5-3 简单线性回归的实现
Last updated
Last updated
import numpy as np
import matplotlib.pyplot as plt
x = np.array([1., 2., 3., 4., 5.])
y = np.array([1., 3., 2.
plt.scatter(x, y)
plt.axis([0, 6, 0, 6])
plt.show()
输出结果:
x_mean = np.mean(x)
y_mean = np.mean(y)
num = 0.0
d = 0.0
for x_i, y_i in zip(x, y):
num += (x_i - x_mean) * (y_i - y_mean)
d += (x_i - x_mean) ** 2
a = num / d
b = y_mean - a * x_mean
y_hat = a * x + b
plt.scatter(x, y)
plt.plot(x, y_hat, color='r')
plt.axis([0, 6, 0, 6])
plt.show()
输出结果:
import numpy as np
class SimpleLinearRegression1:
def __init__(self):
"""初始化Single Linear Regression模型"""
self.a_ = None
self.b_ = None
def fit(self, x_train, y_train):
"""根据训练数据集X_train, y_train训练Single Linear Regression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_i, y_i in zip(x_train, y_train):
num += (x_i - x_mean) * (y_i - y_mean)
d += (x_i - x_mean) ** 2
self.a_ = num / d
self.b_ = y_mean - self.a_ * x_mean
def predict(self, x_predict):
"""给定待测数据集X_predict,返回表示x_predict的结果向量"""
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 [self._predict(x) for x in x_predict]
def _predict(self, x_single):
"""给定单个待预测数据s_single,返回x_single的预测结果"""
return self.a_ * x_single + self.b_
def __repr__(self):
return "SimpleLinearRegression1()"
reg1 = SimpleLinearRegression1()
reg1.fit(x, y)
y_hat1 = a * x + b
plt.scatter(x, y)
plt.plot(x, y_hat1, color='r')
plt.axis([0, 6, 0, 6])
plt.show()
输出结果: