linreg_residuals_plot.ipynb

Kernel: Unknown Kernel

# Plot resisudal from 1d linear regression
# Based on https://github.com/probml/pmtk3/blob/master/demos/linregResiduals.m


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

try:
    import probml_utils as pml
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    import probml_utils as pml

np.random.seed(0)
N = 21
x = np.linspace(0.0, 20, N)
X0 = x.reshape(N, 1)
X = np.c_[np.ones((N, 1)), X0]
w = np.array([-1.5, 1 / 9.0])
y = w[0] * x + w[1] * np.square(x)
y = y + np.random.normal(0, 1, N) * 2

w = np.linalg.lstsq(X, y, rcond=None)[0]
# print(w)
y_estim = np.dot(X, w)

plt.plot(X[:, 1], y, "o")
plt.plot(X[:, 1], y_estim, "-")
pml.savefig("linregResidualsNoBars.pdf")
plt.show()

for x0, y0, y_hat in zip(X[:, 1], y, y_estim):
    plt.plot([x0, x0], [y0, y_hat], "k-")
plt.plot(X[:, 1], y, "o")
plt.plot(X[:, 1], y_estim, "-")
plt.plot(X[:, 1], y_estim, "x", color="r", markersize=12)
pml.savefig("linregResidualsBars.pdf")
plt.show()

import probml_utils