背景

计算线性回归a、b值后，希望计算r-squared，对比是否为最佳拟合

Excel拟合

数据源

拟合结果

Python拟合

import math
import numpy as np
from scipy import stats

testX = [174.5,171.2,172.9,161.6,123.6,112.1,107.1,98.6,98.7,97.5,95.8,93.5,91.1,85.2,75.6,72.7,68.6,69.1,63.8,60.1,65.2,71,75.8,77.8]
testY = [88.3,87.1,88.7,85.8,89.4,88,83.7,73.2,71.6,71,71.2,70.5,69.2,65.1,54.8,56.7,62,68.2,71.1,76.1,79.8,80.9,83.7,85.8]
 
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)
    print ("使用math库：r：", SSR / SST,"r-squared：", (SSR / SST)**2)
    return 
 
computeCorrelation(testX, testY)

x = np.array(testX)
y = np.array(testY)
#拟合 y = ax + b
poly = np.polyfit(x, y, deg=1)
print("使用numpy库：a：" + str(poly[0]) + "，b：" + str(poly[1]))


def rsquared(x, y): 
    slope, intercept, r_value, p_value, std_err = stats.linregress(x, y) 
    #a、b、r
    print("使用scipy库：a：",slope,"b：", intercept,"r：", r_value,"r-squared：", r_value**2)

rsquared(testX, testY)