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1、学生学号0120814440111实验课成绩学生实验报告书实验课程名称统计计算（R软件）开课学院理学院指导教师姓名毛树华学生姓名李旭升学生专业班级统计学080120102011学年第2学期实验项目名称多元分析的R软件实现实验者李旭升专业班级统计学0801同组者实验日期2011-6-1实验题目卫星应用推动了银-锌电池的发展，表1列出了表征电池的在其寿命周期内失效的性能失效数据，利用这些数据：利用一下数据对电池的失效周期的影响因素进行分析，选出最优的变量子集充电率XI放电率X2放电深度X3温度X4充电电压极限X5失效周期Y0.3753.136040210113.1376.8301.9914113.
2、13602029613.1360201.981251.6253.1343.2102.01431.6253.1360202161.6253.1360202.021880.375576.8102.01101543.2101.9931543.2302.013861510020451.625576.8101.9920.3751.2576.8102.017611.2543.2101.997811.2576.830216011.25600231.6251.2543.2301.992161.6251.2560202730.3753.1376.8301.993140.3753.1360202170、实验步骤及
3、结果分析(R语言程序)1、数据的读取及初步的多元回归分析模型Mv-read.table(1234.txt,head=TRUE) Yv-M,1;X1v-M,2;X2v-M,3;X3v-M,4;X4v-M,5;X5v-M,6;X6v-M,7 Yv-M,6;X1v-M,1;X2v-M,2;X3v-M,3;X4v-M,4;X5v-M,5;#vectorassignment mul_rev-lm(Y1+X1+X2+X3+X4+X5)#establishthemultipleregressionmodel summary(mul_re)Call:lm(formula=Y1+X1+X2+X3+X4+X5)R
4、esiduals:Min1QMedian3QMax-178.735-26.345-1.32722.221167.110Coefficients:EstimateStd.ErrortvaluePr(ltl)(Intercept)214.066222.6020.9620.353X1-32.21445.401-0.7100.490X21.11114.7560.0750.941X3-1.5751.671-0.9430.362X46.8731.9993.4380.004*X5-53.05459.835-0.8870.390Signif.codes:0*0.001*0.01*0.05.0.11Residu
5、alstandarderror:86.27on14degreesoffreedomMultipleR-squared:0.4997,AdjustedR-squared:0.321F-statistic:2.796on5and14DF,p-value:0.05913由系数的显著性可以知道，X4有较强的显著性，回归系数显著性检验通过，但其他变量去不行，尽管有回归方程的P值知道回归方程也不显著，需要做进一步的分析。2、利用逐步回归法进行更进一步的回归工作。mul_stepv-step(mul_re)Start:AIC=183.16Y1+X1+X2+X3+X4+X5DfSumofSqRSSAIC-X2
6、142104228181.17-X113747107933181.87-X515851110037182.26-X316614110801182.40vnone104186183.16-X4187953192139193.41Step:AIC=181.17YX1+X3+X4+X5DfSumofSqRSSAIC-X11-X51-X31-X413850108079179.906552110780180.396641110869180.41104228181.1787911192140191.41Step:AIC=179.9YX3+X4+X5-X3-X5DfSumofSqRSSAIC13996112
7、075178.625191113270178.84108079179.90-X493574201652190.37Step:AIC=178.62YX4+X5DfSumofSqRSSAIC-X511976114051176.97112075178.62-X4191305203380188.54Step:AIC=176.97YX4DfSumofSqRSSAIC114051176.97-X4194179208230187.01summary(mul_step)Call:lm(formula=YX4)Residuals:MaxMin1QMedian3Q-151.803-46.733-4.66432.0
8、62198.853Coefficients:EstimateStd.ErrortvaluePr(ltl)(Intercept)-9.81936.334-0.2700.79004X46.5661.7033.8550.00116*Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:79.6on18degreesoffreedomMultipleR-squared:0.4523,AdjustedR-squared:0.4219F-statistic:14.86on1and18DF,p-value:0.001159最终结果，回归系数检验每一
9、个变量都非常显著，且回归方程的显著性也通过。并且残差的平方和有原来的86.17下降为79.6，有了一定的改善。4、回归诊断对残差进行分析 res2v-residuals(mul_step) par(mfrow=c(1,2) plot(Y,res2);qqnorm(res2) sdresv-rstandard(mul_step) sdres123456-2.21633551-0.61434217-0.328722260.04523956-0.16847822-1.360341077891011120.85763938-0.60160701-0.693482822.647260580.576988
10、08-0.706607931314151617180.264650570.29090080-0.361401540.180999310.38410766-0.6253126719201.688748750.62552515残差分布较分散，无明显趋势，且QQ图显示叫符合正态分布的假设。同时分析标准化残差，也得到每一个自变量对应的标准化残差都小于2,满足要求。NormalQ-QPlot052SPoo002051ool05o05-s-l-ca匕Qepas050100200300400YTheoreticalQuantiles二、实验结果分析逐步回归法：根据逐步回归法选入的自变量为X4,则回归方程为：y二9.819-6.566x4由此可知，对电池影响最大的是温度因素。
