3.1.6.5. 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](http://www.statsmodels.org/stable/generated/statsmodels.stats.anova.anova_lm.html#statsmodels.stats.anova.anova_lm "View documentation for statsmodels.stats.anova.anova_lm")

Generate and show the data

# We generate a 2D grid
X, Y = [np.meshgrid](https://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html#numpy.meshgrid "View documentation for numpy.meshgrid")(x, x)

# To get reproducable values, provide a seed value
[np.random.seed](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.seed.html#numpy.random.seed "View documentation for numpy.random.seed")(1)

# Z is the elevation of this 2D grid
Z = -5 + 3*X - 0.5*Y + 8 * [np.random.normal](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.normal.html#numpy.random.normal "View documentation for numpy.random.normal")(size=X.shape)

# Plot the data
fig = [plt.figure](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure "View documentation for matplotlib.pyplot.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')

../../../_images/sphx_glr_plot_regression_3d_001.png

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](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.html#pandas.DataFrame "View documentation for 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](http://www.statsmodels.org/stable/generated/statsmodels.stats.anova.anova_lm.html#statsmodels.stats.anova.anova_lm "View documentation for statsmodels.stats.anova.anova_lm")(model)

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

[plt.show](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show "View documentation for matplotlib.pyplot.show")()