-c-interface-utilize-c-libraries/
While not technically supported, note that you can use ccall to control Xeon Phi acceleration cards: http://www.stochasticlifestyle.com/interfacing-xeon-phi-via-julia/