ダミー変数について考えるとき、OLS回帰のコンテキストでそれらを使用することを考え、次のようにします。
import numpy as np
import pandas as pd
import statsmodels.api as sm
my_data = np.array([[5, 'a', 1],
[3, 'b', 3],
[1, 'b', 2],
[3, 'a', 1],
[4, 'b', 2],
[7, 'c', 1],
[7, 'c', 1]])
df = pd.DataFrame(data=my_data, columns=['y', 'dummy', 'x'])
just_dummies = pd.get_dummies(df['dummy'])
step_1 = pd.concat([df, just_dummies], axis=1)
step_1.drop(['dummy', 'c'], inplace=True, axis=1)
# to run the regression we want to get rid of the strings 'a', 'b', 'c' (obviously)
# and we want to get rid of one dummy variable to avoid the dummy variable trap
# arbitrarily chose "c", coefficients on "a" an "b" would show effect of "a" and "b"
# relative to "c"
step_1 = step_1.applymap(np.int)
result = sm.OLS(step_1['y'], sm.add_constant(step_1[['x', 'a', 'b']])).fit()
print result.summary()