Returns:
 - - - - 
 model: an "optimal" fitted statsmodels linear model
 with an intercept
 selected by backward selection
 """
 # begin with all factors and intercept
 possible_factors = set(data.columns)
 possible_factors.remove(response)
 formula = "{} ~ {} + 1".format(response, ' + '.join(possible_factors))
 best_aic = sm.ols(formula, data).fit().aic
 current_aic = best_aic

 # create a non-empty set of columns that will be labeled as "to remove and try"
 to_try_remove = possible_factors

 # check which features remain
 while to_try_remove and current_aic == best_aic:
 aic_candidates = []
 for candidate in to_try_remove:

 columns = possible_factors - set([candidate])
 # removing the candidate column
 formula = "{} ~ {} + 1".format(response, ' + '.join(columns))
 # print AIC
 aic = sm.ols(formula, data).fit().aic

 # append tuple of the form (aic, response)
 aic_candidates.append((aic, candidate))

 # sort all the pairs by the first entry of tuple 
 aic_candidates.sort()
 # change sort/pop order!
 best_new_aic, best_candidate = aic_candidates.pop(0)

 # check if we have something better:
 if best_new_aic < current_aic:
 # Remove the best candidate's name from possible_factors

 possible_factors.remove(best_candidate)
 current_aic = best_new_aic

 # repeat the process with all the remaining candidate columns