机器学习-逻辑回归之考试通过与否预测
逻辑回归预测考试是否通过
声明：本篇是对课程学习的记录，如有侵权请联系我删除。
注：本篇文章基于sklearn库，这里我们应该掌握的基础知识有：logistic回归。
目标：基于数据集建立逻辑回归模型，并预测给定两门分数的情况下，预测第三门分数是否能通过；建立二阶边界，提高模型的准确率。
# 加载数据
import pandas as pd
import numpy as np
data = pd.read_csv('examdata.csv')
data.head()
| Exam1 | Exam2 | Pass | |
|---|---|---|---|
| 0 | 34.623660 | 78.024693 | 0 |
| 1 | 30.286711 | 43.894998 | 0 |
| 2 | 35.847409 | 72.902198 | 0 |
| 3 | 60.182599 | 86.308552 | 1 |
| 4 | 79.032736 | 75.344376 | 1 |
# 可视化数据
import matplotlib.pyplot as plt
fig1 = plt.figure()
plt.figure(figsize=(8,8))
plt.scatter(data.loc[:,'Exam1'],data.loc[:,'Exam2'])
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.show()
#添加标签
mask = data.loc[:,'Pass']==1
fig2 = plt.figure()
plt.figure(figsize=(8,8))
passed = plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed = plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()
# 对变量进行数据赋值
x = data.drop(['Pass'],axis=1)
#x.head()
y = data.loc[:,'Pass']
#y.head()
x1 = data.loc[:,'Exam1']
#x1.head()
x2 = data.loc[:,'Exam2']
#x2.head()
# 建立并训练模型
from sklearn.linear_model import LogisticRegression
LR = LogisticRegression()
LR.fit(x,y)
LogisticRegression()
# 显示预测结果
y_predict = LR.predict(x)
print(y_predict)
[0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1
1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1
1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1]
from sklearn.metrics import accuracy_score
accuracy = accuracy_score(y,y_predict)
print(accuracy)
0.89
# 进行结果测试
y_test = LR.predict([[70,65]])
#print(y_test)
print('passed' if y_test==1 else 'failed')
#画出直线
theta0 = LR.intercept_ #截距
theta1,theta2 = LR.coef_[0][0],LR.coef_[0][1]
print(theta0,theta1,theta2)
[-25.05219314] 0.20535491217790372 0.20058380395469036
边界函数为： θ 0 + θ 1 × x 1 + θ 2 × x 2 = 0 \theta_0+\theta_1 × x_1+\theta_2 × x_2 = 0 θ0+θ1×x1+θ2×x2=0
x2_new = -(theta0+theta1*x1)/theta2
print(x2_new)
0 89.449169
1 93.889277
2 88.196312
3 63.282281
4 43.983773
...
95 39.421346
96 81.629448
97 23.219064
98 68.240049
99 48.341870
Name: Exam1, Length: 100, dtype: float64
fig3 = plt.figure()
passed = plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed = plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.plot(x1,x2_new)
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()
二阶边界函数： θ 0 + θ 1 x 1 + θ 2 x 2 + θ 3 x 1 2 + θ 4 x 2 2 + θ 5 x 1 x 2 = 0 \theta_0+\theta _1x_1+\theta _2x_2+\theta _3x_{1}^{2}+\theta _4x_{2}^{2}+\theta _5x_1x_2=0 θ0+θ1x1+θ2x2+θ3x12+θ4x22+θ5x1x2=0
#创建新的数据集
x1_2 = x1*x1
x2_2 = x2*x2
x1_x2 = x1*x2
#print(x1,x1_2)
x_new = {'x1':x1,'x2':x2,'x1_2':x1_2,'x2_2':x2_2,'x1_x2':x1_x2}
x_new = pd.DataFrame(x_new)
print(x_new)
x1 x2 x1_2 x2_2 x1_x2
0 34.623660 78.024693 1198.797805 6087.852690 2701.500406
1 30.286711 43.894998 917.284849 1926.770807 1329.435094
2 35.847409 72.902198 1285.036716 5314.730478 2613.354893
3 60.182599 86.308552 3621.945269 7449.166166 5194.273015
4 79.032736 75.344376 6246.173368 5676.775061 5954.672216
.. ... ... ... ... ...
95 83.489163 48.380286 6970.440295 2340.652054 4039.229555
96 42.261701 87.103851 1786.051355 7587.080849 3681.156888
97 99.315009 68.775409 9863.470975 4730.056948 6830.430397
98 55.340018 64.931938 3062.517544 4216.156574 3593.334590
99 74.775893 89.529813 5591.434174 8015.587398 6694.671710
[100 rows x 5 columns]
LR2 = LogisticRegression()
LR2.fit(x_new,y)
LogisticRegression()
y2_predict = LR2.predict(x_new)
accuracy2 = accuracy_score(y,y2_predict)
print(accuracy2)
1.0
LR2.coef_
array([[-8.95942818e-01, -1.40029397e+00, -2.29434572e-04,
3.93039312e-03, 3.61578676e-02]])
x1_new = x1.sort_values()#排序,原因是让后面画图按照次序画图以防止画图很凌乱无序。
print(x1,x1_new)
0 34.623660
1 30.286711
2 35.847409
3 60.182599
4 79.032736
...
95 83.489163
96 42.261701
97 99.315009
98 55.340018
99 74.775893
Name: Exam1, Length: 100, dtype: float64 63 30.058822
1 30.286711
57 32.577200
70 32.722833
36 33.915500
...
56 97.645634
47 97.771599
51 99.272527
97 99.315009
75 99.827858
Name: Exam1, Length: 100, dtype: float64
theta0 = LR2.intercept_
theta1 = LR2.coef_[0][0]
theta2 = LR2.coef_[0][1]
theta3 = LR2.coef_[0][2]
theta4 = LR2.coef_[0][3]
theta5 = LR2.coef_[0][4]
a = theta4
b = theta2+theta5*x1_new
c = theta0+theta1*x1_new+theta3*x1_new*x1_new
x2_new_boundary = (-b+(np.sqrt(b*b-4*a*c)))/(2*a)
plt.plot(x1_new,x2_new_boundary)
[]
fig4 = plt.figure()
passed = plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed = plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.plot(x1_new,x2_new_boundary)
plt.title('Exam1 VS Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()
如果想要进行本例子实战的数据链接如下：https://pan.baidu.com/s/1dPKCOMse7Ai1WkrJs64xBw
提取码：1234，支持flare老师课程！