I prefer the formula api for statsmodels. At least for that, model.fit().predict
wants a DataFrame where the columns have the same names as the predictors. Here's an example:
In [2]: df = pd.DataFrame({'X': np.arange(10), 'Y': np.arange(10) + np.random.randn(10)})
In [3]: mod = sm.OLS.from_formula("Y ~ X", df)
In [4]: res = mod.fit()
In [5]: exog = pd.DataFrame({"X": np.linspace(0, 10, 100)})
In [6]: res.predict(exog)
Out[6]:
array([ 0.99817045, 1.07854804, 1.15892563, 1.23930322, 1.31968081,
1.40005839, 1.48043598, 1.56081357, 1.64119116, 1.72156875,
1.80194634, 1.88232393, 1.96270152, 2.04307911, 2.1234567 ,
2.20383429, 2.28421188, 2.36458947, 2.44496706, 2.52534465,
2.60572224, 2.68609983, 2.76647742, 2.84685501, 2.92723259,
3.00761018, 3.08798777, 3.16836536, 3.24874295, 3.32912054,
3.40949813, 3.48987572, 3.57025331, 3.6506309 , 3.73100849,
3.81138608, 3.89176367, 3.97214126, 4.05251885, 4.13289644,
4.21327403, 4.29365162, 4.3740292 , 4.45440679, 4.53478438,
4.61516197, 4.69553956, 4.77591715, 4.85629474, 4.93667233,
5.01704992, 5.09742751, 5.1778051 , 5.25818269, 5.33856028,
5.41893787, 5.49931546, 5.57969305, 5.66007064, 5.74044823,
5.82082582, 5.9012034 , 5.98158099, 6.06195858, 6.14233617,
6.22271376, 6.30309135, 6.38346894, 6.46384653, 6.54422412,
6.62460171, 6.7049793 , 6.78535689, 6.86573448, 6.94611207,
7.02648966, 7.10686725, 7.18724484, 7.26762243, 7.34800002,
7.4283776 , 7.50875519, 7.58913278, 7.66951037, 7.74988796,
7.83026555, 7.91064314, 7.99102073, 8.07139832, 8.15177591,
8.2321535 , 8.31253109, 8.39290868, 8.47328627, 8.55366386,
8.63404145, 8.71441904, 8.79479663, 8.87517421, 8.9555518 ])