线性回归中 MSE 和 RMSE 的计算

Question

我使用scipy.stats 中的linregress 编写了一个线性回归代码，我想将它与我在互联网上找到的使用sklearn.linear_model 中的LinearRegression 的另一个代码进行比较。

使用scipy，真实值和预测值似乎很容易提取（如果我做得正确的话），但在sklearn 代码中，当我尝试计算 MSE 和 RMSE 时收到错误。

在使用sklearn 计算线性回归的 MSE 和 RMSE 时，我应该选择什么作为预测值和真实值？

scipy代码：

from scipy.stats import linregress
import math
from sklearn.metrics import mean_squared_error
import pandas as pd
import statistics
import numpy as np


data_y = [76.6,118.6,200.8,362.3,648.9]
data_x = [10,20,40,80,160]
s_data_y = pd.Series(data_y)
s_data_x = pd.Series(data_x)

slope, intercept, r_value, p_value, std_err = linregress(s_data_x,s_data_y)
linregress(s_data_x,s_data_y)

true_val = s_data_y
predicted_val = intercept + slope * s_data_x

mse = mean_squared_error(true_val, predicted_val)
rmse = math.sqrt(mse)

plt.scatter(s_data_x,s_data_y)
plt.plot(s_data_x, predicted_val, 'r', label='fitted line')
plt.xlabel("X",fontweight='bold')
plt.ylabel("Y",fontweight='bold')
plt.grid(True)
plt.show()

print(dev_contact_resistance_params_all)
print(f'{slope=}\n{intercept=}\n{r_value=}\n{p_value=}\n{std_err=}\n')
print('Mean square error:',mse)
print('Root mean square error:',rmse)

sklearn代码（来自互联网）：

from sklearn import linear_model
import matplotlib.pyplot as plt
import numpy as np
import random

#----------------------------------------------------------------------------------------#
# Step 1: training data

Y = [76.6,118.6,200.8,362.3,648.9]
X = [10,20,40,80,160]

X = np.asarray(X)
Y = np.asarray(Y)

X = X[:,np.newaxis]
Y = Y[:,np.newaxis]

plt.scatter(X,Y)

#----------------------------------------------------------------------------------------#
# Step 2: define and train a model

model = linear_model.LinearRegression()
model.fit(X, Y)

print(model.coef_, model.intercept_)

#----------------------------------------------------------------------------------------#
# Step 3: prediction

x_new_min = 0.0
x_new_max = 200.0

X_NEW = np.linspace(x_new_min, x_new_max, 100)
X_NEW = X_NEW[:,np.newaxis]

Y_NEW = model.predict(X_NEW)

plt.plot(X_NEW, Y_NEW, color='coral', linewidth=3)

plt.grid()
plt.xlim(x_new_min,x_new_max)
plt.ylim(0,1000)

plt.title("Simple Linear Regression using scikit-learn and python 3",fontsize=10)
plt.xlabel('x')
plt.ylabel('y')

plt.savefig("simple_linear_regression.png", bbox_inches='tight')
plt.show()

true_val = Y
predicted_val = Y_NEW

mse = mean_squared_error(true_val, predicted_val)
rmse = math.sqrt(mse)

print('Mean square error:',mse)
print('Root mean square error:',rmse)

来自sklearn 代码的错误：

Traceback (most recent call last):
  File "C:\Users\test.py", line 21, in <module>
    mse = mean_squared_error(r_value, p_value)
  File "C:\lib\site-packages\sklearn\metrics\_regression.py", line 423, in mean_squared_error
    y_type, y_true, y_pred, multioutput = _check_reg_targets(
  File "C:\Users\lib\site-packages\sklearn\metrics\_regression.py", line 89, in _check_reg_targets
    check_consistent_length(y_true, y_pred)
  File "C:\Users\lib\site-packages\sklearn\utils\validation.py", line 328, in check_consistent_length
    lengths = [_num_samples(X) for X in arrays if X is not None]
  File "C:\Users\lib\site-packages\sklearn\utils\validation.py", line 328, in <listcomp>
    lengths = [_num_samples(X) for X in arrays if X is not None]
  File "C:\Users\lib\site-packages\sklearn\utils\validation.py", line 268, in _num_samples
    raise TypeError(
ValueError: Found input variables with inconsistent numbers of samples: [5, 100]

Answer 1

您可以使用sklearn.linear_model.LinearRegression 复制scipy.stats.linregress 的结果，如下所示：

import numpy as np
from scipy.stats import linregress
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

# input data
y = np.array([76.6, 118.6, 200.8, 362.3, 648.9])
x = np.array([10, 20, 40, 80, 160])

# scipy linear regression
slope, intercept, r_value, p_value, std_err = linregress(x, y)
y_pred = intercept + slope * x

mse = mean_squared_error(y_true=y, y_pred=y_pred, squared=True)
rmse = mean_squared_error(y_true=y, y_pred=y_pred, squared=False)

print('scipy intercept: {:.6f}'.format(intercept))
print('scipy slope: {:.6f}'.format(slope))
print('scipy MSE: {:.6f}'.format(mse))
print('scipy RMSE: {:.6f}'.format(rmse))
# scipy intercept: 45.058333
# scipy slope: 3.812608
# scipy MSE: 49.793366
# scipy RMSE: 7.056441

# sklearn linear regression
reg = LinearRegression().fit(x.reshape(- 1, 1), y)
y_pred = reg.predict(x.reshape(- 1, 1))

mse = mean_squared_error(y_true=y, y_pred=y_pred, squared=True)
rmse = mean_squared_error(y_true=y, y_pred=y_pred, squared=False)

print('sklearn intercept: {:.6f}'.format(reg.intercept_))
print('sklearn slope: {:.6f}'.format(reg.coef_[0]))
print('sklearn MSE: {:.6f}'.format(mse))
print('sklearn RMSE: {:.6f}'.format(rmse))
# sklearn intercept: 45.058333
# sklearn slope: 3.812608
# sklearn MSE: 49.793366
# sklearn RMSE: 7.056441