多元线性回归 matlab中求解.doc

多元线性回归 matlab中求解源代码：y=data(:,1); x=data(:,2:3); b,bint,r,rint,stats=regress(y,x)结果：b =1.6031 21.0280bint =0.6449 2.5612 14.4526 27.6034r =-16.2442 8.8754 17.5828 8.3155 7.6692 -20.7990 0.1578 9.1298 21.1145 -28.9567rint =-54.5200 22.0316 -28.0267 45.7775 -15.2745 50.4401 -29.9540 46.5850 -30.7374 46.0758 -57.6551 16.0572 -40.7942 41.1098 -30.8252 49.0848 -15.2155 57.4446 -59.3228 1.4095stats =1.0148 742.1191 0.0000 322.5068分析结果：stats四个值说明：判决系数r2，,F统计值，p值，误差方差y=a1*x（1）+a2*x（2）;其中a1=1.6031,a2=21.0280,a1的置信区间【0.6449,2.5612】，a2的置信区间【14.45426，27.6043】，p小于0.05，说明显著效果很好，越小越好在spss中求解：线性规划 matlab求解例1：c=2;3;1; mix z=2*x1+3*x2+x3 a=1 4 2;3 2 0; s.t 1.x1+4*x2+2*x3=8; b=8;6; 2.3*x1+2*x2=6; x,y=linprog(c,-a,-b,zeros(3,1) ) 3.x1=0,x2=0,x3=0结果：x =0.8066 1.7900 0.0166 %最优解y =7.0000 %最优值例2：c=2;3;-5; max z=2*x1+3*x2-5*x3a=-2,5,-1;b=-10; s.t 1.x1+x2+x3=7;aeq=1,1,1; 2.2*x1-5*x2+x3=10;beq=7; 3.x1=0,x2=0,x3=0%是求最大值而不是最小值,注意这里是-c而不是cx=linprog(-c,a,b,aeq,beq,zeros(3,1)value=c*x结果：x =6.4286 0.5714 0.0000 %最优解value = 14.5714 %最优值例3.（整数规划）灰色预测clearsyms a b;c=a b;A=89677,99215,109655,120333,135823,159878,182321,209407,246619,300670;B=cumsum(A); %原始数据累加n=length(A);for i=1:(n-1) C(i)=(B(i)+B(i+1)/2; %生成累加矩阵end% 计算待定参数的值D=A;D(1)=;D=D ;E=-C;ones(1,n-1);c=inv(E*E)*E*D;c=c ;a=c(1);b=c(2);% 预测后续数据F=;F(1)=A(1);for i=2:(n+10) F(i)=(A(1)-b/a)/exp(a*(i-1)+b/a ;endG=;G(1)=A(1);for i=2:(n+10) G(i)=F(i)-F(i-1); %得到预测出来的数据endt1=1999:2008;t2=1999:2018;Gplot(t1,A,o,t2,G)结果; 1.0e+006 * 0.0897 0.0893 0.1034 0.1196 0.1385 0.1602 0.1854 0.2146 0.2