"""
# 利用 diabetes數(shù)據(jù)集來學(xué)習(xí)線性回歸 
# diabetes 是一個(gè)關(guān)于糖尿病的數(shù)據(jù)集， 該數(shù)據(jù)集包括442個(gè)病人的生理數(shù)據(jù)及一年以后的病情發(fā)展情況。 
# 數(shù)據(jù)集中的特征值總共10項(xiàng), 如下: 
 # 年齡 
 # 性別 
 #體質(zhì)指數(shù) 
 #血壓 
 #s1,s2,s3,s4,s4,s6 (六種血清的化驗(yàn)數(shù)據(jù)) 
 #但請注意，以上的數(shù)據(jù)是經(jīng)過特殊處理， 10個(gè)數(shù)據(jù)中的每個(gè)都做了均值中心化處理，然后又用標(biāo)準(zhǔn)差乘以個(gè)體數(shù)量調(diào)整了數(shù)值范圍。
 #驗(yàn)證就會(huì)發(fā)現(xiàn)任何一列的所有數(shù)值平方和為1. 
"""
 
import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets, linear_model
from sklearn.metrics import mean_squared_error, r2_score
 
# Load the diabetes dataset
diabetes = datasets.load_diabetes() 
 
# Use only one feature 
# 增加一個(gè)維度，得到一個(gè)體質(zhì)指數(shù)數(shù)組[[1],[2],...[442]]
diabetes_X = diabetes.data[:, np.newaxis,2]
print(diabetes_X)
 
# Split the data into training/testing sets
diabetes_X_train = diabetes_X[:-20]
diabetes_X_test = diabetes_X[-20:]
 
# Split the targets into training/testing sets
diabetes_y_train = diabetes.target[:-20]
diabetes_y_test = diabetes.target[-20:]
 
# Create linear regression object
regr = linear_model.LinearRegression()
 
# Train the model using the training sets
regr.fit(diabetes_X_train, diabetes_y_train)
 
# Make predictions using the testing set
diabetes_y_pred = regr.predict(diabetes_X_test)
 
# The coefficients 
# 查看相關(guān)系數(shù) 
print('Coefficients: \n', regr.coef_)
 
 
# The mean squared error 
# 均方差
# 查看殘差平方的均值(mean square error,MSE) 
print("Mean squared error: %.2f"
  % mean_squared_error(diabetes_y_test, diabetes_y_pred))
 
 
# Explained variance score: 1 is perfect prediction 
# R2 決定系數(shù)（擬合優(yōu)度）
# 模型越好：r2→1
# 模型越差：r2→0
print('Variance score: %.2f' % r2_score(diabetes_y_test, diabetes_y_pred))
 
 
# Plot outputs
plt.scatter(diabetes_X_test, diabetes_y_test, color='black')
plt.plot(diabetes_X_test, diabetes_y_pred, color='blue', linewidth=3)
 
plt.xticks(())
plt.yticks(())
 
plt.show()