数据集：公开的World Happiness Report | Kaggle中的happiness dataset2017.

目标：基于GDP值预测幸福指数。（单特征预测）

代码：

文件一：prepare_for_traning.py

"""用于科学计算的一个库，提供了多维数组对象以及操作函数"""
from utils.features import prepare_for_training
"""数据预处理的一个私库"""

class LinearRegression:
    def __init__(self,data,labels,polynomial_degree = 0,sinusoid_degree = 0,normalize_data = True):
        """
        进行预处理操作
        :param data:
        :param labels:
        :param polynomial_degree:
        :param sinusoid_degree:
        :param normalize_data:
        """
        (data_processed,
            features_mean,
            features_deviation) = prepare_for_training(data,polynomial_degree = 0,sinusoid_degree = 0,normalize_data = True)
        self.data = data_processed
        self.labels = labels
        self.features_mean = features_mean
        self.features_deviation = features_deviation
        self.polynomial_degree = polynomial_degree
        self.sinusoid_degree = sinusoid_degree
        self.normalize_data = normalize_data
        num_features = self.data.shape[1]
        self.theta = np.zeros((num_features,1))
    """"数据，学习率，训练次数"""
    def train(self,alpha,num_iterations = 500):
        """训练模块：梯度下降"""
        cost_history = self.gradient_descent(alpha,num_iterations)
        return self.theta,cost_history

    def gradient_descent(self,alpha,num_iterations):
        """迭代模块"""
        cost_history = []
        for _ in range(num_iterations):
            self.gradient_step(alpha)
            cost_history.append(self.cost_function(self.data,self.labels))
        return cost_history

    def gradient_step(self,alpha):
        """
        梯度下降参数更新算法，矩阵计算，使用小批量梯度下降算法
        :param self:
        :param alpha:
        :return:
        """
        num_examples = self.data.shape[0]
        prediction = LinearRegression.hypothesis(self.data,self.theta)
        delta = prediction - self.labels
        theta = self.theta
        theta = theta - alpha*(1/num_examples)*(np.dot(delta.T,self.data)).T
        self.theta = theta

    def cost_function(self,data,labels):
        """
        损失计算模块
        :param self:
        :param data:
        :param labels:
        :return:
        """
        num_examples = data.shape[0]
        delta = LinearRegression.hypothesis(self.data,self.theta) - labels
        cost = (1/2)*np.dot(delta.T,delta)/num_examples
        """print(cost.shape)"""
        return cost[0][0]

    """装饰器"""
    @staticmethod
    def hypothesis(data,theta):
        prediction = np.dot(data,theta)
        return prediction

    def get_cost(self,data,labels):
        data_processed = prepare_for_training(data,
         self.polynomial_degree,
         self.sinusoid_degree,
         self.normalize_data
         )[0]

        return self.cost_function(data_processed,labels)

    def predict(self,data):
        data_processed = prepare_for_training(data,
        self.polynomial_degree,
        self.sinusoid_degree,
        self.normalize_data
        )[0]
        predictions = LinearRegression.hypothesis(data_processed,self.theta)

        return predictions

文件2：Linear_regression.py 

import numpy as np
"""用于科学计算的一个库，提供了多维数组对象以及操作函数"""
import pandas as pd
"""一个用于数据导入、导出、清洗和分析的库，本文中导入csv格式数据等等"""
import matplotlib.pyplot as plt
"""pyplot提供了绘图接口"""
import matplotlib
"""一个强大的绘图库"""

# 设置matplotlib正常显示中文和负号
matplotlib.rcParams['font.family'] = 'SimHei'  # 指定默认字体为黑体
matplotlib.rcParams['axes.unicode_minus'] = False  # 正确显示负号


from prepare_for_training import LinearRegression

data = pd.read_csv("D:/machine_learning/archive/2017.csv")
train_data = data.sample(frac = 0.8)
test_data = data.drop(train_data.index)

input_param_name = 'Economy..GDP.per.Capita.'
output_param_name = 'Happiness.Score'

x_train = train_data[[input_param_name]].values
y_train = train_data[[output_param_name]].values

x_test = test_data[[input_param_name]].values
y_test = test_data[[output_param_name]].values

plt.scatter(x_train,y_train,label ='Train data')
plt.scatter(x_test,y_test,label ='Test data')
plt.xlabel(input_param_name)
plt.ylabel(output_param_name)
plt.title('Happy')
plt.legend()
plt.show()

"""训练次数，学习率"""
num_iterations = 500
learning_rate = 0.01

linear_regression = LinearRegression(x_train,y_train)
(theta,cost_history) = linear_regression.train(learning_rate,num_iterations)
print('开始时的损失',cost_history[0])
print('训练后的损失',cost_history[-1])

plt.plot(range(num_iterations),cost_history)
plt.xlabel('Iter')
plt.ylabel('cost')
plt.title('损失值')
plt.show()

predictions_num = 100
x_predictions = np.linspace(x_train.min(),x_train.max(),predictions_num).reshape(predictions_num,1)
y_predictions = linear_regression.predict(x_predictions)

plt.scatter(x_train,y_train,label ='Train data')
plt.scatter(x_test,y_test,label ='Test data')
plt.plot(x_predictions,y_predictions,'r',label = 'Prediction')
plt.xlabel(input_param_name)
plt.ylabel(output_param_name)
plt.title('Happy')
plt.legend()
plt.show()

效果图：