1、皮尔逊相关系数 (Pearson Correlation Coefficient)是衡量两个值线性相关强度的量，取值范围：[-1, 1]，正向相关：>0，负向相关：<0，无相关性：=0
上式又可以表示为：
R^2是皮尔逊相关系数的平方，依然是表示两个值线性相关强度的量，取值范围：[0, 1]，值越大，相关性越强。
import numpy as np
def computeCorrelation(x, y):
xBar = np.mean(x)
yBar = np.mean(y)
covXY = 0
varX = 0
varY = 0
for i in range(0, len(x)):
diffxx = x[i] - xBar
diffyy = y[i] - yBar
covXY += (diffxx * diffyy)
varX += diffxx ** 2
varY += diffyy ** 2
return covXY / np.sqrt(varX * varY)
x=np.linspace(-0.5,0.5,10)
noise=np.random.normal(0,0.02,10)
y=2*x+1+noise
R = computeCorrelation(x, y)
R2 = np.square(R)
print(R2)
运行结果：
0.9994448592313179
2、R^2还可以由下式计算得到，yihat表示预测值，yi表示真实值，ybar表示真实值的均值
import numpy as np
def computeCorrelation(x, y, degree):
result = {}
coeffs = np.polyfit(x, y, degree) # degree表示N次拟合
result['coeffs'] = coeffs.tolist()
p = np.poly1d(coeffs) # 得到拟合方程
yhat = p(x) # 得到预测值
ybar = np.sum(y) / len (y)
SSR = np.sum((yhat -ybar)**2)
SST = np.sum((y - ybar)**2)
result['R2'] = SSR / SST
return result['R2']
x=np.linspace(-0.5,0.5,10)
noise=np.random.normal(0,0.02,10)
y=2*x+1+noise
R2 = computeCorrelation(x, y, 1)
print(R2)
运行结果：
0.999732826660141