线性模型之Linear Regression

numpy和pandas的使用 

相关系数的计算 

import random
import numpy as np

a = []
b = []

# 随机生成两个3x3矩阵
for i in range(3):
    a.append([random.randint(0, 10) for j in range(3)])
    b.append([random.randint(0, 10) for j in range(3)])

# 将二维列表转成numpy中的ndarray类型
np_a = np.array(a)
np_b = np.array(b)
print('矩阵a如下：')
print(np_a)
print('矩阵b如下：')
print(np_b)
print('矩阵a和b相乘：')
print(np.dot(a, b))

A = [[-1, 1, 0], [-4, 3, 0], [1, 0, 2]]
np_A = np.array(A)
print('矩阵A如下：')
print(np_A)
v, w = np.linalg.eig(A)
print('特征值：')
print(v)
print('特征向量：')
print(w)

A = [[5, 2, 1], [2, 0, 1]]
np_A = np.array(A)
print('矩阵A如下：')
print(np_A)
U, sigma, VT = np.linalg.svd(np_A)
print('分解后矩阵如下：')
print(U)
print(sigma)
print(VT)

2.第二题

(ps: 判定系数等于相关系数的平方) 

import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression

data_x = [
    [3.18, 1.15, 9.4, 17.6, 3],
    [3.8, 0.79, 5.1, 30.5, 3.8],
    [3.6, 1.1, 9.2, 9.1, 3.65],
    [2.73, 0.73, 14.5, 12.8, 4.68],
    [3.4, 1.48, 7.6, 16.5, 4.5],
    [3.2, 1, 10.8, 10.1, 8.1],
    [2.6, 0.61, 7.3, 16.1, 16.16],
    [4.1, 2.3, 3.7, 17.8, 6.7],
    [3.72, 1.94, 9.9, 36.1, 4.1],
    [4.1, 1.66, 8.2, 29.4, 13]
]
data_y = [0.7, 0.7, 1, 1.1, 1.5, 2.6, 2.7, 3.1, 6.1, 9.6]

estimator = LinearRegression()            # 实例化线性回归方法
estimator.fit(data_x, data_y)             # 训练模型
coef_vector = np.append(estimator.coef_, estimator.intercept_)
print('系数向量(包括常数项)n', coef_vector)

col_index = ['x1', 'x2', 'x3', 'x4', 'x5']
row_index = [i+1 for i in range(len(data_x))]
data_df = pd.Dataframe(data_x, index=row_index, columns=col_index)
data_df['y'] = data_y
print('数据以二维表格呈现如下n', data_df)
# 相关系数
correlation_coef = [data_df.x1.corr(data_df.y), data_df.x2.corr(data_df.y), data_df.x3.corr(data_df.y), data_df.x4.corr(data_df.y), data_df.x5.corr(data_df.y)]
# 判定系数
determination_coef = [item * item for item in correlation_coef]
print('x1~x5与y的判定系数分别为', determination_coef)

print('预测结果', estimator.predict([[3.5, 1.8, 8, 17, 10]]))

3.第三题