Matlab软件包与Logistic回归

Matlab软件包与Logistic回归在回归 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 中，因变量可能有两种情形：（１）是一个定量的变量，这时就用通常的regress函数对进行回归；（２）是一个定性的变量，比如，０或１，这时就不能用通常的regress函数对进行回归，而是使用所谓的Logistic回归。Logistic回归的基本思想是，不是直接对进行回归，而是先定义一种概率函数，令要求。此时，如果直接对进行回归，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。直接求的 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 达式，是比较困难的一件事，于是，人们改为考虑一般的，。人们经过研究发现，令即，是一个Logistic型的函数，效果比较理想。于是，我们将其变形得到：然后，对进行通常的线性回归。例如，Logistic型概率函数的图形如下：ezplot('1/(1+300*exp(-2*x))',[0,10])例１　企业到金融商业机构贷款，金融商业机构需要对企业进行评估。例如，Moody公司就是NewYork的一家专门评估企业的贷款信誉的公司。设：下面列出美国66家企业的具体情况：YX1X2X30-62.8-89.51.703.3-3.51.10-120.8-103.22.50-18.1-28.81.10-3.8-50.60.90-61.2-56.21.70-20.3-17.41.00-194.5-25.80.5020.8-4.31.00-106.1-22.91.50-39.4-35.71.20-164.1-17.71.30-308.9-65.80.807.2-22.62.00-118.3-34.21.50-185.9-280.06.70-34.6-19.43.40-27.96.31.30-48.26.81.60-49.2-17.20.30-19.2-36.70.80-18.1-6.50.90-98.0-20.81.70-129.0-14.21.30-4.0-15.82.10-8.7-36.32.80-59.2-12.82.10-13.1-17.60.90-38.01.61.20-57.90.70.80-8.8-9.10.90-64.7-4.00.10-11.44.80.9143.016.41.3147.016.01.91-3.34.02.7135.020.81.9146.712.60.9120.812.52.4133.023.61.5126.110.42.1168.613.81.6137.333.43.5159.023.15.5149.623.81.9112.57.01.8137.334.11.5135.34.20.9149.525.12.6118.113.54.0131.415.71.9121.5-14.41.018.55.81.5140.65.81.8134.626.41.8119.926.72.3117.412.61.3154.714.61.7153.520.61.1135.926.42.0139.430.51.9153.17.11.9139.813.81.2159.57.02.0116.320.41.0121.7-7.81.6其中，建立破产特征变量的回归方程。解：在这个破产问题中，我们讨论，概率。设＝企业２年后具备还款能力的概率，即，＝企业不破产的概率。因为66个数据有33个为0，33个为1，所以，取分界值0.5，令由于我们并不知道企业在没有破产前概率的具体值，也不可能通过的数据把这个具体的概率值算出来，于是，为了方便做回归运算，我们取区间的中值，。数据表变为：X1X2X30.25-62.8-89.51.70.253.3-3.51.10.25-120.8-103.22.50.25-18.1-28.81.10.25-3.8-50.60.90.25-61.2-56.21.70.25-20.3-17.41.00.25-194.5-25.80.50.2520.8-4.31.00.25-106.1-22.91.50.25-39.4-35.71.20.25-164.1-17.71.30.25-308.9-65.80.80.257.2-22.62.00.25-118.3-34.21.50.25-185.9-280.06.70.25-34.6-19.43.40.25-27.96.31.30.25-48.26.81.60.25-49.2-17.20.30.25-19.2-36.70.80.25-18.1-6.50.90.25-98.0-20.81.70.25-129.0-14.21.30.25-4.0-15.82.10.25-8.7-36.32.80.25-59.2-12.82.10.25-13.1-17.60.90.25-38.01.61.20.25-57.90.70.80.25-8.8-9.10.90.25-64.7-4.00.10.25-11.44.80.90.7543.016.41.30.7547.016.01.90.75-3.34.02.70.7535.020.81.90.7546.712.60.90.7520.812.52.40.7533.023.61.50.7526.110.42.10.7568.613.81.60.7537.333.43.50.7559.023.15.50.7549.623.81.90.7512.57.01.80.7537.334.11.50.7535.34.20.90.7549.525.12.60.7518.113.54.00.7531.415.71.90.7521.5-14.41.00.758.55.81.50.7540.65.81.80.7534.626.41.80.7519.926.72.30.7517.412.61.30.7554.714.61.70.7553.520.61.10.7535.926.42.00.7539.430.51.90.7553.17.11.90.7539.813.81.20.7559.57.02.00.7516.320.41.00.7521.7-7.81.6于是，在Matlab软件包中编程如下，对进行通常的线性回归：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,-17.4,1;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;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;1,59,23.1,5.5;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;1,59.5,7,2;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);[b,bint,r,rint,stats]=regress(Y,X)rcoplot(r,rint)执行后得到结果：b=0.3914-0.0069-0.0093-0.3263bint=0.00730.7755-0.0105-0.0032-0.0156-0.0030-0.5253-0.1273r=-0.00371.0561-0.26830.67330.50280.31790.7320-0.70441.13610.25530.4955-0.1593-1.76431.19840.0662-0.99371.39830.99880.96210.30720.49420.81610.39570.11411.21761.22250.86700.74680.85310.57770.85560.25880.9675-0.6179-0.3984-0.5943-0.4360-0.7585-0.4476-0.5541-0.5288-0.36870.21940.9248-0.3078-0.7516-0.4266-0.9150-0.06800.0653-0.5082-1.1506-0.8882-0.5701-0.4191-0.3540-0.8289-0.4239-0.5720-0.3449-0.3153-0.4396-0.6967-0.3640-0.8616-0.8919rint=-1.43201.4245-0.39902.5113-1.69751.1608-0.78822.1349-0.92221.9277-1.14981.7856-0.73322.1971-2.06960.6609-0.30702.5791-1.20481.7154-0.97301.9640-1.56261.2441-2.9063-0.6223-0.24992.6466-1.39251.5249-1.7217-0.2657-0.00512.8018-0.46092.4585-0.49092.4152-1.15051.7649-0.95561.9439-0.64772.2799-1.06481.8562-1.32381.5521-0.23402.6692-0.21622.6613-0.59112.3250-0.71362.2073-0.61172.3178-0.88682.0421-0.60442.3156-1.19441.7120-0.49142.4264-2.08620.8504-1.87291.0760-2.05580.8671-1.91081.0389-2.21250.6955-1.91861.0234-2.02710.9190-2.00340.9459-1.83401.0967-1.19511.6340-0.31862.1681-1.78191.1662-2.22380.7205-1.89811.0449-2.36430.5342-1.53191.3959-1.33781.4683-1.98340.9669-2.58500.2839-2.35560.5793-2.04220.9020-1.89291.0547-1.81951.1116-2.29610.6383-1.89551.0476-2.03550.8916-1.81781.1280-1.78761.1571-1.91051.0313-2.16200.7686-1.83351.1055-2.32370.6005-2.35440.5707stats=0.569927.38410.00000.5526即，得到：值＝0.5699（说明回归方程刻画原问题不是太好），F_检验值＝27.3841>0.0000（这个值比较好），与显著性概率相关的p值＝0.5526>，说明变量之间存在线性相关关系。回归方程为：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,-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,-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;1,31.4,15.7,1.9;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)corrcoef(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，可以去掉列。根据经济意义，我们去掉列，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,-17.4,1;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;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;1,59,23.1,5.5;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;1,59.5,7,2;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=-0.34780.8917-0.21590.4445-0.03430.24080.59920.21700.83080.73580.36930.7342-0.34970.97490.5361-1.37691.68611.15841.30750.27550.16460.74510.86650.79611.14191.10681.19490.54891.02860.82560.69920.41530.9449-0.8603-0.5868-0.4249-0.5020-1.1145-0.4149-0.6395-0.5923-0.76600.46881.2219-0.4490-0.7927-0.4540-1.2630-0.09870.3509-0.5921-1.5450-0.9541-0.8139-0.4498-0.2107-0.9275-0.7051-0.8796-0.3563-0.3306-0.7441-0.9530-0.6992-0.9299-1.1478rint=-1.92801.2325-0.72202.5054-1.78771.3560-1.17462.0636-1.63821.5696-1.37431.8558-1.01892.2173-1.38981.8237-0.78332.4449-0.88452.3561-1.24961.9882-0.88532.3537-1.93301.2335-0.63852.5883-1.08522.1574-2.1813-0.57240.14353.2286-0.44632.7631-0.29092.9059-1.32751.8785-1.44601.7752-0.86952.3597-0.75142.4843-0.82222.4144-0.46452.7482-0.48832.7020-0.40912.7988-1.06802.1659-0.58132.6384-0.78512.4364-0.91632.3146-1.18272.0132-0.66382.5535-2.47500.7543-2.20821.0345-2.03921.1894-2.12301.1190-2.71550.4865-2.03321.2034-2.25860.9795-2.21331.0287-2.38500.8531-1.08942.0270-0.14532.5892-2.06951.1715-2.41210.8268-2.07161.1637-2.85750.3315-1.70761.5102-1.19781.8995-2.21351.0292-3.12300.0331-2.56860.6603-2.43290.8052-2.06991.1704-1.82581.4044-2.54070.6858-2.32540.9152-2.49080.7316-1.97551.2629-1.94901.2879-2.36440.8761-2.56430.6582-2.31980.9215-2.53830.6785-2.75540.4598stats=0.471628.11750.00000.6681以及残差图：残差图仍然显示变量之间的相关性，这说明，最开始调查数据时，３个指标没有选好。最后得到：将企业的具体数据代入的表达式计算，再结合金融机构就可以知道，是否应该贷款给这家企业。注：一个通常的Regress回归，可以用等参数评价回归结果的好坏，但对Logistic回归来说，不存在这样简单而令人满意的评价参数，所以，一般应该进行回归诊断。Logistic回归的诊断所谓的回归诊断，就是将的原始数据代入求得的回归方程中，计算值，看看有多少个由回归方程计算所得的值与原始的值不同，因而判断回归方程的好坏。（1）用回归方程进行诊断。①在Matlab软件包中，编程诊断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,-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,-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;1,31.4,15.7,1.9;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];forj=1:66;f=1/(1+exp(0.3914-0.0069*X(j,2)-0.0093*X(j,3)-0.3263*X(j,4)));iff<=0.5;jy=0elsejy=1endend②在Mathematica软件包中编程如下：执行后得到结果（只列出不相同的）：序号的原始值Logistic回归值序号的原始值Logistic回归值13423533643753863974084190142104311441245134614014715481649170150185119521020532154225523562457250158260159276028612962306331643265336666个数据，有6个不同，出错率为9％，即，正确率为91％。（1）用回归方程进行诊断，在Mathematica软件包中编程如下：执行后得到结果（只列出不相同的）：序号的原始值Logistic序号的原始值Logistic回归值回归值13423533643753810639740841942104311441245134614471548101649170150180151190152102053215422552356245725015826015927016028612962306331643265336666个数据，有9个不同，出错率为13.64％，即，正确率为86.36％。评价：有3个自变量的Logistic回归方程的效果好一些。（注：可编辑下载，若有不当之处，请指正，谢谢!）推荐精选推荐精选推荐精选