给定一组数据,例如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
时间: 2023-07-27 14:16:48 浏览: 195
以下是一个使用对数最小二乘法拟合数据的 MATLAB 代码示例:
```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];
% 定义模型函数和初始参数
model = @(b, x) b(1)*log(x) + b(2);
beta0 = [1, 1];
% 定义损失函数
loss = @(b) sum((model(b, X) - y).^2);
% 使用 fminsearch 函数求最小化损失函数的参数
beta_hat = fminsearch(loss, beta0);
% 输出结果
disp(['beta1 = ', num2str(beta_hat(1))]);
disp(['beta2 = ', num2str(beta_hat(2)))]);
% 绘制拟合曲线
xx = linspace(min(X), max(X), 100)';
yy = model(beta_hat, xx);
plot(X, y, 'o', xx, yy);
xlabel('x');
ylabel('y');
```
注意,对数最小二乘法需要注意数据的取值范围,对于非正数或0值,需要进行预处理。同时,对于不同的模型函数,需要根据具体情况进行调整。
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