X=[0.017,0.020,0.025,0.085,0.087,0.119,0.171,0.174,0.210,0.211,0.233,0.783,0.999,1.11,1.29,1.32,1.35,1.69,1.74,2.75,3.02,3.04,3.34,4.09,4.28,4.29,4.58,4.68,4.83,5.30,5.45,5.48,5.53,5.96]; y=[0.154,0.181,0.234,0.260,0.296,0请编写一个求对数最小二乘法参数的matlab代码,不使用损失函数
时间: 2023-07-27 21:16:48 浏览: 118
以下是一个使用对数最小二乘法拟合数据的 MATLAB 代码示例,不使用损失函数:
```matlab
% 给定数据
X = [0.017,0.020,0.025,0.085,0.087,0.119,0.171,0.174,0.210,0.211,0.233,0.783,0.999,1.11,1.29,1.32,1.35,1.69,1.74,2.75,3.02,3.04,3.34,4.09,4.28,4.29,4.58,4.68,4.83,5.30,5.45,5.48,5.53,5.96];
y = [0.154,0.181,0.234,0.260,0.296,0.313,0.375,0.379,0.418,0.422,0.436,0.550,0.578,0.604,0.632,0.635,0.637,0.689,0.697,0.772,0.787,0.788,0.821,0.872,0.885,0.885,0.901,0.907,0.918,0.948,0.956,0.957,0.959,0.982];
% 使用线性回归函数 polyfit 进行对数最小二乘法拟合
beta_hat = polyfit(log(X), y, 1);
% 输出结果
disp(['beta1 = ', num2str(beta_hat(1))]);
disp(['beta2 = ', num2str(exp(beta_hat(2)))]);
% 绘制拟合曲线
xx = linspace(min(X), max(X), 100)';
yy = exp(polyval(beta_hat, log(xx)));
plot(X, y, 'o', xx, yy);
xlabel('x');
ylabel('y');
```
注意,本例中使用了 MATLAB 自带的线性回归函数 polyfit 进行对数最小二乘法拟合,其中 log(X) 作为自变量进行拟合,最终输出的结果需要对 beta2 进行 exp 运算才能得到真正的参数。
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