Linear Regression

Sample program to model the data using linear regression, and show the graph.

Environment

• Python 2.7.6
• Numpy
• Matplotlib

Run

$ python linear_regression.py

Logic

Use the polynomial basis as the basis function.

Then, the function can be expressed as below.

This time, I define the basis function as 4 dimensional. Thence,

Using matrix, these "omega" can be solved by this equation.

Phi is the matrix as following.

Graph

Numpy

• numpy.linalg.solve : Sove a linear matrix equation. ref. http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.solve.html
• numpy.dot : Scalar product, Inner product ref. http://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html

Reference

(Japanese) http://gihyo.jp/dev/serial/01/machine-learning/0011?page=1