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