import numpy as np
import matplotlib.pyplot as plt
x = np.array([1,2,3,4,5])
y = np.array([1,3,2,3,5])
​
x_mean = np.mean(x)
y_mean = np.mean(y)
​
a = np.sum(np.subtract(x,x_mean)*np.subtract(y,y_mean))/np.sum(np.power((x-x_mean),2))
b = y_mean-a*x_mean
y_predict = a*x + b
print("a =",a,"\n","b = ",b)
print(y_predict)
plt.scatter(x,y)
plt.plot(x,y_predict)

class SimpleLinearRegression:
    def __init__(self):
        """初始化简单线性模型"""
        self.a_ = None
        self.b_ = None
    def fit(self,trainX,trainY):
        """根据数据训练简单线性模型"""
        assert trainX.ndim==1,"SimpleLinearRegression must be input 1D"
        x_mean = np.mean(trainX)
        y_mean = np.mean(trainY)
        self.a_ = np.dot(np.subtract(trainX,x_mean),np.subtract(trainY,y_mean))/np.sum(np.power((trainX-x_mean),2))
        self.b_ = y_mean-self.a_*x_mean
        return self
    def _predict(self,test_x):
        """给定单个待测数，返回预测值"""
        test_y = self.a_*test_x + self.b_
        return test_y
    def predict(self,testX):
        """给定待测数据集，返回结果向量"""
        return np.array([self._predict(i) for i in testX])

simpleLinearRegression = SimpleLinearRegression()
simpleLinearRegression.fit(x,y)
print(simpleLinearRegression.a_)
print(simpleLinearRegression.b_)
simpleLinearRegression.predict(x)

mae = np.sum(np.abs(test_y-testY))/test_y.shape[0]
mae
 >>>4.399066068730565

r = 1-mse/np.var(testY)
r
>>>0.2541624531120106


from sklearn.metrics import r2_score
​
r2_score(testY,test_y)
 
>>>0.2541624531120107

from sklearn.metrics import r2_score
​
class LinearRegressor:
    def __init__(self):
        self.coef_ = None # θ向量
        self.intercept_ = None # 截距
        self._theta = None
    def fit(self,trainX,trainY):
        x = np.hstack((np.ones((trainX.shape[0],1)),trainX))
        self._theta = np.linalg.inv(np.dot(x.T,x)).dot(x.T).dot(trainY)
        self.intercept_ = self._theta[0] # 截距
        self.coef_ = self._theta[1:] # 权重参数weights
        return self
    def predict(self,testX):
        x = np.hstack((np.ones((testX.shape[0],1)),testX))
#         y = np.dot(x,self._theta.reshape(-1,1))
        y = np.dot(x,self._theta)
        return y
    def score(self,testX,testY):
        return r2_score(testY,self.predict(testX))

boston = datasets.load_boston()
x = boston.data
y = bsoton.target
x = x[y<50]
y = y[y<50]
x.shape
 
>>>(490, 13)

 
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
​
​
trainX,testX,trainY,testY = train_test_split(x,y,test_size=0.2,random_state=666)
lin_reg = LinearRegression()
lin_reg.fit(trainX,trainY)
print(lin_reg.predict(testX).shape)
print(lin_reg.coef_)
print(lin_reg.intercept_)
print(lin_reg.score(testX,testY))
 
 
 
>>>(98,)
>>>[-1.18919477e-01  3.63991462e-02 -3.56494193e-02  5.66737830e-02
    -1.16195486e+01  3.42022185e+00 -2.31470282e-02 -1.19509560e+00
     2.59339091e-01 -1.40112724e-02 -8.36521175e-01  7.92283639e-03
    -3.81966137e-01]
 >>>34.16143549624665
 >>>0.8129802602658495