《机器学习的数学修炼》

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目录：

 

 

 

 

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第六章 线性回归：

1.1三种方法实现：

import numpy as np
import pandas as pd
from scipy import stats

df = pd.read_csv("DBS_SingDollar.csv")
# X = df[df.columns[0]]
# y = df[df.columns[1]]
X = df["DBS"]
Y = df["SGD"]
slope,intercept,r_value,p_value,std_err= stats.linregress(Y,X)
print(slope,intercept)

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from sklearn import linear_model

df_DBS = pd.read_csv("DBS_SingDollar.csv")
model = linear_model.LinearRegression()

X = df_DBS['DBS']
Y = df_DBS['SGD']

X = np.array(X).reshape(-1,1)
model.fit(X,Y)
Y_predict = model.predict(X)
print(Y_predict)

plt.scatter(X,Y,color = (0,0,0))

plt.plot(X,Y_predict,color = "blue",linewidth = 2)
plt.xlabel("  ",fontsize = 16)
plt.ylabel("  ",fontsize = 16)
plt.show()

import pandas as pd
df = pd.read_csv("DBS_SingDollar.csv")
#print(dir(pd))
X = df.loc[:,["SGD"]]
Y = df.loc[:,["DBS"]]
from sklearn import linear_model
model = linear_model.LinearRegression()
model.fit(X,Y)
a = model.coef_
b = model.intercept_
a = float(a)
b = float(b)
print("the output of the trained model is")
print("Y = ",a,"*X + ",b)

pred = model.predict(X)
print(pred)

#rmse
from sklearn.metrics import mean_squared_error
rmse = mean_squared_error(Y,pred)**0.5
print(rmse)

1.2 相关链接：

python中loc函数的用法：

https://blog.csdn.net/weixin_29288653/article/details/113500824

python中 .reshape 的用法：reshape(1,-1)：

https://blog.csdn.net/qq_44391957/article/details/120090486?ops_request_misc=%257B%2522request%255Fid%2522%253A%2522165854506016782390589615%2522%252C%2522scm%2522%253A%252220140713.130102334..%2522%257D&request_id=165854506016782390589615&biz_id=0&utm_medium=distribute.pc_search_result.none-task-blog-2~all~sobaiduend~default-1-120090486-null-null.142^v33^pc_search_v2,185^v2^control&utm_term=X%20%3D%20np.array%28X%29.reshape%28-1%2C1%29&spm=1018.2226.3001.4187

2.1 普通最小二乘法的计算：

 

 

同时：

 

 

 

2.2关于MSE RMSE MAE R-Squared（主要看前两个）：

https://blog.csdn.net/lch551218/article/details/113573931?ops_request_misc=%257B%2522request%255Fid%2522%253A%2522165854608116781683916161%2522%252C%2522scm%2522%253A%252220140713.130102334.pc%255Fall.%2522%257D&request_id=165854608116781683916161&biz_id=0&utm_medium=distribute.pc_search_result.none-task-blog-2~all~first_rank_ecpm_v1~rank_v31_ecpm-2-113573931-null-null.142^v33^pc_search_v2,185^v2^control&utm_term=MAE%E3%80%81R-Squared&spm=1018.2226.3001.4187

2.3 线性回归模型的基本假定：

 

 

 

 

 6.4之后暂时没看，需要大把时间。

 

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 （未完待续，暂时不看这本书）