一元线性回归模型案例（机器学习）

1.什么是机器学习

简单来说：从数据中学习

步骤：

2.机器学习分类

通过对数据的学习,寻找属性和标记之间的映射关系

回归（regression）： 预测连续值

分类（classification）： 预测离散值

一元线性回归问题

模型：y = wx + b

模型变量：x

最佳拟合直线：拟合误差和最小

损失函数/代价函数：模型的预测值与真实值的不一致的程度

最值问题（极值问题）

思路：极值点的偏导数为0

注：使用上述方法求得的解成为解析解或封闭解，后续会讲解使用迭代方法求极值

一元线性回归实例

问题导入（参照慕课：《tensorflow2.0神经网络与深度学习实践》）

程序代码：

第一种方法，使用python方法

#实现房屋销售预测实例

import tensorflow as tf
import numpy as np

#test database
area = [128.15, 45.0, 141.43, 106.27, 99.0, 53.84, 85.36, 70.00]
#step
"""
1,load sample data
2,learning model:calculate w,b
3,forecast house price
"""
# 加载样本数据
x = [137.97, 104.50, 100.00, 124.32, 79.20, 99.00, 124.00, 114.00,  # 商品房面积
     106.69, 138.05, 53.75, 46.91, 68.00, 63.02, 81.26, 86.21]
y = [145.00, 110.00, 93.00, 116.00, 65.32, 104.00, 118.00, 91.00,  # 房价
     62.00, 133.00, 51.00, 45.00, 78.50, 69.65, 75.69, 95.30]

#python预测房价
class python_realization:
    _meanX = sum(x) / len(x)  # x平均数
    _meanY = sum(y) / len(y)  # y平均数

    _sumXY = 0
    _sumX = 0
    _x = []
    _y = []

    _w = 0.
    _b = 0.

    x_test = []

    def __init__(self, x, y):
        self._x = x
        self._y = y

    def calc(self):
        for i in range(len(x)):
            self._sumXY += (x[i] - self._meanX) * (y[i] - self._meanY)
            self._sumX += (x[i] - self._meanX) * (x[i] - self._meanX)

        self._w = self._sumXY / self._sumX
        self._b = self._meanY - self._w * self._meanX

        print(type(self._w), type(self._b), "\n")

        print("w = ", self._w, "\nb = ", self._b, "\n")
    def forecast(self,x_test):
        # 预测房价
        #x_test = [128.15, 45.00, 141.43, 106.27, 99.00, 53.84, 85.36, 70.00]
        self.x_test.append(x_test)

        print("面积\t      预测价格")
        for i in range(len(x_test)):
            print(x_test[i], "\t", round(self._w * x_test[i] + self._b, 2))  # round保留两位小数

第二种方法：使用tensorflow

# tensorflow实现房屋销售预测实例
import tensorflow as tf
import numpy as np

x = tf.constant([137.97, 104.50, 100.00, 124.32, 79.20, 99.00, 124.00, 114.00,  # 商品房面积
                 106.69, 138.05, 53.75, 46.91, 68.00, 63.02, 81.26, 86.21])
y = tf.constant([145.00, 110.00, 93.00, 116.00, 65.32, 104.00, 118.00, 91.00,  # 房价
                 62.00, 133.00, 51.00, 45.00, 78.50, 69.65, 75.69, 95.30])

meanX = tf.reduce_mean(x)
meanY = tf.reduce_mean(y)

sumXY = tf.reduce_sum((x - meanX) * (y - meanY))#降维
sumX = tf.reduce_sum((x - meanX) * (x - meanX))

w = sumXY / sumX
b = meanY - w * meanX

print(type(w), type(b))

print("权值：w = ", w, "\n偏置值b = ", b, )
print("线性模型：y=", w.numpy(), "x+", b.numpy())

x_test = np.array([128.15, 45.00, 141.43, 106.27, 99.00, 53.84, 85.36, 70.00])
y_pred = (w * x_test + b).numpy()

print("\n面积\t预测价格")
for i in range(len(x_test)):
    print(x_test[i], "\t", round(y_pred[i], 2))  # round保留两位小数

import matplotlib.pyplot as plt

plt.rcParams['font.sans-serif']=['SimHei']   #中文字体配置
plt.rcParams['axes.unicode_minus']=False  #符号显示

plt.figure()

plt.scatter(x,y,color='blue',label='销售记录')
plt.scatter(x_test,y_pred,color='red',label='预测房价')
plt.plot(x_test,y_pred,color='yellow',label='拟合直线',linewidth=2)

plt.xlabel("面积（平方米）",fontsize=14)
plt.ylabel("价格（万元）",fontsize=14)

plt.xlim((40,150))
plt.ylim((40,150))

plt.suptitle("商品房销售价格预测图",fontsize=20)

plt.legend(loc="upper left")
plt.show()

结果图：

参考链接：慕课《tensorflow2.0神经网络与深度学习实践》