advanced-algorithmic-trading

241
)
)
lr_model.coef_[0]
# Create a scatterplot of the test data for features
# against responses, plotting the estimated line
# of best fit from the ordinary least squares procedure
plt.scatter(X_test, y_test)
plt.plot(
X_test,
lr_model.predict(X_test),
color=’black’,
linewidth=1.0
)
plt.xlabel("X")
plt.ylabel("y")
plt.show()
17.6 Bibliographic Note
An elementary introduction to linear regression as well as shrinkage, regularisation and dimensionality
reduction in the framework of supervised learning can be found James et al (2013)[59].
A more rigourous explanation of the techniques including recent developments can be found
in Hastie et al (2009)[51].
A probabilistic (mainly Bayesian) approach to linear regression, along with a comprehensive
derivation of the maximum likelihood estimate via ordinary least squares, and extensive
discussion of shrinkage and regularisation, can be found in Murphy (2012)[71].
A "real world" example-based overview of linear regression in a high-collinearity regime, with
extensive discussion on dimensionality reduction and partial least squares can be found in Kuhn
et al (2013)[67].