數(shù)學(xué)模型實(shí)驗(yàn)課二ppt課件

1、數(shù)學(xué)模型實(shí)驗(yàn)課二最小二乘法與直線擬合v康爾乃奶粉v 32.4元 400g; 67.1元 900g.v 4 k1 + 42/3 k2 = 32.4v 9 k1 + 92/3 k2 = 67.1v 解得: k1 = 5.3791, k2 = 4.3192v 模型: C(W)=5.3791 W + 4.3192 W2/3.v 預(yù)測(cè): W=1800, C(W) = 126.49.v W=2500, C(W) = 154.36v 實(shí)踐: W=1800, C(W)=115.9v W=2500, C(W)=146.85vx=4,9,18,25;y=32.4,67.1,115.9,146.85;vx1=x(1

2、),x(2),x2=x1.(2/3);vy1=y(1),y(2);X=x1,x2;vk=Xy1vx1=x(1),x(2),x(3);x2=x1.(2/3);vy1=y(1),y(2),y(3);X=x1,x2;vk=Xy1.求解線性方程組：A x = y 假設(shè)4321214232221241312111,yyyyyxxxaaaaaaaaA設(shè)：設(shè)：Ax+= y，求，求 x 使得誤差使得誤差 | 最小。最小。Qxaxayiiiiii4122211412)(0)(2122111iiiiiaxaxayxQ0)(2222112iiiiiaxaxayxQiiiiiiiiiiiiiiiiiiyaxaaxaa

3、yaxaaxaa22221121221111AA x = Ayx = (AA)-1Ay二. 直線擬合 1. 矩陣左除數(shù)據(jù)xi, yi,擬合直線 y = a + bx, 誤差最小模型：yi = a + bxi +nnyyyybabxxxX2121,111X b = yvy=17,16,17,23,26,27,41,49;vx=1953,2021,2021,2821,3049,3049,5133,5592;vX=ones(8,1),x;b=Xy;vy1=b(1)+b(2).*x;vplot(x,y1,r,x,y,*r)2)()(xxyyxxLLbxbyaiiixxxyv 2. 直線擬合的效果相關(guān)系

4、數(shù)直線擬合的效果相關(guān)系數(shù)v iibxayNoImageiiiiiiiyyyyyyyyL222)()()(UQ22)()(ybxayyUiixxiLbxbbx22)(yyxxxyyyxxyyLLLLLbLUr222yJnIxyyxxLiixy)1( )(vX1=x,y;m=size(X1);n=m(1);p=m(2);vX=ones(n,1),x;B=Xy;a=B(1);b=B(2:p);vy1=a+b*x;plot(x,y1,r,x,y,*r);vCov=X1*(eye(n)-ones(n)./n)*X1;vLyy=Cov(p,p);Lxx=Cov(1:(p-1),1:(p-1);vR=(b*Lxx*b)/Lyy;r=sqrt(R