Matlab与Logistic回归

1、MatlabMatlab 软件包与 LogisticLogistic 回归在回归分析中，因变量y可能有两种情形：（1）y是一个定量的变量，这时就用通常的 regress 函数对y进行回归；（2）y是一个定性的变量，比如，丫=0或1,这时就不能用通常的 regress 函数对y进行回归，而是使用所谓的 Logistic 回归。Logistic 回归的基本思想是，不是直接对y进行回归，而是先定义一种概率函数冗，令二二PrY=1|XiX2，,Xn二xn要求0工冗工1。此时，如果直接对冗进行回归，得到的回归方程可能不满足这个条件。 在现实生活中， 一般有。n0.0000 （这个值比较好） ， 与显著性

2、概率3=0.05相关的p值=0.5526=0.05,说明变量x1，&,&之间存在线性相关关系。回归方程为：logJ-1=0.3914-0.0069x1-0.0093x22.42640.85041.07600.86711.03890.69551.02340.91900.94591.09671.63402.16811.16620.72051.04490.53421.39591.46830.96690.28390.57930.90201.05471.11160.63831.04760.8916-0.3263x3711J1311/0.3914-0.0069x1-0.0093x2-0.3

3、263x31e以及残差图：通过残差图看出，残差连续的出现在0的上方，或者连续地出现在0的下方，这也暗示变量%42，%之间存在线性相关。编程计算它们的相关系数：X=1,-62.8,-89.5,1.7;1,3.3,-3.5,1.1;1,-120.8,-103.2,2.5;1,-18.1,-28.8,1.1;1,-3.8,-50.6,0.9;1,-61.2,-56.2,1.7;1,-20.3,-17.4,1;1,-194.5,-25.8,0.5;1,20.8,-4.3,1;1,-106.1,-22.9,1.5;1,-39.4,-35.7,1.2;1,-164.1,-17.7,1.3;1,-308.9

4、,-65.8,0.8;1,7.2,-22.6,2.0;1,-118.3,-34.2,1.5;1,-185.9,-280,6.7;1,-34.6,-19.4,3.4;1,-27.9,6.3,1.3;1,-48.2,6.8,1.6;1,-49.2,-17.2,0.3;1,-19.2,-36.7,0.8;1,-18.1,-6.5,0.9;1,-98,-20.8,1.7;1,-129,-14.2,1.3;1,-4,-15.8,2.1;1,-8.7,-36.3,2.8;1,-59.2,-12.8,2.1;1,-13.1,-17.6,0.9;1,-38,1.6,1.2;1,-57.9,0.7,0.8;1,

5、-8.8,-9.1,0.9;1,-64.7,-4,0.1;1,-11.4,4.8,0.9;1,43,16.4,1.3;1,47,16,1.9;1,-3.3,4,2.7;1,35,20.8,1.9;1,46.7,12.6,0.9;1,20.8,12.5,2.4;1,33,23.6,1.5;1,26.1,10.4,2.1;1,68.6,13.8,1.6;1,37.3,33.4,3.5;1,59,23.1,5.5;1,49.6,23.8,1.9;1,12.5,7,1.8;1,37.3,34.1,1.5;1,35.3,4.2,0.9;1,49.5,25.1,2.6;1,18.1,13.5,4;1,31

6、.4,15.7,1.9;1,21.5,-14.4,1;1,8.5,5.8,1.5;1,40.6,5.8,1.8;1,34.6,26.4,1.8;1,19.9,26.7,2.3;1,17.4,12.6,1.3;1,54.7,14.6,1.7;1,53.5,20.6,1.1;1,35.9,26.4,2;1,39.4,30.5,1.9;1,53.1,7.1,1.9;1,39.8,13.8,1.2;1,59.5,7,2;1,16.3,20.4,1;1,21.7,-7.8,1.6;X1=X(:,2);X2=X(:,3);X3=X(:,4);corrcoef(X1,X2)corrcoef(X1,X3)co

7、rrcoef(X2,X3)执行后得到结果：ans=1.00000.64090.64091.0000ans=1.00000.04670.04671.0000ans=1.0000-0.3501-0.35011.0000可见corrcoef(X1,X2)=0.64,这说明， 在做回归时， 可以去掉x1 列，或者去掉用列。根据经济意义，我们去掉XI歹 I，再进行回归X=1,-62.8,-89.5,1.7;1,3.3,-3.5,1.1;1,-120.8,-103.2,2.5;1,-18.1,-28.8,1.1;1,-3.8,-50.6,0.9;1,-61.2,-56.2,1.7;1,-20.3,-17.

8、4,1;1,-194.5,-25.8,0.5;1,20.8,-4.3,1;1,-106.1,-22.9,1.5;1,-39.4,-35.7,1.2;1,-164.1,-17.7,1.3;1,-308.9,-65.8,0.8;1,7.2,-22.6,2.0;1,-118.3,-34.2,1.5;1,-185.9,-280,6.7;1,-34.6,-19.4,3.4;1,-27.9,6.3,1.3;1,-48.2,6.8,1.6;1,-49.2,-17.2,0.3;1,-19.2,-36.7,0.8;1,-18.1,-6.5,0.9;1,-98,-20.8,1.7;1,-129,-14.2,1.3

9、;1,-4,-15.8,2.1;1,-8.7,-36.3,2.8;1,-59.2,-12.8,2.1;1,-13.1,-17.6,0.9;1,-38,1.6,1.2;1,-57.9,0.7,0.8;1,-8.8,-9.1,0.9;1,-64.7,-4,0.1;1,-11.4,4.8,0.9;1,43,16.4,1.3;1,47,16,1.9;1,-3.3,4,2.7;1,35,20.8,1.9;1,46.7,12.6,0.9;1,20.8,12.5,2.4;1,33,23.6,1.5;1,26.1,10.4,2.1;1,68.6,13.8,1.6;1,37.3,33.4,3.5;1,59,23

10、.1,5.5;1,49.6,23.8,1.9;1,12.5,7,1.8;1,37.3,34.1,1.5;1,35.3,4.2,0.9;1,49.5,25.1,2.6;1,18.1,13.5,4;1,31.4,15.7,1.9;1,21.5,-14.4,1;1,8.5,5.8,1.5;1,40.6,5.8,1.8;1,34.6,26.4,1.8;1,19.9,26.7,2.3;1,17.4,12.6,1.3;1,54.7,14.6,1.7;1,53.5,20.6,1.1;1,35.9,26.4,2;1,39.4,30.5,1.9;1,53.1,7.1,1.9;1,39.8,13.8,1.2;1,

11、59.5,7,2;1,16.3,20.4,1;1,21.7,-7.8,1.6;a0=0.25*ones(33,1);a1=0.75*ones(33,1);y0=a0;a1;Y=log(1-y0)./y0);X1=X(:,2);X2=X(:,3);X3=X(:,4);E=ones(66,1);B=E,X2,X3;b,bint,r,rint,stats=regress(Y,B)rcoplot(r,rint)执行后得到：b=0.6594-0.0177-0.4676bint=0.26721.0516-0.0226-0.0127-0.6702-0.2649r=-0.34780.8917-0.21590.

12、4445-0.03430.24080.59920.21700.83080.73580.36930.7342-0.34970.97490.5361-1.37691.68611.15841.30750.27550.16460.74510.86650.79611.14191.10681.19490.54891.02860.82560.69920.41530.9449-0.8603-0.5868-0.4249-0.5020-1.1145-0.4149-0.6395-0.5923-0.76600.46881.2219-0.4490-0.7927-0.4540-1.2630-0.09870.3509-0.5921-1.5450-0.9541-0.8139-0.4498-0.2107-0.9275-0.705