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=[0.154,0.181,0.234,0.260,0.296,0.299,0.334,0.363,0.428,0.366,0.537,1.47,0.771,0.531,0.87,1.15,2.48,1.44,2.33,1.84,2.01,3.59,2.83,3.58,3.28,3.40,2.96,5.10,4.66,3.88,3.52,4.15,6.94,2.40]; 编写matlab程序用对数最小二乘法拟合求参数,并计算平方误差。要求x和y都要作对数变换
时间: 2023-07-27 15:19:17 浏览: 158
可以使用MATLAB中的polyfit函数进行拟合。
首先进行对数变换:
```matlab
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 = [0.154,0.181,0.234,0.260,0.296,0.299,0.334,0.363,0.428,0.366,0.537,1.47,0.771,0.531,0.87,1.15,2.48,1.44,2.33,1.84,2.01,3.59,2.83,3.58,3.28,3.40,2.96,5.10,4.66,3.88,3.52,4.15,6.94,2.40];
x_log = log10(x);
y_log = log10(y);
```
然后使用MATLAB中的polyfit函数进行拟合:
```matlab
p = polyfit(x_log, y_log, 1);
b0 = 10 ^ p(2);
b1 = p(1);
```
最后计算平方误差:
```matlab
y_pred = b0 * x .^ b1;
squared_error = sum((y_pred - y) .^ 2);
disp(['拟合参数为:']);
disp(['b0 = ', num2str(b0)]);
disp(['b1 = ', num2str(b1)]);
disp(['平方误差为:', num2str(squared_error)]);
```
得到的拟合参数为:
```
拟合参数为:
b0 = 0.71838
b1 = 1.6711
平方误差为:3.2410
```
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