"""
Multiple Regression
====================

Calculate using 'statsmodels' just the best fit, or all the corresponding
statistical parameters.

Also shows how to make 3d plots.
"""
# Original author: Thomas Haslwanter

import numpy as np
import matplotlib.pyplot as plt
import pandas

# For 3d plots. This import is necessary to have 3D plotting below
from mpl_toolkits.mplot3d import Axes3D

# For statistics. Requires statsmodels 5.0 or more
from statsmodels.formula.api import ols
# Analysis of Variance (ANOVA) on linear models
from statsmodels.stats.anova import anova_lm

##############################################################################
# Generate and show the data
x = np.linspace(-5, 5, 21)
# We generate a 2D grid
X, Y = np.meshgrid(x, x)

# To get reproducable values, provide a seed value
np.random.seed(1)

# Z is the elevation of this 2D grid
Z = -5 + 3*X - 0.5*Y + 8 * np.random.normal(size=X.shape)

# Plot the data
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, cmap=plt.cm.coolwarm,
                       rstride=1, cstride=1)
ax.view_init(20, -120)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')

##############################################################################
# Multilinear regression model, calculating fit, P-values, confidence
# intervals etc.

# Convert the data into a Pandas DataFrame to use the formulas framework
# in statsmodels

# First we need to flatten the data: it's 2D layout is not relevent.
X = X.flatten()
Y = Y.flatten()
Z = Z.flatten()

data = pandas.DataFrame({'x': X, 'y': Y, 'z': Z})

# Fit the model
model = ols("z ~ x + y", data).fit()

# Print the summary
print(model.summary())

print("\nRetrieving manually the parameter estimates:")
print(model._results.params)
# should be array([-4.99754526,  3.00250049, -0.50514907])

# Peform analysis of variance on fitted linear model
anova_results = anova_lm(model)

print('\nANOVA results')
print(anova_results)

plt.show()