#!/usr/bin/env python

# DO NOT EDIT
# Autogenerated from the notebook predict.ipynb.
# Edit the notebook and then sync the output with this file.
#
# flake8: noqa
# DO NOT EDIT

# # Prediction (out of sample)

import numpy as np
import matplotlib.pyplot as plt

import statsmodels.api as sm

plt.rc("figure", figsize=(16, 8))
plt.rc("font", size=14)

# ## Artificial data

nsample = 50
sig = 0.25
x1 = np.linspace(0, 20, nsample)
X = np.column_stack((x1, np.sin(x1), (x1 - 5)**2))
X = sm.add_constant(X)
beta = [5.0, 0.5, 0.5, -0.02]
y_true = np.dot(X, beta)
y = y_true + sig * np.random.normal(size=nsample)

# ## Estimation

olsmod = sm.OLS(y, X)
olsres = olsmod.fit()
print(olsres.summary())

# ## In-sample prediction

ypred = olsres.predict(X)
print(ypred)

# ## Create a new sample of explanatory variables Xnew, predict and plot

x1n = np.linspace(20.5, 25, 10)
Xnew = np.column_stack((x1n, np.sin(x1n), (x1n - 5)**2))
Xnew = sm.add_constant(Xnew)
ynewpred = olsres.predict(Xnew)  # predict out of sample
print(ynewpred)

# ## Plot comparison

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
ax.plot(x1, y, "o", label="Data")
ax.plot(x1, y_true, "b-", label="True")
ax.plot(np.hstack((x1, x1n)),
        np.hstack((ypred, ynewpred)),
        "r",
        label="OLS prediction")
ax.legend(loc="best")

# ## Predicting with Formulas

# Using formulas can make both estimation and prediction a lot easier

from statsmodels.formula.api import ols

data = {"x1": x1, "y": y}

res = ols("y ~ x1 + np.sin(x1) + I((x1-5)**2)", data=data).fit()

# We use the `I` to indicate use of the Identity transform. Ie., we do not
# want any expansion magic from using `**2`

res.params

# Now we only have to pass the single variable and we get the transformed
# right-hand side variables automatically

res.predict(exog=dict(x1=x1n))
