1. 皮尔逊相关系数 (Pearson Correlation Coefficient):
1.1 衡量两个值线性相关强度的量
1.2 取值范围 [-1, 1]: 
正向相关: >0, 负向相关：<0, 无相关性：=0

http://www.cda.cn/uploadfile/image/20180125/20180125090152_62846.png
2. R平方值:

2.1定义：决定系数，反应因变量的全部变异能通过回归关系被自变量解释的比例。

2.2 描述：如R平方为0.8，则表示回归关系可以解释因变量80%的变异。换句话说，如果我们能控制自变量不变，则因变量的变异程度会减少80%

2.3： 简单线性回归：R^2 = r * r
多元线性回归：

http://www.cda.cn/uploadfile/image/20180125/20180125090151_27941.png

http://www.cda.cn/uploadfile/image/20180125/20180125090151_74709.png

http://www.cda.cn/uploadfile/image/20180125/20180125090151_50165.png

Python实现;

import numpy as np  
    from astropy.units import Ybarn  
    import math  
      
    def computeCorrelation(X, Y):  
        xBar = np.mean(X)  
        yBar = np.mean(Y)  
        SSR = 0  
        varX = 0  
        varY = 0  
        for i in range(0 , len(X)):  
            diffXXBar = X[i] - xBar  
            diffYYBar = Y[i] - yBar  
            SSR = (diffXXBar * diffYYBar)  
            varX =  diffXXBar**2  
            varY = diffYYBar**2  
          
        SST = math.sqrt(varX * varY)  
        return SSR / SST  
      
    testX = [1, 3, 8, 7, 9]  
    testY = [10, 12, 24, 21, 34]  
      
    print (computeCorrelation(testX, testY))