MATLAB数学建模与仿真（第2版·微课视频版）程序代码 第11章-高校研究生指标分配问题

首先进行数据处理，每个岗位等级所对应的各个因素的平均值。然后以岗位级别为横坐标，招生人数、科研经费、发表中英文论文数、申请专利数、获奖数和获得优秀论文数量分别作为纵坐标。利用MATLB软件绘制出他们的直方图，MATLAB程序如下：%级岗合并clc,clear;loadxsum.matloadgw1.matloadgw2.matloadgw3.matloadgw4.matloadgw5.matloadgw6.matloadgw7.matn0=size(xsum);n1=size(gw1);n2=size(gw2);n3=size(gw3);n4=size(gw4);n5=size(gw5);n6=size(gw6);n7=size(gw7);renshu1=[0,0,0,0,0,0,0];keyan1=[0,0,0,0,0,0,0];zhongyw1=[0,0,0,0,0,0,0];zhuanli1=[0,0,0,0,0,0,0];huoj1=[0,0,0,0,0,0,0];youxlw1=[0,0,0,0,0,0,0];fori=1:n1(1,1)renshu1(1,1)=renshu1(1,1)+gw1(i,9);keyan1(1,1)=keyan1(1,1)+gw1(i,14);zhongyw1(1,1)=zhongyw1(1,1)+gw1(i,20)+gw1(i,29);zhuanli1(1,1)=zhuanli1(1,1)+gw1(i,35);huoj1(1,1)=huoj1(1,1)+gw1(i,41);youxlw1(1,1)=youxlw1(1,1)+gw1(i,42)+gw1(i,43);endfori=1:n2(1,1)renshu1(1,2)=renshu1(1,2)+gw2(i,9);keyan1(1,2)=keyan1(1,2)+gw2(i,14);zhongyw1(1,2)=zhongyw1(1,2)+gw2(i,20)+gw2(i,29);zhuanli1(1,2)=zhuanli1(1,2)+gw2(i,35);huoj1(1,2)=huoj1(1,2)+gw2(i,41);youxlw1(1,2)=youxlw1(1,2)+gw2(i,42)+gw2(i,43);endfori=1:n3(1,1)renshu1(1,3)=renshu1(1,3)+gw3(i,9);keyan1(1,3)=keyan1(1,3)+gw3(i,14);zhongyw1(1,3)=zhongyw1(1,3)+gw3(i,20)+gw3(i,29);zhuanli1(1,3)=zhuanli1(1,3)+gw3(i,35);huoj1(1,3)=huoj1(1,3)+gw3(i,41);youxlw1(1,3)=youxlw1(1,3)+gw3(i,42)+gw3(i,43);endfori=1:n4(1,1)renshu1(1,4)=renshu1(1,4)+gw4(i,9);keyan1(1,4)=keyan1(1,4)+gw4(i,14);zhongyw1(1,4)=zhongyw1(1,4)+gw4(i,20)+gw4(i,29);zhuanli1(1,4)=zhuanli1(1,4)+gw4(i,35);huoj1(1,4)=huoj1(1,4)+gw4(i,41);youxlw1(1,4)=youxlw1(1,4)+gw4(i,42)+gw4(i,43);endfori=1:n5(1,1)renshu1(1,5)=renshu1(1,5)+gw5(i,9);keyan1(1,5)=keyan1(1,5)+gw5(i,14);zhongyw1(1,5)=zhongyw1(1,5)+gw5(i,20)+gw5(i,29);zhuanli1(1,5)=zhuanli1(1,5)+gw5(i,35);huoj1(1,5)=huoj1(1,5)+gw5(i,41);youxlw1(1,5)=youxlw1(1,5)+gw5(i,42)+gw5(i,43);endfori=1:n6(1,1)renshu1(1,6)=renshu1(1,6)+gw6(i,9);keyan1(1,6)=keyan1(1,6)+gw6(i,14);zhongyw1(1,6)=zhongyw1(1,6)+gw6(i,20)+gw6(i,29);zhuanli1(1,6)=zhuanli1(1,6)+gw6(i,35);huoj1(1,6)=huoj1(1,6)+gw6(i,41);youxlw1(1,6)=youxlw1(1,6)+gw6(i,42)+gw6(i,43);endfori=1:n1(1,1)renshu1(1,7)=renshu1(1,7)+gw7(i,9);keyan1(1,7)=keyan1(1,7)+gw7(i,14);zhongyw1(1,7)=zhongyw1(1,7)+gw7(i,20)+gw7(i,29);zhuanli1(1,7)=zhuanli1(1,7)+gw7(i,35);huoj1(1,7)=huoj1(1,7)+gw7(i,41);youxlw1(1,7)=youxlw1(1,7)+gw7(i,42)+gw7(i,43);endsubplot(2,3,1)bar(1:7,renshu1)gtext('级岗')gtext('招生人数')subplot(2,3,2)bar(1:7,keyan1)gtext('级岗')gtext('科研经费')subplot(2,3,3)bar(1:7,zhongyw1)gtext('级岗')gtext('中英文论文数')subplot(2,3,4)bar(1:7,zhuanli1)gtext('级岗')gtext('专利数')subplot(2,3,5)bar(1:7,huoj1)gtext('级岗')gtext('获奖数')subplot(2,3,6)bar(1:7,youxlw1)gtext('级岗')gtext('优秀论文数')运行结果如图11-1所示。图11-1每个岗位招生人数和科研经费等指标与岗位的统计直方图我们将招生人数、科研经费、发表中英文论文数、申请专利、获奖数和获得优秀论文数量等都求了一个平均值：x再利用MATLAB软件编程如下：%求平均值renshu1(1,1)=renshu1(1,1)/n1(1,1);keyan1(1,1)=keyan1(1,1)/n1(1,1);zhongyw1(1,1)=zhongyw1(1,1)/n1(1,1);zhuanli1(1,1)=zhuanli1(1,1)/n1(1,1);huoj1(1,1)=huoj1(1,1)/n1(1,1);youxlw1(1,1)=youxlw1(1,1)/n1(1,1);%求平均值renshu1(1,2)=renshu1(1,2)/n2(1,1);keyan1(1,2)=keyan1(1,2)/n2(1,1);zhongyw1(1,2)=zhongyw1(1,2)/n2(1,1);zhuanli1(1,2)=zhuanli1(1,2)/n2(1,1);huoj1(1,2)=huoj1(1,2)/n2(1,1);youxlw1(1,2)=youxlw1(1,2)/n2(1,1);%求平均值renshu1(1,3)=renshu1(1,3)/n3(1,1);keyan1(1,3)=keyan1(1,3)/n3(1,1);zhongyw1(1,3)=zhongyw1(1,3)/n3(1,1);zhuanli1(1,3)=zhuanli1(1,3)/n3(1,1);huoj1(1,3)=huoj1(1,3)/n3(1,1);youxlw1(1,3)=youxlw1(1,3)/n3(1,1);%求平均值renshu1(1,4)=renshu1(1,4)/n4(1,1);keyan1(1,4)=keyan1(1,4)/n4(1,1);zhongyw1(1,4)=zhongyw1(1,4)/n4(1,1);zhuanli1(1,4)=zhuanli1(1,4)/n4(1,1);huoj1(1,4)=huoj1(1,4)/n4(1,1);youxlw1(1,4)=youxlw1(1,4)/n4(1,1);%求平均值renshu1(1,5)=renshu1(1,5)/n5(1,1);keyan1(1,5)=keyan1(1,5)/n5(1,1);zhongyw1(1,5)=zhongyw1(1,5)/n5(1,1);zhuanli1(1,5)=zhuanli1(1,5)/n5(1,1);huoj1(1,5)=huoj1(1,5)/n5(1,1);youxlw1(1,5)=youxlw1(1,5)/n5(1,1);%求平均值renshu1(1,6)=renshu1(1,6)/n6(1,1);keyan1(1,6)=keyan1(1,6)/n6(1,1);zhongyw1(1,6)=zhongyw1(1,6)/n6(1,1);zhuanli1(1,6)=zhuanli1(1,6)/n6(1,1);huoj1(1,6)=huoj1(1,6)/n6(1,1);youxlw1(1,6)=youxlw1(1,6)/n6(1,1);%求平均值renshu1(1,7)=renshu1(1,7)/n7(1,1);keyan1(1,7)=keyan1(1,7)/n7(1,1);zhongyw1(1,7)=zhongyw1(1,7)/n7(1,1);zhuanli1(1,7)=zhuanli1(1,7)/n7(1,1);huoj1(1,7)=huoj1(1,7)/n7(1,1);youxlw1(1,7)=youxlw1(1,7)/n7(1,1);figure(2),subplot(2,3,1)bar(1:7,renshu1)gtext('级岗')gtext('平均招生人数')subplot(2,3,2)bar(1:7,keyan1)gtext('级岗')gtext('平均科研经费')subplot(2,3,3)bar(1:7,zhongyw1)gtext('级岗')gtext('平均中英文论文数')subplot(2,3,4)bar(1:7,zhuanli1)gtext('级岗')gtext('平均专利数')subplot(2,3,5)bar(1:7,huoj1)gtext('级岗')gtext('平均获奖数')subplot(2,3,6)bar(1:7,youxlw1)gtext('级岗')gtext('平均优秀论文数')运行程序输出结果如图11-2所示：图11-2处理后的各项指标与岗位级别间的统计直方图模型的求解：Stepl：根据题目所给的数据，提取出回归变量和因变量，并用相应的字母表示。Step2：运用最小二乘估计法，计算回归系数(以2008年为例)，MATLAB编程程序如下：%级岗合并clc,clear;loadxsum.matn0=size(xsum);j=1;fori=1:n0(1,1)ifxsum(i,3)~=0zq(j,:)=xsum(i,:);j=j+1;endendn1=size(zq);%08招生人数fori=1:n1(1,1)fpfa08(i,1)=zq(i,3);fpfa08(i,2)=zq(i,15);fpfa08(i,3)=zq(i,24);fpfa08(i,4)=zq(i,30);fpfa08(i,5)=zq(i,36);fpfa08(i,6)=zq(i,5);endfori=1:n1(1,1)iffpfa08(i,1)==1fpfa08(i,1)=7;endiffpfa08(i,1)==2fpfa08(i,1)=6;endiffpfa08(i,1)==3fpfa08(i,1)=5;endiffpfa08(i,1)==4fpfa08(i,1)=4;endiffpfa08(i,1)==5fpfa08(i,1)=3;endiffpfa08(i,1)==6fpfa08(i,1)=2;endiffpfa08(i,1)==7fpfa08(i,1)=1;endendn2=size(fpfa08);%Bfpfa08=zscore(fpfa08(:,1:n2(1,2)-1));%标准化数据矩阵%Bfpfa08(:,n2(1,2))=fpfa08(:,n2(1,2));%figure(1),%subplot(2,3,1)%plot(fpfa08(:,1),fpfa08(:,6));%级岗%subplot(2,3,2)%plot(fpfa08(:,2),fpfa08(:,6));%英文论文%subplot(2,3,3)%plot(fpfa08(:,2),fpfa08(:,6));%中文论文%subplot(2,2,3)%plot(fpfa08(:,4),fpfa08(:,6));%专利数%subplot(2,2,4)%plot(fpfa08(:,5),fpfa08(:,6));%获奖个数figure(1),X=fpfa08(:,1:5);X=[ones(n2(1,1),1),X];Y=fpfa08(:,n2(1,2));[b,bint,r,rint,s]=regress(Y,X);rcoplot(r,rint)%删除一些点j=1;fori=1:n1(1,1)ifi~=1&&i~=115&&i~=21&&i~=33&&i~=41&&i~=78&&i~=91&&i~=105&&i~=131&&i~=162&&i~=173&&i~=214&&i~=215&&i~=220&&i~=234&&i~=242&&i~=244&&i~=255&&i~=261&&i~=264&&i~=269&&i~=279Cfpfa08(j,:)=fpfa08(i,:);j=j+1;endendfigure(2),n3=size(Cfpfa08);X=Cfpfa08(:,1:5);X=[ones(n3(1,1),1),X];Y=Cfpfa08(:,n2(1,2));[b,bint,r,rint,s]=regress(Y,X);rcoplot(r,rint)%删除一些点j=1;fori=1:n3(1,1)ifi~=64&&i~=69&&i~=87&&i~=92&&i~=106&&i~=128&&i~=122&&i~=134&&i~=136&&i~=157&&i~=163&&i~=164&&i~=201&&i~=194&&i~=205&&i~=220&&i~=223&&i~=234&&i~=261&&i~=235&&i~=239&&i~=279&&i~=316CCfpfa08(j,:)=Cfpfa08(i,:);j=j+1;endendfigure(3),n3=size(CCfpfa08);X=CCfpfa08(:,1:5);X=[ones(n3(1,1),1),X];Y=CCfpfa08(:,n2(1,2));[b,bint,r,rint,s]=regress(Y,X);rcoplot(r,rint)运行结果如11-3所示，从残差图11-3中可看出，异常值较多，因此可将异常点剔除。图11-32008年研究生招生人数回归方程的残差检验图将异常点数据剔除之后，再次进行回归分析，然后再删除异常点，如此循环多次，得到的残差检验图如图11-4所示。%删除一些点j=1;fori=1:n3(1,1)ifi~=4&&i~=73&&i~=89&&i~=93&&i~=99&&i~=158&&i~=160&&i~=204&&i~=211&&i~=222&&i~=224&&i~=225&&i~=226&&i~=281&&i~=287&&i~=293CCCfpfa08(j,:)=CCfpfa08(i,:);j=j+1;endendfigure(4),n3=size(CCCfpfa08);X=CCCfpfa08(:,1:5);X=[ones(n3(1,1),1),X];Y=CCCfpfa08(:,n2(1,2));[b,bint,r,rint,s]=regress(Y,X);rcoplot(r,rint)%删除一些点j=1;fori=1:n3(1,1)ifi~=24&&i~=32&&i~=33&&i~=64&&i~=69&&i~=72&&i~=74&&i~=79&&i~=88&&i~=93&&i~=101&&i~=236&&i~=238&&i~=243CCCCfpfa08(j,:)=CCCfpfa08(i,:);j=j+1;endendfigure(5),n3=size(CCCCfpfa08);X=CCCCfpfa08(:,1:5);X=[ones(n3(1,1),1),X];Y=CCCCfpfa08(:,n2(1,2));[b,bint,r,rint,s]=regress(Y,X);rcoplot(r,rint)图11-4剔除异常点后2008年研究生招生人数回归方程的残差检验图将各指标数据代入招生回归方程中，得出预测值，然后与实际招生值进行比较验证，2010年的预测对比图如图11-4所示。%级岗合并clc,clear;loadxsum.matn0=size(xsum);j=1;fori=1:n0(1,1)ifxsum(i,3)~=0zq(j,:)=xsum(i,:);j=j+1;endendn1=size(zq);%08招生人数fori=1:n1(1,1)fpfa10(i,1)=zq(i,3);fpfa10(i,2)=zq(i,17);fpfa10(i,3)=zq(i,26);fpfa10(i,4)=zq(i,32);fpfa10(i,5)=zq(i,38);fpfa10(i,6)=zq(i,7);endfori=1:n1(1,1)iffpfa10(i,1)==1fpfa10(i,1)=7;endiffpfa10(i,1)==2fpfa10(i,1)=6;endiffpfa10(i,1)==3fpfa10(i,1)=5;endiffpfa10(i,1)==4fpfa10(i,1)=4;endiffpfa10(i,1)==5fpfa10(i,1)=3;endiffpfa10(i,1)==6fpfa10(i,1)=2;endiffpfa10(i,1)==7fpfa10(i,1)=1;endendn2=size(fpfa10);fori=1:n2(1,1)yucers(i,1)=0.0344+0.5442*fpfa10(i,1)+0.2518*fpfa10(i,2)+0.1768*fpfa10(i,3)+0.0417*fpfa10(i,4)+0.3944*fpfa10(i,5);yucers(i,1)=floor(yucers(i,1))+1;yucers(i,2)=fpfa10(i,6);endplot(1:n2(1,1),yucers(:,1))holdonplot(1:n2(1,1),yucers(:,2))图11-42010年预测值与实际值比较图2011年的预测对比图如图11-5所示。%级岗合并clc,cl