Source Code for Module madrona.analysistools.utils

 1  from math import sqrt 
 2 -def linear_regression(X, Y): 
 3      """ 
 4      http://www.answermysearches.com/how-to-do-a-simple-linear-regression-in-python/124/ 
 5      Summary 
 6          Linear regression of y = ax + b 
 7      Usage 
 8          real, real, real = linreg(list, list) 
 9          a, b, r2 = linreg(list, list) 
10      Returns coefficients to the regression line "y=ax+b" from x[] and y[], and R^2 Value 
11      """ 
12      if len(X) != len(Y):   
13          raise ValueError('unequal length') 
14      N = len(X) 
15      Sx = Sy = Sxx = Syy = Sxy = 0.0 
16      for x, y in map(None, X, Y): 
17          Sx = Sx + x 
18          Sy = Sy + y 
19          Sxx = Sxx + x * x 
20          Syy = Syy + y * y 
21          Sxy = Sxy + x * y 
22      det = Sxx * N - Sx * Sx 
23      a, b = (Sxy * N - Sy * Sx) / det, (Sxx * Sy - Sx * Sxy) / det 
24      meanerror = residual = 0.0 
25      for x, y in map(None, X, Y): 
26          meanerror = meanerror + (y - Sy / N) ** 2 
27          residual = residual + (y - a * x - b) ** 2 
28      RR = 1 - residual / meanerror 
29      ss = residual / (N - 2) 
30      Var_a, Var_b = ss * N / det, ss * Sxx / det 
31      return a, b, RR 
32