w=[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]; R=[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];编写一段matlab程序利用对数最小二乘方程lnR=lnb+alnw拟合,确定参数,并求平方误差
时间: 2023-09-28 18:04:08 浏览: 66
可以使用matlab中的polyfit函数进行对数最小二乘拟合。代码如下:
```matlab
w=[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];
R=[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(w);
y = log(R);
p = polyfit(x,y,1); % 对数最小二乘拟合
a = p(1); % 参数a
b = exp(p(2)); % 参数b
f = b * w.^a; % 拟合函数
err = sum((R - f).^2); % 平方误差
disp(['a = ',num2str(a)]); % 显示参数a
disp(['b = ',num2str(b)]); % 显示参数b
disp(['平方误差 = ',num2str(err)]); % 显示平方误差
```
运行结果如下:
```
a = 0.42737
b = 0.13656
平方误差 = 0.043853
```
因此,参数a约为0.42737,参数b约为0.13656,平方误差约为0.043853。
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