min_square

Posted 2020-12-22 heimazaifei

最小二乘法

测量一个棍子，10次数据如下：

12.3 , 11.8,11.2,11.6,12.5,12.1.11.6.12.0,12.4,11.2

怎样获取最后结果？？？？

这样做有道理吗？用调和平均数行不行？用中位数行不行？用几何平均数行不行？

从概论的角度考虑，每次测量结果的概率值为 Pi, 那么，产生以上结果的概率为： P1*P2....P10;如果方差为高斯分布，要使以上结果概论最大（最大似然），通过推导，可知满足最小二乘法即可。

最小二乘可以通过求导解决。

python3

# 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_y[:-20]
diabetes_y_test = diabetes_y[-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
print(‘Coefficients: 
‘, regr.coef_)
# The mean squared error
print(‘Mean squared error: %.2f‘
      % mean_squared_error(diabetes_y_test, diabetes_y_pred))
# The coefficient of determination: 1 is perfect prediction
print(‘Coefficient of determination: %.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()