Basic GAM example with formula after merge

ex_gam_mpg_basic.ipynb

Thanks for the link to Patsy. That's a really useful package!

From the link, I note:

In patsy one can specify the number of degrees of freedom directly (actual number of columns of the resulting design matrix) whereas in mgcv one has to specify the number of knots to use. For instance, in the case of cyclic regression splines (with no additional constraints) the actual degrees of freedom is the number of knots minus one.

So, it seems that df (statsmodels) is k (mgcv) minus one.

Also, it seems that you're right about degree=3 meaning cubic splines:

bs() can produce B-spline bases of arbitrary degrees – e.g., degree=0 will give produce piecewise-constant functions, degree=1 will produce piecewise-linear functions, and the default degree=3 produces cubic splines.

To be honest, I really don't understand the mathematics behind splines and all that, but at least with this information, I can line up your documentation with mgcv's. Thanks!