请问如何用MATLAB求最小二乘解的未知系数？

liu_zhi_ping 发表于 2007-4-8 13:48

题目如下：有一组实测数据<table class="MsoNormalTable" cellspacing="0" cellpadding="0" border="1" style="BORDER-RIGHT: medium none; BORDER-TOP: medium none; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext;"><tbody><tr><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 1pt solid; WIDTH: 37.65pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt;">   x </td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.65pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.1</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.65pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.2</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.3</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.4</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.5</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.6</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.7</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.8</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">0.9</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt;">1</td></tr><tr style="mso-yfti-lastrow: yes;"><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 1pt solid; WIDTH: 37.65pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">y</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.65pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">2.3201</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.65pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">2.6470</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">2.9070</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">3.2885</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">3.6008</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">3.9090</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">4.2147</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">4.5191</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">4.8232</td><td valign="top" width="50" style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 37.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt;">5.1275</td></tr></tbody></table>假设已知该数据可能满足的原型函数为y(x)=a*x+b*x^2*exp(-c*x)+d,求出满足上面数据的最小二乘解的a,b,c,d的值。请问高手：如何写这段程序？

zsx001 发表于 2007-5-3 01:53

用函数 <span lang="EN-US" style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'; mso-fareast-font-family: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN;">lsqcurvefit 可以。<div class="O" vshape="_x0000_s1026" style="TEXT-ALIGN: center; mso-line-spacing: '100 50 0'; mso-char-wrap: 1; mso-kinsoku-overflow: 1;"><span lang="EN-US" style="FONT-SIZE: 24pt; COLOR: black; FONT-FAMILY: "Times New Roman"; mso-ascii-font-family: "Times New Roman"; mso-fareast-font-family: 宋体; mso-hansi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </div>

chaos 发表于 2007-5-23 23:16

clc;clear; x=;  y=; myfunc=inline('beta(1)*x+beta(2)*x.*x.*exp(-beta(3)*x)+beta(4)','beta','x'); beta=nlinfit(x,y,myfunc,); a=beta(1),b=beta(2),c=beta(3),d=beta(4) %test hte model; xx=0:0.01:1; yy=a*xx+b*xx.*xx.*exp(-c*xx)+d; plot(x,y,'o',xx,yy,'r')不失高手，照猫画虎

chaos 发表于 2007-5-23 23:16

不小心多发了一个
[此贴子已经被作者于2007-5-23 23:16:58编辑过]

vikki0838 发表于 2007-6-2 20:34

如果数据相差不大是不是就不能做了？

Jennykong 发表于 2007-6-4 12:24

用SPSS更简单

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数学建模社区-数学中国's Archiver

请问如何用MATLAB求最小二乘解的未知系数？