嶺回歸在財政收入中的應(yīng)用

1、1嶺回歸在財政收入中的應(yīng)用信息與計算科學(xué) 2003 級 母培松指導(dǎo)老師 杜世平 副教授摘要摘要：本論文介紹了嶺回歸的統(tǒng)計學(xué)原理和方法,闡述了嶺回歸和最小偏二乘法的差別和關(guān)系,總結(jié)了評價嶺回歸的效應(yīng)的性質(zhì)和其確定方法,討論了嶺回歸在經(jīng)濟領(lǐng)域中的具體k應(yīng)用，并用 matlab 軟件來實現(xiàn)計算程序。關(guān)鍵詞關(guān)鍵詞：嶺回歸，嶺跡，病態(tài)矩陣，有偏估計Ridge regression return for revenueMu Peisong Information and Computational Science, Grade 2003Directed by Du shiping（Associate Pr

2、ofessor）Abstract : This paper introduced the ridge regression statistical theory and methods, Described the differences and relationships in the ridge regression and the partial least two multiplication , Raised ridge Regression evaluation of the k effect of nature and its method, More detailed disc

3、ussions on the ridge regression in the economic field the specific application, using Matlab software to achieve program. Keywords : Ridge Regression, Ridge Trace, Pathological Matrix ,Biased Estimate 1 引言引言 在回歸分析中最小二乘法是最常用的方法，使用最小二乘法的一個前提是不為X X零，即矩陣非奇異，當(dāng)所有變量之間有較強的線性相關(guān)性時，或者變量之XXX X0間的數(shù)據(jù)變化比較小或者部分變量之間

4、有線性相關(guān)性時，矩陣的行列式比較小，甚X X至趨近于 0，一般在實際應(yīng)用中處理：當(dāng)10 %需滿足小于 10 break else continue end end for l=1:6 if C(l,l)=10 k C hold on break else end endend程序程序 5 嶺回歸嶺回歸f=inv(z*z+0.0199.*eye(6)*z*y; %嶺回歸，f 為標(biāo)注化數(shù)據(jù)的嶺回歸系數(shù)cc=inv(z*z+0.0199.*eye(6);b1(1,1)=mean(y); %常數(shù)項for i=2:718 b1(i,1)=f(i-1,1);endb1for i=1:6 by(i+1,1)

5、=f(i,1)/qx(1,i); %還原ends=0;for i=1:6 s=s+by(i+1,1)*ax(1,i);endby(1,1)=mean(y)-s;by%計算嶺回歸 s，qs=0;for i=1:24 Y(i,1)=by(1,1)+by(2,1)*x(i,1)+by(3,1)*x(i,2)+by(4,1)*x(i,3)+by(5,1)*x(i,4)+by(6,1)*x(i,5)+by(7,1)*x(i,6); s=s+(y(i,1)-Y(i,1)2;endq=sss=q/17sb=ss*(cc(1,1)+cc(2,2)+cc(3,3)+cc(4,4)+cc(5,5)+cc(6,6)

6、程序程序 6 繪嶺圖繪嶺圖k=0;for j=1:10001 f=inv(z*z+k.*eye(6)*z*y;%嶺回歸 cc=inv(z*z+k.*eye(6); b1(1,1)=mean(y); for i=2:7 b1(i,1)=f(i-1,1); end for i=1:6 by(i+1,1)=f(i,1)/qx(1,i);%還原 end s=0; for i=1:6 s=s+by(i+1,1)*ax(1,i); end by(1,1)=mean(y)-s; aa(j,1)=k; k=k+0.0001; m1(j,1)=by(2,1); m2(j,1)=by(3,1); m3(j,1)=

7、by(4,1); m4(j,1)=by(5,1);19 m5(j,1)=by(6,1); m6(j,1)=by(7,1);endplot(aa,m1,R-,aa,m2,G-,aa,m3,B-,aa,m4,y-,aa,m5,m-,aa,m6,K-)程序程序 7 嶺嶺分析嶺嶺分析k=0.00;for j=1:11 f=inv(z*z+k.*eye(6)*z*y;%嶺回歸 cc=inv(z*z+k.*eye(6); b1(1,1)=mean(y); j for i=2:7 b1(i,1)=f(i-1,1); end for i=1:6 by(i+1,1)=f(i,1)/qx(1,i);%還原 end s=0; for i=1:6 s=s+by(i+1,1)*ax(1,i); end by(1,1)=mean(y)-s; by %計算嶺回歸 s，q s=0; for i=1:24Y(i,1)=by(1,1)+by(2,1)*x(i,1)+by(3,1)*x(i,2)+by(4,1)*x(i,3)+by(5,1)*x(i,4)+by(6,1)*x(i,5)+by