Python 绘制线性回归散点图和置信区间线2

Posted 2022-07-18 空中旋转篮球

和上一篇类似，绘制线性回归方程和置信区间线。使用到的库：

import matplotlib as mpl
import seaborn as sns
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

使用的数据，采用随机创建方法，不同于上一篇，这里的x，y分别是二维数组。

完整代码如下：

import matplotlib as mpl
import seaborn as sns
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

# 构造数据
np.random.seed(1000)
x = np.random.randint(1,100,(100,1))
y = [2*i+(np.random.randint(-9,9))**2+np.random.randint(100) for i in x]
print(x,y)

size1 = 20
fontdict = 'weight': 'bold','size':size1,'color':'k','family':'SimHei'
mpl.rcParams.update(
    
    'text.usetex': False,
    'font.family': 'stixgeneral',
    'mathtext.fontset': 'stix',
    "font.family":'serif',
    "font.size": size1,
    "font.serif": ['Times New Roman'],
    
    )
fig,ax = plt.subplots(figsize = (8,6))
sns.regplot(x,y,ax = ax)
ax.set_xlim(0,100)
ax.set_ylim(0,400)
ax.set_xlabel('xlabel')
ax.set_ylabel('ylabel')

# 拟合方程
model = LinearRegression()
model.fit(x,y)
a = model.coef_[0][0]
b = model.intercept_[0]
ax.text(8,350,'$y$ = :.2f$x$ + :.2f'.format(a,b))

# R2
r2 = r2_score(y,model.predict(x)).round(2)
ax.text(8,300,f'$R$$^2$ = r2')

std=np.std(model.predict(x))
std_z = 1.96 # from z-table for 95%
confidence_interval = std * std_z
plt.plot(x, model.predict(x) - confidence_interval,label="95%-")
plt.plot(x, model.predict(x) + confidence_interval,label="95%+")
plt.tight_layout()
plt.savefig('out.png',dpi = 600)
plt.show()

 显示效果如下：

 实际应用中，一般选取不同比例数据作为训练数据和测试数据，我们可以采用：

from sklearn.model_selection import train_test_split库实现数据的分割。
具体代码如下：

# splits the training and test data set in 80% : 20%
# assign random_state to any value.This ensures consistency.
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2, random_state=5)