Question

用最小二乘法求一个形如y=a+bx^2拟合函数去拟合下列数据： x=19,25,31,38,44 y=19.0,32.3,49.0,73.3,97.8

最好是能有图和详细的讲解以及代码之类的

Answer 1

x=[19,25,31,38,44];
y=[19.0,32.3,49.0,73.3,97.8];
fun1=inline('c(1)+c(2)*x.^2','c','x'); %拟合函数
c=lsqcurvefit(fun1,[0,0],x,y) %求拟合系数
['y=',num2str(c(1)),'+',num2str(c(2)),'x^2']%拟合函数表达式
y1=c(1)+c(2)*x.^2; %拟合函数表达式值
plot (x,y,'b*', x, y1,'r-');%绘制x，y点与拟合函数，比较拟合程度
进行结果：
fun1 =
Inline function:
fun1(c,x) = c(1)+c(2)*x.^2
Optimization terminated: first-order optimality less than OPTIONS.TolFun,
and no negative/zero curvature detected in trust region model.
c =
0.972578657321613 0.0500351242188565
ans =
y=0.97258+0.050035x^2