Python绘制多元线性回归模型时薪资预测值全为0的问题排查

使用Python构建多元线性回归模型时出现异常：作为因变量的薪资（依赖年龄、工作年限等特征）预测值全部为0，但实际薪资范围应为30000至50000，与输出结果不符。以下是实现代码及异常可视化图：

# all required libraries 
import pandas as pd 
import warnings  
import numpy as np  

# For data visualizing   
import seaborn as sns  

#%matplotlib notebook
import matplotlib.pyplot as plt  
from mpl_toolkits.mplot3d import Axes3D  
#%matplotlib inline 
%matplotlib widget

 
# For building the required model  
from sklearn import linear_model  


df = pd.read_csv('ml_data_salary.csv')

# Plotting a 3-D plot for visualizing the Multiple Linear Regression Model  
  
# Preparing the data  
X = df[['age', 'YearsExperience']].values.reshape(-1,2)  
Y = df['Salary']  
  
# Create range for each dimension
x = X[:, 0]
y = X[:, 1]
z = Y

xx_pred = np.linspace(25, 40, 30)  # range of age values
yy_pred = np.linspace(1, 10, 30)  # range of experience values
xx_pred, yy_pred = np.meshgrid(xx_pred, yy_pred)
model_viz = np.array([xx_pred.flatten(), yy_pred.flatten()]).T

# Predict using model built on previous step
ols = linear_model.LinearRegression()
model1 = ols.fit(X, Y)
predicted = model1.predict(model_viz)

# Evaluate model by using it's R^2 score 
r2 = model.score(X, Y)

# Plot model visualization
plt.style.use('default')

fig = plt.figure(figsize=(12, 4))

ax1 = fig.add_subplot(131, projection='3d')
ax2 = fig.add_subplot(132, projection='3d')
ax3 = fig.add_subplot(133, projection='3d')

axes = [ax1, ax2, ax3]

for ax in axes:
    ax.plot(x, y, z, color='k', zorder=15, linestyle='none', marker='o', alpha=0.5)
    ax.scatter(xx_pred.flatten(), yy_pred.flatten(), predicted, facecolor=(0,0,0,0), s=20, edgecolor='#70b3f0')
    ax.set_xlabel('Age', fontsize=12)
    ax.set_ylabel('Experience', fontsize=12)
    ax.set_zlabel('Salary', fontsize=12)
    ax.locator_params(nbins=4, axis='x')
    ax.locator_params(nbins=5, axis='x')

ax1.view_init(elev=27, azim=112)
ax2.view_init(elev=16, azim=-51)
ax3.view_init(elev=60, azim=165)

fig.suptitle('Multi-Linear Regression Model Visualization ($R^2 = %.2f$)' % r2, fontsize=15, color='k')

fig.tight_layout()

核心问题分析 #

1. 模型调用错误：计算R²得分时，代码使用了未定义的model变量，实际训练完成的模型是model1，这会导致报错或异常结果（若环境中存在残留的同名变量）。
2. 数据验证缺失：预测值全为0的最可能原因是训练数据异常——要么Salary列被误读为全0，要么X特征与Y之间完全无线性相关性，或者数据读取时出现错误。
3. 坐标轴设置重复：代码中重复对x轴设置刻度数量，其中一处应为y轴。

修正步骤 #

1. 验证数据正确性：添加数据统计打印，确认Salary列的数值范围是否符合预期（30000-50000）。
2. 修正模型调用：将model.score(X, Y)替换为model1.score(X, Y)，确保使用训练好的模型计算R²得分。
3. 检查模型参数：打印模型的系数和截距，确认模型是否正常训练（若系数和截距全为0，说明数据存在问题）。
4. 修复坐标轴设置：将重复的x轴刻度设置改为y轴。

修正后代码 #

# 导入所需库
import pandas as pd 
import warnings  
import numpy as np  

# 可视化相关库
import seaborn as sns  
import matplotlib.pyplot as plt  
from mpl_toolkits.mplot3d import Axes3D  
%matplotlib widget

# 模型构建库
from sklearn import linear_model  


df = pd.read_csv('ml_data_salary.csv')

# 验证数据是否正确加载
print("数据基本统计信息：")
print(df.describe())

# 准备训练数据
X = df[['age', 'YearsExperience']].values
Y = df['Salary']  

# 生成预测用的特征网格
x = X[:, 0]
y = X[:, 1]
z = Y

xx_pred = np.linspace(25, 40, 30)  # 年龄范围
yy_pred = np.linspace(1, 10, 30)  # 工作年限范围
xx_pred, yy_pred = np.meshgrid(xx_pred, yy_pred)
model_viz = np.array([xx_pred.flatten(), yy_pred.flatten()]).T

# 训练模型并预测
ols = linear_model.LinearRegression()
model1 = ols.fit(X, Y)
# 打印模型参数，确认训练状态
print("\n模型系数：", model1.coef_)
print("模型截距：", model1.intercept_)
predicted = model1.predict(model_viz)

# 计算模型R²得分
r2 = model1.score(X, Y)
print("\n模型R²得分：", r2)

# 绘制可视化图
plt.style.use('default')

fig = plt.figure(figsize=(12, 4))

ax1 = fig.add_subplot(131, projection='3d')
ax2 = fig.add_subplot(132, projection='3d')
ax3 = fig.add_subplot(133, projection='3d')

axes = [ax1, ax2, ax3]

for ax in axes:
    ax.plot(x, y, z, color='k', zorder=15, linestyle='none', marker='o', alpha=0.5)
    ax.scatter(xx_pred.flatten(), yy_pred.flatten(), predicted, facecolor=(0,0,0,0), s=20, edgecolor='#70b3f0')
    ax.set_xlabel('Age', fontsize=12)
    ax.set_ylabel('Experience', fontsize=12)
    ax.set_zlabel('Salary', fontsize=12)
    ax.locator_params(nbins=4, axis='x')
    ax.locator_params(nbins=5, axis='y')  # 修正重复设置x轴的问题

ax1.view_init(elev=27, azim=112)
ax2.view_init(elev=16, azim=-51)
ax3.view_init(elev=60, azim=165)

fig.suptitle(f'Multi-Linear Regression Model Visualization ($R^2 = {r2:.2f}$)', fontsize=15, color='k')

fig.tight_layout()
plt.show()

内容的提问来源于stack exchange，提问作者Muhammad Ali Siddiqui