def _do_analysis_no_cross_validation(self):
        """
        Find the best model (fit) and create self.list_of_fits and self.fit
        """

        # first model is just the mean
        response_term = [Term([LookupFactor(self.y)])]
        model_terms = [Term([])] # empty term is the intercept
        all_model_terms_dict = {x:Term([LookupFactor(x)]) for x in self.list_of_x}
        # ...then add another term for each candidate
        #model_terms += [Term([LookupFactor(c)]) for c in candidates]
        model_desc = ModelDesc(response_term, model_terms)
        self._list_of_fits.append(fm.ols(model_desc, data=self.df).fit())
        # try to improve the model until no improvements can be found

        while all_model_terms_dict:
            # try each x and overwrite the best_fit if we find a better one
            # the first best_fit is the one from the previous round
            ref_fit = self._list_of_fits[-1]
            best_fit = self._list_of_fits[-1]
            best_bic = best_fit.bic
            for x, term in all_model_terms_dict.items():
                # make new_fit, compare with best found so far
                model_desc = ModelDesc(response_term, ref_fit.model.formula.rhs_termlist + [term])
                fit = fm.ols(model_desc, data=self.df).fit()
                if fit.bic < best_bic:
                    best_bic = fit.bic
                    best_fit = fit
                    best_x = x
            # Sometimes, the obtained fit may be better, but contains unsignificant parameters.
            # Correct the fit by removing the unsignificant parameters and estimate again
            best_fit = self._prune(best_fit, p_max=self.p_max)

            # if best_fit does not contain more variables than ref fit, exit
            if len(best_fit.model.formula.rhs_termlist) == len(ref_fit.model.formula.rhs_termlist):
                break
            else:
                self._list_of_fits.append(best_fit)
                all_model_terms_dict.pop(best_x)
        self._fit = self._list_of_fits[-1]