使用岭回归根据多个因素预测医疗费用

主要步骤流程：

数据集链接：

1. 导入包

In [1]:

# 导入包
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

2. 导入数据集

In [2]:

# 导入数据集
data = pd.read_csv('insurance.csv')
data.head()

Out[2]:

	age	sex	bmi	children	smoker	region	charges
0	19	female	27.900	0	yes	southwest	16884.92400
1	18	male	33.770	1	no	southeast	1725.55230
2	28	male	33.000	3	no	southeast	4449.46200
3	33	male	22.705	0	no	northwest	21984.47061
4	32	male	28.880	0	no	northwest	3866.85520

 

3. 数据预处理

3.1 检测缺失值

In [3]:

# 检测缺失值
null_df = data.isnull().sum()
null_df

Out[3]:

age         0
sex         0
bmi         0
children    0
smoker      0
region      0
charges     0
dtype: int64

3.2 标签编码&独热编码

In [4]:

# 标签编码&独热编码
data = pd.get_dummies(data, drop_first = True)
data.head()

Out[4]:

	age	bmi	children	charges	sex_male	smoker_yes	region_northwest	region_southeast	region_southwest
0	19	27.900	0	16884.92400	0	1	0	0	1
1	18	33.770	1	1725.55230	1	0	0	1	0
2	28	33.000	3	4449.46200	1	0	0	1	0
3	33	22.705	0	21984.47061	1	0	1	0	0
4	32	28.880	0	3866.85520	1	0	1	0	0

3.3 得到自变量和因变量

In [5]:

# 得到自变量和因变量
y = data['charges'].values
data = data.drop(['charges'], axis = 1)
x = data.values

3.4 拆分训练集和测试集

In [6]:

# 拆分训练集和测试集
from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.2, random_state = 1)
print(x_train.shape)
print(x_test.shape)
print(y_train.shape)
print(y_test.shape)

(1070, 8)
(268, 8)
(1070,)
(268,)

 

4. 构建不同参数的岭回归模型

4.1 模型1：构建岭回归模型

4.1.1 构建岭回归模型

In [7]:

# 构建不同参数的岭回归模型
# 模型1：构建岭回归模型（alpha = 20）
from sklearn.linear_model import Ridge
regressor = Ridge(alpha = 20, normalize = True, fit_intercept = True)
regressor.fit(x_train, y_train)

Out[7]:

Ridge(alpha=20, normalize=True)

4.1.2 得到数学表达式

In [8]:

# 得到数学表达式
print('数学表达式是：\n Charges = ', end='')
columns = data.columns
coefs = regressor.coef_
for i in range(len(columns)):
    print('%s * %.2f + ' %(columns[i], coefs[i]), end='')
print(regressor.intercept_)

数学表达式是：
 Charges = age * 12.48 + bmi * 17.21 + children * 14.86 + sex_male * 60.23 + smoker_yes * 1121.22 + region_northwest * -34.52 + region_southeast * 61.62 + region_southwest * -33.53 + 11938.446490743021

4.1.3 预测测试集

In [9]:

# 预测测试集
y_pred = regressor.predict(x_test)

4.1.4 得到模型MSE

In [10]:

# 得到模型 MSE
from sklearn.metrics import mean_squared_error
mse_score = mean_squared_error(y_test, y_pred)
print('alpha=20时，岭回归模型的MSE是：' , format(mse_score, ','))

alpha=20时，岭回归模型的MSE是： 138,769,173.1285671

4.2 模型2：构建岭回归模型

In [11]:

# 模型2：构建岭回归模型（alpha = 0.1）
regressor = Ridge(alpha = 0.1, normalize = True, fit_intercept = True)
regressor.fit(x_train, y_train)

Out[11]:

Ridge(alpha=0.1, normalize=True)

In [12]:

# 得到线性表达式
print('数学表达式是：\n Charges = ', end='')
columns = data.columns
coefs = regressor.coef_
for i in range(len(columns)):
    print('%s * %.2f + ' %(columns[i], coefs[i]), end='')
print(regressor.intercept_)

数学表达式是：
 Charges = age * 234.53 + bmi * 291.63 + children * 361.72 + sex_male * -88.02 + smoker_yes * 21586.00 + region_northwest * -266.87 + region_southeast * -672.40 + region_southwest * -691.71 + -9237.600606458109

In [13]:

# 预测测试集
y_pred = regressor.predict(x_test)

In [14]:

# 得到模型的MSE
mse_score = mean_squared_error(y_test, y_pred)
print('alpha=0.1时，岭回归模型的MSE是：' , format(mse_score, ','))

alpha=0.1时，岭回归模型的MSE是： 36,841,099.26516503

4.3 模型3：构建岭回归模型

In [15]:

# 模型3：构建岭回归模型（alpha = 0.01）
regressor = Ridge(alpha = 0.01, normalize = True, fit_intercept = True)
regressor.fit(x_train, y_train)

Out[15]:

Ridge(alpha=0.01, normalize=True)

In [16]:

# 得到线性表达式
print('数学表达式是：\n Charges = ', end='')
columns = data.columns
coefs = regressor.coef_
for i in range(len(columns)):
    print('%s * %.2f + ' %(columns[i], coefs[i]), end='')
print(regressor.intercept_)

数学表达式是：
 Charges = age * 255.00 + bmi * 318.27 + children * 402.86 + sex_male * -223.99 + smoker_yes * 23546.28 + region_northwest * -377.66 + region_southeast * -992.59 + region_southwest * -875.29 + -11075.028462288014

In [17]:

# 预测测试集
y_pred = regressor.predict(x_test)

In [18]:

# 得到模型的MSE
mse_score = mean_squared_error(y_test, y_pred)
print('alpha=0.01时，岭回归模型的MSE是：' , format(mse_score, ','))

alpha=0.01时，岭回归模型的MSE是： 35,539,055.332710184

4.4 模型4：构建岭回归模型

In [19]:

# 模型4：构建岭回归模型（alpha = 0.0001）
regressor = Ridge(alpha = 0.0001, normalize = True, fit_intercept = True)
regressor.fit(x_train, y_train)

Out[19]:

Ridge(alpha=0.0001, normalize=True)

In [20]:

# 得到线性表达式
print('数学表达式是：\n Charges = ', end='')
columns = data.columns
coefs = regressor.coef_
for i in range(len(columns)):
    print('%s * %.2f + ' %(columns[i], coefs[i]), end='')
print(regressor.intercept_)

数学表达式是：
 Charges = age * 257.47 + bmi * 321.59 + children * 408.01 + sex_male * -241.97 + smoker_yes * 23784.06 + region_northwest * -395.90 + region_southeast * -1037.90 + region_southwest * -902.75 + -11295.364555495733

In [21]:

# 预测测试集
y_pred = regressor.predict(x_test)

In [22]:

# 得到模型的MSE
mse_score = mean_squared_error(y_test, y_pred)
print('alpha=0.0001时，岭回归模型的MSE是：' , format(mse_score, ','))

alpha=0.0001时，岭回归模型的MSE是： 35,479,846.30114783

 

结论： 由上面4个模型可见，不同的模型超参数对岭回归模型性能的影响不同。