線性迴歸的定義：線性迴歸在假設特證滿足線性關係，根據給定的訓練數據訓練一個模型，並用此模型進行預測。

簡單線性迴歸的實現

手動生成五個點 (1,1),(2,3),(3,2),(4,3),(5,5) (1,1),(2,3),(3,2),(4,3),(5,5)(1,1),(2,3),(3,2),(4,3),(5,5) 求一條最佳直線來擬合這五個點

#SimpleLinearRegression.py

import numpy as np

class SimpleLinearRegression1:

def __init__(self):

"""初始化Simple Linear Regression模型"""

self.a_ = None

self.b_ = None

def fit(self, x_train, y_train):

"""根據訓練數據集x_train, y_train訓練 SimpleLinearRegression模型"""

assert x_train.ndim == 1,\

"Simple Linear Regressor can only solve single feature training data."

assert len(x_train) == len(y_train),\

"the size of x_train must be equal to the size of y_train"

x_mean = np.mean(x_train)

y_mean = np.mean(y_train)

num = 0.0

d = 0.0

for x,y in zip(x_train, y_train):

num += (x - x_mean) * (y - y_mean)

d += (x - x_mean) ** 2 self.a_ = num/d

self.b_ = y_mean - self.a_ * x_mean

return self

def predict(self, x_predict):

"""給定待預測數據集x_predict，返回x_predict的結果向量"""

assert x_predict.ndim == 1,\

"Simple Linear Regressor can only solve single feature training data."

assert self.a_ is not None and self.b_ is not None,\

"must fit before predict!"

return np.array([self._predict(x) for x in x_predict])

def _predict(self, x_single):

"""給定單個待預測數據x_single，返回x_single的預測結果"""

return self.a_ * x_single + self.b_

def __repr__(self):

return "SimpleLinearRegression1()"

*****************************************************************************

#test.py

import numpy as np

from SimpleLinearRegression import SimpleLinearRegression1

import matplotlib.pyplot as plt

x = np.array([1.,2.,3.,4.,5.])

y = np.array([1.,3.,2.,3.,5.])

x_predict = 6 reg1= SimpleLinearRegression1()

reg1.fit(x, y)

y_predict = reg1.predict(np.array([x_predict]))

print(y_predict)

y_hat = reg1.a_ * x + reg1.b_

plt.scatter(x, y)

plt.plot(x, y_hat, color = 'r')

plt.axis([0,6,0,6])

plt.show()

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