advanced-algorithmic-trading

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if __name__ == "__main__":
# Set up the X and Y dimensions
fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(0, 20, 0.25)
Y = np.arange(-10, 10, 0.25)
X, Y = np.meshgrid(X, Y)
# Create the univarate normal coefficients
# of intercept and slope, as well as the
# conditional probability density
beta0 = -5.0
beta1 = 0.5
Z = norm.pdf(Y, beta0 + beta1*X, 1.0)
# Plot the surface with the "coolwarm" colormap
surf = ax.plot_surface(
X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,
linewidth=0, antialiased=False
)
# Set the limits of the z axis and major line locators
ax.set_zlim(0, 0.4)
ax.zaxis.set_major_locator(LinearLocator(5))
ax.zaxis.set_major_formatter(FormatStrFormatter(’%.02f’))
# Label all of the axes
ax.set_xlabel(’X’)
ax.set_ylabel(’Y’)
ax.set_zlabel(’P(Y|X)’)
# Adjust the viewing angle and axes direction
ax.view_init(elev=30., azim=50.0)
ax.invert_xaxis()
ax.invert_yaxis()
# Plot the probability density
plt.show()
The output is given in Figure 17.1.
The plot highlights how the expectation of the response y is linearly dependent upon x. The
"peak" of the distribution follows a linear path as x increases. The uncertainty associated with
the ɛ error of the model is represented by a normally-distributed spread around the peak for
each x. Notice in particular that the spread width does not change as x increases. This is a key
assumption used in linear regression models, namely that the variance does not increase with