數據集：世界幸福指數數據集中的變量有幸福指數排名、國家/地區、幸福指數得分、人均國內生產總值、健康預期壽命、自由權、社會支持、慷慨程度、清廉指數。我們選擇GDP per Capita和Freedom，來預測幸福指數得分。
文件一：linear，在上一篇博客里。
文件二：multivariate_linear_regression.py
import numpy as np
"""用于科學計算的一個庫，提供了多維數組對象以及操作函數"""
import pandas as pd
"""一個用于數據導入、導出、清洗和分析的庫，本文中導入csv格式數據等等"""
import matplotlib.pyplot as plt
"""pyplot提供了繪圖接口"""
import matplotlib
"""一個強大的繪圖庫"""
import plotly
"""網頁交互數據可視化工具，可以直接從https://plotly.com/python/官網copy代碼進行修改"""
import plotly.graph_objs as goplotly.offline.init_notebook_mode()
# 設置matplotlib正常顯示中文和負號
matplotlib.rcParams['font.family'] = 'SimHei' # 指定默認字體為黑體
matplotlib.rcParams['axes.unicode_minus'] = False # 正確顯示負號from prepare_for_training import LinearRegressiondata = pd.read_csv("D:/machine_learning/archive/2017.csv")
train_data = data.sample(frac = 0.8)
"""從數據集中隨機抽取80%的數據進行訓練"""
test_data = data.drop(train_data.index)
"""從數據集中移除訓練集得到測試機"""input_param_name_1 = 'Economy..GDP.per.Capita.'
input_param_name_2 = 'Freedom'
output_param_name = 'Happiness.Score'x_train = train_data[[input_param_name_1,input_param_name_2]].values
y_train = train_data[[output_param_name]].valuesx_test = test_data[[input_param_name_1,input_param_name_2]].values
y_test = test_data[[output_param_name]].valuesplot_training_trace = go.Scatter3d(x = x_train[:,0].flatten(),y = x_train[:,1].flatten(),z = y_train.flatten(),name = 'Training Set',mode = 'markers',marker = {'size':10,'opacity':1,'line':{'color':'rgb(255,255,255)','width':1},}
)plot_test_trace = go.Scatter3d(x = x_test[:,0].flatten(),y = x_test[:,1].flatten(),z = y_test.flatten(),name = 'Test Set',mode = 'markers',marker = {'size':10,'opacity':1,'line':{'color':'rgb(255,255,255)','width':1},}
)plot_layout = go.Layout(title = 'Data Sets',scene = {'xaxis':{'title':input_param_name_1},'yaxis':{'title':input_param_name_2},'zaxis':{'title':output_param_name}},margin = {'l':0,'r':0,'b':0,'t':0}
)
plot_data = [plot_training_trace,plot_test_trace]
plot_figure = go.Figure(data = plot_data,layout=plot_layout)
plotly.offline.plot(plot_figure)
"""plt.scatter(x_train,y_train,label ='Train data')
plt.scatter(x_test,y_test,label ='Test data')
plt.xlabel(input_param_name_1)
plt.ylabel(output_param_name)
plt.title('Happy')
plt.legend()
plt.show()""""""訓練次數，學習率"""
num_iterations = 500
learning_rate = 0.01
polynomial_degree = 0
sinusoid_degree = 0linear_regression = LinearRegression(x_train,y_train,polynomial_degree,sinusoid_degree)
(theta,cost_history) = linear_regression.train(learning_rate,num_iterations)
print('開始時的損失',cost_history[0])
print('訓練后的損失',cost_history[-1])plt.plot(range(num_iterations),cost_history)
plt.xlabel('Iter')
plt.ylabel('cost')
plt.title('gradient descent progress')
plt.show()predictions_num = 10x_min = x_train[:,0].min()
x_max = x_train[:,0].max()y_min = x_train[:,1].min()
y_max = x_train[:,1].max()x_axis = np.linspace(x_min,x_max,predictions_num)
y_axis = np.linspace(y_min,y_max,predictions_num)x_predictions = np.zeros((predictions_num * predictions_num,1))
y_predictions = np.zeros((predictions_num * predictions_num,1))x_y_index = 0
for x_index,x_value in enumerate(x_axis):for y_index,y_value in enumerate(y_axis):x_predictions[x_y_index] = x_valuey_predictions[x_y_index] = y_valuex_y_index += 1z_predictions = linear_regression.predict(np.hstack((x_predictions,y_predictions)))plot_predictions_trace = go.Scatter3d(x = x_predictions.flatten(),y = y_predictions.flatten(),z = z_predictions.flatten(),name = 'Prediction Plane',mode = 'markers',marker = {'size':1,},opacity=0.8,surfaceaxis=2,
)plot_data = [plot_training_trace,plot_test_trace,plot_predictions_trace]
plot_figure = go.Figure(data = plot_data,layout=plot_layout)
plotly.offline.plot(plot_figure)效果：
損失值較單變量而言，由降低約0.1.
)
