如何在绘制 R2 值时使趋势线穿过原点 - python

Question

我正在使用一个数据框 df，它看起来像这样：

index       var1      var2      var3
0           0.0       0.0       0.0 
10          43940.7   2218.3    6581.7
100         429215.0  16844.3   51682.7

我想绘制每个变量，绘制它们强制到原点的趋势线，计算并绘制 R2 值。

我在中找到了我想要的东西，但是趋势线没有穿过原点，我找不到让它起作用的方法。

我尝试手动修改趋势线第一个点的值，但结果似乎不太好。

for var in df.columns[1:]:
    fig, ax = plt.subplots(figsize=(10,7))
    
    x = df.index
    y = df[var]
    
    z = numpy.polyfit(x, y, 1)
    p = numpy.poly1d(z)
    pylab.plot(x,p(x),"r--")
    
    plt.plot(x,y,"+", ms=10, mec="k")
    z = np.polyfit(x, y, 1)
    y_hat = np.poly1d(z)(x)
    y_hat[0] = 0     ###--- Here I tried to replace the first value with 0 but it doesn't seem right to me.

    plt.plot(x, y_hat, "r--", lw=1)
    text = f"$y={z[0]:0.3f}\;x{z[1]:+0.3f}$\n$R^2 = {r2_score(y,y_hat):0.3f}$"
    plt.gca().text(0.05, 0.95, text,transform=plt.gca().transAxes, fontsize=14, verticalalignment='top')

有什么办法吗？任何帮助将不胜感激。

Answer 1

您可以使用 Scipy 和 curve_fit。确定您的趋势线为 y=ax，以便它穿过原点。

import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

def func(x, a):
    return a * x

xdata = (0,10,20,30,40)
ydata = (0,12,18,35,38)

popt, pcov = curve_fit(func, xdata, ydata)
plt.scatter(xdata, ydata)
plt.plot(xdata, func(xdata, popt),"r--")
plt.show()

Answer 2

您可以使用 statsmodels 进行无截距的简单线性回归

import statsmodels.api as sm

xdata = [0,10,20,30,40]
ydata = [0,12,18,35,38]

res = sm.OLS(ydata, xdata).fit()

然后将斜率和 R2 存储在属性中：

res.params
#array([1.01666667])

res.rsquared
#0.9884709382637339

还有大量其他信息：

res.summary()

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.988
Model:                            OLS   Adj. R-squared (uncentered):              0.986
Method:                 Least Squares   F-statistic:                              342.9
Date:                Tue, 29 Sep 2020   Prob (F-statistic):                    5.00e-05
Time:                        15:39:50   Log-Likelihood:                         -12.041
No. Observations:                   5   AIC:                                      26.08
Df Residuals:                       4   BIC:                                      25.69
Df Model:                           1                                                  
Covariance Type:            nonrobust                                                  
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
x1             1.0167      0.055     18.519      0.000       0.864       1.169
==============================================================================

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