Linear regression in two dimensions¶

Coefficients:
 intercept: 0.66
 average room per dwelling: 4.76
 percentage of low status in population: -0.63
Mean squared error on test set: 26.45
Variance score on test set: 0.74

import matplotlib.pyplot as plt
import numpy as np
from tick import linear_model
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.utils import shuffle
from sklearn.datasets import load_boston
from mpl_toolkits.mplot3d import axes3d
from matplotlib import cm

# Load the Boston Housing Dataset
features, label = load_boston(return_X_y=True)
features, label = shuffle(features, label, random_state=0)

# Use two features: the average of the number of rooms per dwelling and
# the pencentage of low status of the population
X = features[:, [5, 12]]

# Split the data into training/testing sets
n_train_data = int(0.8 * X.shape[0])

X_train = X[:n_train_data]
X_test = X[n_train_data:]

y_train = label[:n_train_data]
y_test = label[n_train_data:]

# Create linear regression and fit it on the training set
regr = linear_model.LinearRegression()
regr.fit(X_train, y_train)

# Make predictions using the testing set
y_pred = regr.predict(X_test)

print('Coefficients:')
print(' intercept: {:.2f}'.format(regr.intercept))
print(' average room per dwelling: {:.2f}'.format(regr.weights[0]))
print(' percentage of low status in population: {:.2f}'
      .format(regr.weights[1]))

# The mean squared error
print('Mean squared error on test set: {:.2f}'.format(
    mean_squared_error(y_test, y_pred)))

# Explained variance score: 1 is perfect prediction
print('Variance score on test set: {:.2f}'.format(r2_score(y_test, y_pred)))
# To work in 3D

# We first generate a mesh grid
resolution = 10
x = X_test[:, 0]
y = X_test[:, 1]
z = y_test

x_surf = np.linspace(min(x), max(x), resolution)
y_surf = np.linspace(min(y), max(y), resolution)
x_surf, y_surf = np.meshgrid(x_surf, y_surf)

# and then predict the label for all values in the grid
z_surf = np.zeros_like(x_surf)
mesh_points = np.vstack((x_surf.ravel(), y_surf.ravel())).T
z_surf.ravel()[:] = regr.predict(mesh_points)

fig = plt.figure(figsize=(20, 5))

# 3D representation under different rotated angles for a better visualazion
xy_angles = [10, 35, 60, 85]
z_angle = 20

for i, angle in enumerate(xy_angles):
    n_columns = len(xy_angles)
    position = i + 1

    ax = fig.add_subplot(1, n_columns, position, projection='3d')

    ax.view_init(z_angle, angle)

    ax.plot_surface(x_surf, y_surf, z_surf, cmap=cm.hot, rstride=1, cstride=1,
                    alpha=0.3, linewidth=0.2, edgecolors='black')
    ax.scatter(x, y, z)

    ax.set_title('angle: {}°'.format(angle))
    ax.set_zlabel('median house pricing')
    ax.set_xlabel('avg room per dwelling')
    ax.set_ylabel('% low status population')

plt.show()