python - To create loop that lets my regression formula include one variable each tome -

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i've been working on stepwise regression. i'll find loop lets regression formula include 1 variable each time, i'm having trouble loop. code follows:

def forward_selected(data, response):     remaining = set(data.columns)     remaining.remove(response)     selected = []     current_aic, best_new_aic = 0.0, 0.0     while remaining , current_aic == best_new_aic:         aics_with_candidates = []         candidate in remaining:             formula = "{} ~ {} + 1".format(response,' + '.join(selected +     [candidate]))             aic = smf.ols(formula, data).fit().aic             aics_with_candidates.append((aic, candidate))         aics_with_candidates.sort(reverse=true)         best_new_score, best_candidate = aics_with_candidates.pop()         if current_aic < best_new_aic:             remaining.remove(best_candidate)             selected.append(best_candidate)             current_aic = best_new_aic     formula = "{} ~ {} + 1".format(response, ' + '.join(selected))     model = smf.ols(formula, data).fit()     return model

the problem result formula this: y~x+1. it's selecting best x (lowest aic) y~x+1, not formula: y~x1+x2+..+1 lowest aic.


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