https://github.com/takp/linear-regression-sample

Sample program to model the data using linear regression
https://github.com/takp/linear-regression-sample

linear-regression python

Last synced: 3 months ago
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Sample program to model the data using linear regression

• Host: GitHub
• URL: https://github.com/takp/linear-regression-sample
• Owner: takp
• Created: 2014-11-23T10:49:26.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2014-11-23T12:02:17.000Z (over 10 years ago)
• Last Synced: 2024-12-27T09:27:59.494Z (5 months ago)
• Topics: linear-regression, python
• Language: Python
• Size: 191 KB
• Stars: 1
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# 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.

![Polynomial Basis](https://raw.githubusercontent.com/takp/linear-regression-sample/master/images/polynomial_basis.jpg)

Then, the function can be expressed as below.

![General function](https://raw.githubusercontent.com/takp/linear-regression-sample/master/images/general_function.jpg)

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

![function](https://raw.githubusercontent.com/takp/linear-regression-sample/master/images/function.jpg)

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

![omega equation](https://raw.githubusercontent.com/takp/linear-regression-sample/master/images/omega_equation.jpg)

Phi is the matrix as following.

![Phi](https://raw.githubusercontent.com/takp/linear-regression-sample/master/images/Phi.jpg)

### Graph

![Graph](https://raw.githubusercontent.com/takp/linear-regression-sample/master/images/graph.png)

### 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