Python tool for ANOVA analysis and Linear regression

This repository provides a Python script for ANOVA and linear regression anaylses.

Content

The script, functions.py, is designed to provide necessary functions for one-way ANOVA, two-way ANOVA, simple and multiple linear regression.
main.py file is a test script to demonstrate how to use functions with what kind of arguments. It could be used with -w parameter to show output of tests one by one, waiting an input from user.

Example

ANOVA1_test_equality function tests the equality of the means among the groups:

Input:

  Groups: [[6.9, 5.4, 5.8, 4.6, 4.0], 
  		[8.3, 6.8, 7.8, 9.2, 6.5], 
  		[8.0, 10.5, 8.1, 6.9, 9.3], 
  		[5.8, 3.8, 6.1, 5.6, 6.2]]
  alpha: 0.05

ANOVA table:

  | Source         |   df  |   SS  |   MS  |   F  |
  |----------------|:-----:|:-----:|:-----:|:----:|
  | Between groups |  3.00 | 38.82 | 12.94 | 9.72 |
  | Within groups  | 16.00 | 21.29 |  1.33 |      |
  | Total          | 19.00 |       |       |      |

P-value = 0.000684 < alpha = 0.05. Thus, the null hypothesis that the means of the groups are equal is rejected at significance level alpha = 0.05.

ANOVA1_CI_linear_combs function calculates simultaneous confidence intervals of linear combinations given as a matrix, and returns a list of confidence intervals holding simultaneously with 1-alpha probability:

The function offers different methods for calculating the interval:
- Scheffe's method
- Tukey's pairwise comparison
- Bonferroni correction
- Sidak's method
- And the best choice as the function finds the most suitable method for the given linear combinations.
Input:

  Groups: [[6.9, 5.4, 5.8, 4.6, 4.0], 
  		[8.3, 6.8, 7.8, 9.2, 6.5], 
  		[8.0, 10.5, 8.1, 6.9, 9.3], 
  		[5.8, 3.8, 6.1, 5.6, 6.2]]
  alpha: 0.05
  Linear combinations C: [[0.5, 0.5, -0.5, -0.5], [0.5, -0.5, 0.5, -0.5]]

Output:

  Bonferroni:
  	(-1.7758, 0.7758)
  	(-0.9358, 1.6158)
  Scheffe 2.8:
  	(-2.1081, 1.1081)
  	(-1.2681, 1.9481)
  Sidak:
  	(-1.7725, 0.7725)
  	(-0.9325, 1.6125)
  Tukey:
  Error! Given C matrix is not valid for Tukey (expecting pairwise comparisons)

Mult_LR_Least_squares function calculate the least square estimates for the beta vector and the biased and unbiased sigma estimators:

Input:

  |  x0 | Height | Weight | Distance |
  |:---:|:------:|:------:|:--------:|
  | 1.0 |  42.8  |  40.0  |   37.0   |
  | 1.0 |  63.5  |  93.5  |   49.5   |
  | 1.0 |  37.5  |  35.5  |   34.5   |
  | 1.0 |  39.5  |  30.0  |   36.0   |
  | 1.0 |  45.5  |  52.0  |   43.0   |
  | 1.0 |  38.5  |  17.0  |   28.0   |
  | 1.0 |  43.0  |  38.5  |   37.0   |
  | 1.0 |  22.5  |   8.5  |   20.0   |
  | 1.0 |  37.0  |  33.0  |   33.5   |
  | 1.0 |  23.5  |   9.5  |   30.5   |
  | 1.0 |  33.0  |  21.0  |   38.5   |
  | 1.0 |  58.0  |  79.0  |   47.0   |

Output:

  BetaHat: [21.00839777  0.19635663  0.19082778] 
  Biased Sigma Square Hat: 11.6594
  Unbiased Sigma Square Hat: 15.5459

firatkizilirmakk/Anova-Linear-Regression-Toolbox

Python tool for ANOVA analysis and Linear regression

Content

Example