线性回归案例(1)------糖尿病人数据分析

import numpy as np
from sklearn import datasets
import matplotlib.pyplot as plt
%matplotlib inline

diabetes = datasets.load_diabetes
print(type(diabetes))
print(diabetes.data.shape)
print(diabetes.target.shape)
--------------------------
sklearn.utils.Bunch
(442,10)
(442,)

加载数据

diabetes.data = diabetes.data[:,np.newaxis,2]
#只取原数据的第三列(bmi),并(np.newaxis)新增一个轴

将数据分成训练集和测试集

#取出训练集，从0行到倒数20行-1行
x_train = diabetes.data[:-20]
y_train = diabetes.target[:-20]

#取出测试集,从-20行到最后一行
x_test = diabetes.data[-20:0]
y_test = diabetes.data[-20:0]

自定一个计算权重值和预测值的类

class LinearRegression(object):
    def __init__(self):
        self.w = None
    def fit(self,X,y):
        #计算权重的函数
        # y=wx+b   假设b=w0x0 ,x0=1, b=w0
        X = np.insert(X,0,1,axis=1) 在数据集新增一列x0，数值是1
        
        #计算w， w=(x.T * x)**-1 * x.T * y
        #inv():矩阵逆转，即 [矩阵]^-1   dot():数组计算，点乘
        X_ = np.linalg.inv(X.T.dot(X))  # (x.T * x) ** -1
        
        self.w = X_.dot(X.T).dot(y)  #X_ * x.t * y

    def predict(self,X):
        #计算 Ypred的函数
        X = np.insert(X,0,1,axis=1)
        y_pred = X.dot(self.w)   # b = w0x0, Y=wx+b = wx
        return y_pred

clf = LinearRegression()　#创建一个实例对象
clf.fit(x_train,y_train)  #通过训练集计算出w（权重）的值
print(clf.w)  
--------------------------------
array([152.91886183, 938.23786125])

y_pred = clf.predict(x_test)  #计算出预测值
print(y_test)
print(x_test[:,0])
print(y_pred)
------------------------------------
[233.  91. 111. 152. 120.  67. 310.  94. 183.  66. 173.  72.  49.  64.
  48. 178. 104. 132. 220.  57.]
[ 0.07786339 -0.03961813  0.01103904 -0.04069594 -0.03422907  0.00564998
  0.08864151 -0.03315126 -0.05686312 -0.03099563  0.05522933 -0.06009656
  0.00133873 -0.02345095 -0.07410811  0.01966154 -0.01590626 -0.01590626
  0.03906215 -0.0730303 ]

[225.9732401 , 115.74763374, 163.27610621, 114.73638965,
 120.80385422, 158.21988574, 236.08568105, 121.81509832,
 99.56772822, 123.83758651, 204.73711411,  96.53399594,
 154.17490936, 130.91629517,  83.3878227 , 171.36605897,
 137.99500384, 137.99500384, 189.56845268,  84.3990668 ]

#查看真实历史数据与预测值之间误差平方的均值
def mean_squared_error(y_true,y_pred):
    mse = np.mean(np.powerured,2)
    return mse

mean_squared_error(y_test,y_pred)
---------------------------------
2548.072398725972

#画真实数据的散点状图
plt.scatter(x_test[:,0], y_test, color='black', label='true')
#画预测数值的趋势图
plt.plot(x_test[:,0], y_pred, color='blue', linewidth=3, label='pred')
plt.legend()
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