Question

怎样使用matlab，利用最小二乘法得到回归方程

影响结果的变量分别为x1，x2，x3，结果变量为y。
x1=[0.4, 0.4, 0.4, 0.4, 0.2, 0.2, 0.2, 0.2, 0.4, 0.4, 0.4, 0.4, 0.2, 0.2, 0.2, 0.2, 0.3, 0.3, 0.1, 0.5, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3];
x2=[0.08, 0.08, 0.04, 0.04, 0.08, 0.08, 0.04, 0.04, 0.08, 0.08, 0.04, 0.04, 0.08, 0.08, 0.04, 0.04, 0.06, 0.06, 0.06, 0.06, 0.02, 0.1, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06];
x3=[350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 300, 300, 300, 300, 300, 300, 200, 400, 300, 300, 300, 300, 300, 300, 300];
y=[0.99539, 1.0313, 0.88595, 0.92168, 0.30154, 0.32745, 0.21272, 0.24863, 0.94551, 0.96347, 0.95656, 0.97452, 0.20773, 0.21549, 0.20928, 0.23716, 0.48393, 0.53528, 0.18166, 1.56209, 0.48072, 0.54849, 0.54154, 0.48767, 0.50432, 0.52464, 0.52637, 0.51482, 0.50425, 0.50603, 0.51446];
最后求的回归方程为

matlab的代码怎么写啊？

Answer 1

定义函数文件myfun.m
function yhat = myfun(beta,x)
b1 = beta(1);
b2 = beta(2);
b3 = beta(3);
b4 = beta(4);
b5 = beta(5);
b6 = beta(6);
b7 = beta(7);
b8 = beta(8);
b9 = beta(9);
b10 = beta(10);

x1 = x(:,1);
x2 = x(:,2);
x3 = x(:,3);

yhat = b1+b2*x1+b3*x2+b4*x3+b5*x1.*x2+b6*x2.*x3+b7*x1.*x3+b8*x1.^2+b9*x2.^2+b10*x3.^2;

在命令窗口输入
x1=[0.4, 0.4, 0.4, 0.4, 0.2, 0.2, 0.2, 0.2, 0.4, 0.4, 0.4, 0.4, 0.2, 0.2, 0.2, 0.2, 0.3, 0.3, 0.1, 0.5, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3];

x2=[0.08, 0.08, 0.04, 0.04, 0.08, 0.08, 0.04, 0.04, 0.08, 0.08, 0.04, 0.04, 0.08, 0.08, 0.04, 0.04, 0.06, 0.06, 0.06, 0.06, 0.02, 0.1, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06];

x3=[350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 350, 250, 300, 300, 300, 300, 300, 300, 200, 400, 300, 300, 300, 300, 300, 300, 300];
y=[0.99539, 1.0313, 0.88595, 0.92168, 0.30154, 0.32745, 0.21272, 0.24863, 0.94551, 0.96347, 0.95656, 0.97452, 0.20773, 0.21549, 0.20928, 0.23716, 0.48393, 0.53528, 0.18166, 1.56209, 0.48072, 0.54849, 0.54154, 0.48767, 0.50432, 0.52464, 0.52637, 0.51482, 0.50425, 0.50603, 0.51446];

x=[x1' x2' x3'];
y=y';
beta = nlinfit(x,y,@myfun,ones(1,10))