统计建模与R语言习题答案

统计建模与R语言薛毅编的统计建模与R软件习题答案，仅供参考。工作环境仍是LINUX。第二章答案EX21XHISTSERUMDATA,FREQFALSE,COL“PURPLE“,BORDER“RED“,DENSITY3,ANGLE60,MAINPASTE“THEHISTOGRAMOFSERUMDATA“,XLAB“AGE“,YLAB“FREQUENCY“直方图。COL是填充颜色。默认空白。BORDER是边框的颜色，默认前景色。DENSITY是在图上画条纹阴影，默认不画。ANGLE是条纹阴影的倾斜角度（逆时针方向），默认45度。MAIN,XLAB,YLAB是标题，X和Y坐标轴名称。LINESDENSITYSERUMDATA,COL“BLUE“密度估计曲线。XLINESX,DNORMX,MEANSERUMDATA,SDSERUMDATA,COL“GREEN“正态分布的概率密度曲线PLOTECDFSERUMDATA,VERTICALSTRUE,DOPFALSE绘制经验分布图LINESX,PNORMX,MEANSERUMDATA,SDSERUMDATA,COL“BLUE“正态经验分布QQNORMSERUMDATA,COL“PURPLE“绘制QQ图QQLINESERUMDATA,COL“RED“绘制QQ直线EX33STEMSERUMDATA,SCALE1作茎叶图。原始数据小数点后数值四舍五入。THEDECIMALPOINTISATTHE|64|30066|2333368|0088877770|3444444222272|000000077777775555555555574|03333333370000000468888876|555555522678|088855580|35526682|84|3BOXPLOTSERUMDATA,COL“LIGHTBLUE“,NOTCHT作箱线图。NOTCH表示带有缺口。FIVENUMSERUMDATA五数总结1643712735758843EX34SHAPIROTESTSERUMDATA正态性SHAPORIWILK检验方法SHAPIROWILKNORMALITYTESTDATASERUMDATAW09897,PVALUE06437结论P值005，可认为来自正态分布的总体。KSTESTSERUMDATA,“PNORM“,MEANSERUMDATA,SDSERUMDATAKOLMOGROVSMIRNOV检验，正态性ONESAMPLEKOLMOGOROVSMIRNOVTESTDATASERUMDATAD00701,PVALUE07097ALTERNATIVEHYPOTHESISTWOSIDEDWARNINGMESSAGEINKSTESTSERUMDATA,“PNORM“,MEANSERUMDATA,SDSERUMDATACANNOTCOMPUTECORRECTPVALUESWITHTIES结论P值005，可认为来自正态分布的总体。注意，这里的警告信息，是因为数据中有重复的数值，KS检验要求待检数据时连续的，不允许重复值。EX35YFPLOTF,Y,COL“LIGHTGREEN“PLOT生成箱线图XYZBOXPLOTX,Y,Z,NAMESC“1“,“2“,“3“,COLC5,6,7BOXPLOT生成箱线图统计建模与R软件第三章习题答案数据描述性分析结论第2和第3组没有显著差异。第1组合其他两组有显著差异。EX36数据太多，懒得录入。离散图应该用PLOT即可。EX37STUDATADATAFRAMESTUDATA转化为数据框V1V2V3V4V5V611ALICEF1356584022BECKAF1365398033GAILF1464390044KARENF1256377055KATHYF1259884566MARYANDYF1151350588SHARONAMMYF1462810251010ALFREDM1469011251111DUKEM1463510251212GUIDOM1567013301313JAMESM125738301414JEFFERYM136258401515JOHNM125909951616PHILIPM1672015001717ROBERTM1264812801818THOMASM115758501919WILLIAMM156651120NAMESSTUDATAATTACHSTUDATA将数据框调入内存PLOTWEIGHTHEIGHT,COL“RED“体重对于身高的散点图COPLOTWEIGHTHEIGHT|SEX,COL“BLUE“不同性别，体重与身高的散点图COPLOTWEIGHTHEIGHT|AGE,COL“BLUE“不同年龄，体重与身高的散点图COPLOTWEIGHTHEIGHT|AGESEX,COL“BLUE“不同年龄和性别，体重与身高的散点图统计建模与R软件第三章习题答案数据描述性分析EX38XYFZCONTOURX,Y,Z,LEVELSC0,1,2,3,4,5,10,15,20,30,40,50,60,80,100,COL“BLUE“二维等值线统计建模与R软件第三章习题答案数据描述性分析PERSPX,Y,Z,THETA120,PHI0,EXPAND07,COL“LIGHTBLUE“三位网格曲面统计建模与R软件第三章习题答案数据描述性分析EX39ATTACHSTUDATACORTESTHEIGHT,WEIGHTPEARSON相关性检验PEARSONSPRODUCTMOMENTCORRELATIONDATAHEIGHTANDWEIGHTT75549,DF17,PVALUE7887E07ALTERNATIVEHYPOTHESISTRUECORRELATIONISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL0704431409523101SAMPLEESTIMATESCOR08777852由此可见身高和体重是相关的。EX310EX311上述两题原始数据太多，网上找不到，懒得录入。略。EX41只会极大似然法，不会矩法统计建模与R软件第四章习题答案参数估计EX42指数分布，的极大似然估计是N/SUMXIXLAMDAXMEANX11平均为1个。EX44OBJX0NLMOBJ,X0MINIMUM14898425ESTIMATE111412779108968052GRADIENT11411401E081493206E07CODE11ITERATIONS116EX45XTTESTXTTEST做单样本正态分布区间估计ONESAMPLETTESTDATAXT35947,DF9,PVALUE4938E11ALTERNATIVEHYPOTHESISTRUEMEANISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL631585716415SAMPLEESTIMATESMEANOFX674平均脉搏点估计为674，95区间估计为631585716415。TTESTX,ALTERNATIVE“LESS“,MU72TTEST做单样本正态分布单侧区间估计ONESAMPLETTESTDATAXT24534,DF9,PVALUE001828ALTERNATIVEHYPOTHESISTRUEMEANISLESSTHAN7295PERCENTCONFIDENCEINTERVALINF7083705SAMPLEESTIMATESMEANOFX674P值小于005，拒绝原假设，平均脉搏低于常人。要点TTEST函数的用法。本例为单样本；可做双边和单侧检验。EX46XYTTESTX,Y,VAREQUALTRUETWOSAMPLETTESTDATAXANDYT46287,DF18,PVALUE00002087ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL7536262006374SAMPLEESTIMATESMEANOFXMEANOFY14061268期望差的95置信区间为7536262006374。要点TTEST可做两正态样本均值差估计。此例认为两样本方差相等。PS我怎么觉得这题应该用配对T检验EX47XYTTESTX,Y,VAREQUALTRUETWOSAMPLETTESTDATAXANDYT1198,DF7,PVALUE02699ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL00019963510006096351SAMPLEESTIMATESMEANOFXMEANOFY014125013920期望差的95的区间估计为00019963510006096351EX48接EX46VARTESTX,YFTESTTOCOMPARETWOVARIANCESDATAXANDYF02353,NUMDF9,DENOMDF9,PVALUE004229ALTERNATIVEHYPOTHESISTRUERATIOOFVARIANCESISNOTEQUALTO195PERCENTCONFIDENCEINTERVAL005845276094743902SAMPLEESTIMATESRATIOOFVARIANCES02353305要点VARTEST可做两样本方差比的估计。基于此结果可认为方差不等。因此，在EX46中，计算期望差时应该采取方差不等的参数。TTESTX,YWELCHTWOSAMPLETTESTDATAXANDYT46287,DF13014,PVALUE00004712ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL735971320240287SAMPLEESTIMATESMEANOFXMEANOFY14061268期望差的95置信区间为735971320240287。要点TTESTX,Y，VAREQUALTRUE做方差相等的两正态样本的均值差估计TTESTX,Y做方差不等的两正态样本的均值差估计EX49XNTMPMEANX11904762MEANXTMPMEANXTMP1149404112315483平均呼唤次数为19095的置信区间为149,2,32EX410XTTESTX,ALTERNATIVE“GREATER“ONESAMPLETTESTDATAXT239693,DF9,PVALUE9148E10ALTERNATIVEHYPOTHESISTRUEMEANISGREATERTHAN095PERCENTCONFIDENCEINTERVAL9208443INFSAMPLEESTIMATESMEANOFX9971灯泡平均寿命置信度95的单侧置信下限为9208443要点TTEST做单侧置信区间估计EX51XTTESTX,MU225ONESAMPLETTESTDATAXT34783,DF19,PVALUE0002516ALTERNATIVEHYPOTHESISTRUEMEANISNOTEQUALTO22595PERCENTCONFIDENCEINTERVAL17238272119173SAMPLEESTIMATESMEANOFX19215原假设油漆工人的血小板计数与正常成年男子无差异。备择假设油漆工人的血小板计数与正常成年男子有差异。P值小于005，拒绝原假设，认为油漆工人的血小板计数与正常成年男子有差异。上述检验是双边检验。也可采用单边检验。备择假设油漆工人的血小板计数小于正常成年男子。TTESTX,MU225,ALTERNATIVE“LESS“ONESAMPLETTESTDATAXT34783,DF19,PVALUE0001258ALTERNATIVEHYPOTHESISTRUEMEANISLESSTHAN22595PERCENTCONFIDENCEINTERVALINF2084806SAMPLEESTIMATESMEANOFX19215同样可得出油漆工人的血小板计数小于正常成年男子的结论。EX52PNORM1000,MEANX,SDX105087941X11067919119678511269369181156920948PNORM1000,MEANX,SDX105087941XABTTESTA,B,PAIREDTRUEPAIREDTTESTDATAAANDBT06513,DF7,PVALUE05357ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL1562889887889SAMPLEESTIMATESMEANOFTHEDIFFERENCES3375P值大于005，接受原假设，两种方法治疗无差异。EX54（1）正态性W检验XYSHAPIROTESTXSHAPIROWILKNORMALITYTESTDATAXW09699,PVALUE07527SHAPIROTESTYSHAPIROWILKNORMALITYTESTDATAYW0971,PVALUE07754KS检验KSTESTX,“PNORM“,MEANX,SDXONESAMPLEKOLMOGOROVSMIRNOVTESTDATAXD01065,PVALUE0977ALTERNATIVEHYPOTHESISTWOSIDEDWARNINGMESSAGEINKSTESTX,“PNORM“,MEANX,SDXCANNOTCOMPUTECORRECTPVALUESWITHTIESKSTESTY,“PNORM“,MEANY,SDYONESAMPLEKOLMOGOROVSMIRNOVTESTDATAYD01197,PVALUE09368ALTERNATIVEHYPOTHESISTWOSIDEDWARNINGMESSAGEINKSTESTY,“PNORM“,MEANY,SDYCANNOTCOMPUTECORRECTPVALUESWITHTIESPEARSON拟合优度检验，以X为例。SORTX1561614070504071720252528303540164546586071X1PP1004894712024990009062002288090075856098828138PCHISQTESTX1,PPCHISQUAREDTESTFORGIVENPROBABILITIESDATAX1XSQUARED05639,DF4,PVALUE0967WARNINGMESSAGEINCHISQTESTX1,PPCHISQUAREDAPPROXIMATIONMAYBEINCORRECTP值为0967，接受原假设，X符合正态分布。（2）方差相同模型T检验TTESTX,Y,VAREQUALTRUETWOSAMPLETTESTDATAXANDYT06419,DF38,PVALUE05248ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL23261791206179SAMPLEESTIMATESMEANOFXMEANOFY20652625方差不同模型T检验TTESTX,YWELCHTWOSAMPLETTESTDATAXANDYT06419,DF36086,PVALUE0525ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL232926120926SAMPLEESTIMATESMEANOFXMEANOFY20652625配对T检验TTESTX,Y,PAIREDTRUEPAIREDTTESTDATAXANDYT06464,DF19,PVALUE05257ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL23731461253146SAMPLEESTIMATESMEANOFTHEDIFFERENCES056三种检验的结果都显示两组数据均值无差异。（3）方差检验VARTESTX,YFTESTTOCOMPARETWOVARIANCESDATAXANDYF15984,NUMDF19,DENOMDF19,PVALUE03153ALTERNATIVEHYPOTHESISTRUERATIOOFVARIANCESISNOTEQUALTO195PERCENTCONFIDENCEINTERVAL0632650540381795SAMPLEESTIMATESRATIOOFVARIANCES1598361接受原假设，两组数据方差相同。EX55ABKSTESTA,“PNORM“,MEANA,SDAONESAMPLEKOLMOGOROVSMIRNOVTESTDATAAD01464,PVALUE09266ALTERNATIVEHYPOTHESISTWOSIDEDKSTESTB,“PNORM“,MEANB,SDBONESAMPLEKOLMOGOROVSMIRNOVTESTDATABD02222,PVALUE0707ALTERNATIVEHYPOTHESISTWOSIDEDWARNINGMESSAGEINKSTESTB,“PNORM“,MEANB,SDBCANNOTCOMPUTECORRECTPVALUESWITHTIESA和B都服从正态分布。方差齐性检验VARTESTA,BFTESTTOCOMPARETWOVARIANCESDATAAANDBF19646,NUMDF11,DENOMDF9,PVALUE03200ALTERNATIVEHYPOTHESISTRUERATIOOFVARIANCESISNOTEQUALTO195PERCENTCONFIDENCEINTERVAL0502194370488630SAMPLEESTIMATESRATIOOFVARIANCES1964622可认为A和B的方差相同。选用方差相同模型T检验TTESTA,B,VAREQUALTRUETWOSAMPLETTESTDATAAANDBT88148,DF20,PVALUE2524E08ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL48249752978358SAMPLEESTIMATESMEANOFXMEANOFY12558331646000可认为两者有差别。EX56二项分布总体的假设检验BINOMTEST57,400,P0147EXACTBINOMIALTESTDATA57AND400NUMBEROFSUCCESSES57,NUMBEROFTRIALS400,PVALUE08876ALTERNATIVEHYPOTHESISTRUEPROBABILITYOFSUCCESSISNOTEQUALTO014795PERCENTCONFIDENCEINTERVAL0109747701806511SAMPLEESTIMATESPROBABILITYOFSUCCESS01425P值005，故接受原假设，表示调查结果支持该市老年人口的看法EX57二项分布总体的假设检验BINOMTEST178,328,P05,ALTERNATIVE“GREATER“EXACTBINOMIALTESTDATA178AND328NUMBEROFSUCCESSES178,NUMBEROFTRIALS328,PVALUE006794ALTERNATIVEHYPOTHESISTRUEPROBABILITYOFSUCCESSISGREATERTHAN0595PERCENTCONFIDENCEINTERVAL0495761610000000SAMPLEESTIMATESPROBABILITYOFSUCCESS05426829不能认为这种处理能增加母鸡的比例。EX58利用PEARSON卡方检验是否符合特定分布CHISQTESTC315,101,108,32,PC9,3,3,1/16CHISQUAREDTESTFORGIVENPROBABILITIESDATAC315,101,108,32XSQUARED047,DF3,PVALUE09254接受原假设，符合自由组合定律。EX59利用PEARSON卡方检验是否符合泊松分布NYXQP1CHISQTESTY,PPCHISQUAREDTESTFORGIVENPROBABILITIESDATAYXSQUARED21596,DF5,PVALUE08267WARNINGMESSAGEINCHISQTESTY,PPCHISQUAREDAPPROXIMATIONMAYBEINCORRECT重新分组，合并频数小于5的组ZNCHISQTESTZ,PPCHISQUAREDTESTFORGIVENPROBABILITIESDATAZXSQUARED09113,DF3,PVALUE08227可认为数据服从泊松分布。EX510KS检验两个分布是否相同XYKSTESTX,YTWOSAMPLEKOLMOGOROVSMIRNOVTESTDATAXANDYD0375,PVALUE06374ALTERNATIVEHYPOTHESISTWOSIDEDEX511列联数据的独立性检验XDIMXCHISQTESTXPEARSONSCHISQUAREDTESTWITHYATESCONTINUITYCORRECTIONDATAXXSQUARED374143,DF1,PVALUE9552E10P值Y,1,2,31,4512102,4620283,2823304,111235CHISQTESTYPEARSONSCHISQUAREDTESTDATAYXSQUARED40401,DF6,PVALUE3799E07P值FISHERTESTXFISHERSEXACTTESTFORCOUNTDATADATAXPVALUE06372ALTERNATIVEHYPOTHESISTRUEODDSRATIOISNOTEQUALTO195PERCENTCONFIDENCEINTERVAL004624382513272210SAMPLEESTIMATESODDSRATIO0521271P值大于005，两变量独立，两种工艺对产品的质量没有影响。EX514由于是在相同个体上的两次试验，故采用MCNEMAR检验。MCNEMARTESTXMCNEMARSCHISQUAREDTESTDATAXMCNEMARSCHISQUARED28561,DF3,PVALUE04144P值大于005，不能认定两种方法测定结果不同。EX515符号检验H0中位数146H1中位数XBINOMTESTSUMX146,LENGTHX,AL“L“EXACTBINOMIALTESTDATASUMX146ANDLENGTHXNUMBEROFSUCCESSES1,NUMBEROFTRIALS10,PVALUE001074ALTERNATIVEHYPOTHESISTRUEPROBABILITYOFSUCCESSISLESSTHAN0595PERCENTCONFIDENCEINTERVAL0000000003941633SAMPLEESTIMATESPROBABILITYOFSUCCESS01拒绝原假设，中位数小于146WILCOXON符号秩检验WILCOXTESTX,MU146,AL“L“,EXACTFWILCOXONSIGNEDRANKTESTWITHCONTINUITYCORRECTIONDATAXV45,PVALUE001087ALTERNATIVEHYPOTHESISTRUELOCATIONISLESSTHAN146拒绝原假设，中位数小于146EX516符号检验法XYBINOMTESTSUMXY,LENGTHXEXACTBINOMIALTESTDATASUMXYANDLENGTHXNUMBEROFSUCCESSES14,NUMBEROFTRIALS20,PVALUE01153ALTERNATIVEHYPOTHESISTRUEPROBABILITYOFSUCCESSISNOTEQUALTO0595PERCENTCONFIDENCEINTERVAL0457210808810684SAMPLEESTIMATESPROBABILITYOFSUCCESS07接受原假设，无差别。WILCOXON符号秩检验WILCOXTESTX,Y,PAIREDTRUE,EXACTFALSEWILCOXONSIGNEDRANKTESTWITHCONTINUITYCORRECTIONDATAXANDYV136,PVALUE0005191ALTERNATIVEHYPOTHESISTRUELOCATIONSHIFTISNOTEQUALTO0拒绝原假设，有差别。WILCOXON秩和检验WILCOXTESTX,Y,EXACTFALSEWILCOXONRANKSUMTESTWITHCONTINUITYCORRECTIONDATAXANDYW2745,PVALUE004524ALTERNATIVEHYPOTHESISTRUELOCATIONSHIFTISNOTEQUALTO0拒绝原假设，有差别。正态性检验KSTESTX,“PNORM“,MEANX,SDXONESAMPLEKOLMOGOROVSMIRNOVTESTDATAXD01407,PVALUE08235ALTERNATIVEHYPOTHESISTWOSIDEDWARNINGMESSAGEINKSTESTX,“PNORM“,MEANX,SDXCANNOTCOMPUTECORRECTPVALUESWITHTIESKSTESTY,“PNORM“,MEANY,SDYONESAMPLEKOLMOGOROVSMIRNOVTESTDATAYD01014,PVALUE0973ALTERNATIVEHYPOTHESISTWOSIDED两组数据均服从正态分布。方差齐性检验VARTESTX,YFTESTTOCOMPARETWOVARIANCESDATAXANDYF11406,NUMDF19,DENOMDF19,PVALUE07772ALTERNATIVEHYPOTHESISTRUERATIOOFVARIANCESISNOTEQUALTO195PERCENTCONFIDENCEINTERVAL0451478828817689SAMPLEESTIMATESRATIOOFVARIANCES1140639可认为两组数据方差相同。综上，该数据可做T检验。T检验TTESTX,Y,VAREQUALTRUETWOSAMPLETTESTDATAXANDYT22428,DF38,PVALUE003082ALTERNATIVEHYPOTHESISTRUEDIFFERENCEINMEANSISNOTEQUALTO095PERCENTCONFIDENCEINTERVAL081255315877447SAMPLEESTIMATESMEANOFXMEANOFY3321524870拒绝原假设，有差别。综上所述，WILCOXON符号秩检验的差异检出能力最强，符号检验的差异检出最弱。EX517SPEARMAN秩相关检验XYCORTESTX,Y,METHOD“SPEARMAN“,EXACTFSPEARMANSRANKCORRELATIONRHODATAXANDYS95282,PVALUE4536E05ALTERNATIVEHYPOTHESISTRUERHOISNOTEQUALTO0SAMPLEESTIMATESRHO09422536KENDALL秩相关检验CORTESTX,Y,METHOD“KENDALL“,EXACTFKENDALLSRANKCORRELATIONTAUDATAXANDYZ32329,PVALUE0001225ALTERNATIVEHYPOTHESISTRUETAUISNOTEQUALTO0SAMPLEESTIMATESTAU08090398二者有关系，呈正相关。EX518XWILCOXTESTX,Y,EXACTFWILCOXONRANKSUMTESTWITHCONTINUITYCORRECTIONDATAXANDYW266,PVALUE005509ALTERNATIVEHYPOTHESISTRUELOCATIONSHIFTISNOTEQUALTO0P值大于005，不能拒绝原假设，尚不能认为新方法的疗效显著优于原疗法。EX61（1）XYPLOTX,Y由此判断，Y和X有线性关系。（2）LMSOLSUMMARYLMSOLCALLLMFORMULAY1XRESIDUALSMIN1QMEDIAN3QMAX12859170978372749263167228COEFFICIENTSESTIMATESTDERRORTVALUEPR|T|INTERCEPT140951251111270293X36418192618908633E08SIGNIFCODES00001001005011RESIDUALSTANDARDERROR9642ON8DEGREESOFFREEDOMMULTIPLERSQUARED09781,ADJUSTEDRSQUARED09754FSTATISTIC3575ON1AND8DF,PVALUE633E08回归方程为Y1409536418X（3）1项很显著，但常数项0不显著。回归方程很显著。（4）NEWLMPREDLMPREDFITLWRUPR1269022724549712925484故Y72690227,2454971,2925484EX621PHOLMSOLSUMMARYLMSOLCALLLMFORMULAYX1X2X3,DATAPHORESIDUALSMIN1QMEDIAN3QMAX275751116027991157448808COEFFICIENTSESTIMATESTDERRORTVALUEPR|T|INTERCEPT4492901834082450002806X118033052903409000424X201337044400301076771X301668011411462016573SIGNIFCODES00001001005011RESIDUALSTANDARDERROR1993ON14DEGREESOFFREEDOMMULTIPLERSQUARED0551,ADJUSTEDRSQUARED04547FSTATISTIC5726ON3AND14DF,PVALUE0009004回归方程为Y44929018033X101337X201668X3（2）回归方程显著，但有些回归系数不显著。（3）LMSTEP556341112X318498641311118X11461781018121201STEPAIC10932YX1X3DFSUMOFSQRSSAIC559941093X318332643261098X11516951076891191SUMMARYLMSTEPCALLLMFORMULAYX1X3,DATAPHORESIDUALSMIN1QMEDIAN3QMAX297131132429531128648679COEFFICIENTSESTIMATESTDERRORTVALUEPR|T|INTERCEPT4147941388342988000920X117374046693721000205X301548010361494015592SIGNIFCODES00001001005011RESIDUALSTANDARDERROR1932ON15DEGREESOFFREEDOMMULTIPLERSQUARED05481,ADJUSTEDRSQUARED04878FSTATISTIC9095ON2AND15DF,PVALUE0002589X3仍不够显著。再用DROP1函数做逐步回归。DROP1LMSTEPSINGLETERMDELETIONSMODELYX1X3DFSUMOFSQRSSAIC559941093X11516951076891191X318332643261098可以考虑再去掉X3LMOPT|T|INTERCEPT592590742007986567E07X118434047893849000142SIGNIFCODES00001001005011RESIDUALSTANDARDERROR2005ON16DEGREESOFFREEDOMMULTIPLERSQUARED04808,ADJUSTEDRSQUARED04484FSTATISTIC1482ON1AND16DF,PVALUE0001417皆显著。EX63XYPLOTX,YLMSOLSUMMARYLMSOLCALLLMFORMULAY1XRESIDUALSMIN1QMEDIAN3QMAX98413233690021410592178320COEFFICIENTSESTIMATESTDERRORTVALUEPR|T|INTERCEPT145191835307910436X15578028075549793E06SIGNIFCODES00001001005011RESIDUALSTANDARDERROR5168ON26DEGREESOFFREEDOMMULTIPLERSQUARED05422,ADJUSTEDRSQUARED05246FSTATISTIC308ON1AND26DF,PVALUE7931E06线性回归方程为Y1451915578X，通过F检验。常数项参数未通过T检验。ABLINELMSOLYYESYFITYRSTPLOTYYESYFITPLOTYRSTYFIT残差并非是等方差的。修正模型，对相应变量Y做开方。LMNEWSUMMARYLMNEWCALLLMFORMULASQRTYXRESIDUALSMIN1QMEDIAN3QMAX154255045280001177034925212486COEFFICIENTSESTIMATESTDERRORTVALUEPR|T|INTERCEPT0766500255922995000596X0291360039147444664E08SIGNIFCODES00001001005011RESIDUALSTANDARDERROR07206ON26DEGREESOFFREEDOMMULTIPLERSQUARED06806,ADJUSTEDRSQUARED06684FSTATISTIC5541ON1AND26DF,PVALUE6645E08此时所有参数和方程均通过检验。对新模型做标准化残差图，情况有所改善，不过还是存在一个离群值。第24和第28个值存在问题。EX64TOOTHPASTELMSOL|T|INTERCEPT40759062676504100E06X115276023546489104E06X206138010275974363E06SIGNIFCODES00001001005011RESIDUALSTANDARDERROR01767ON24DEGREESOFFREEDOMMULTIPLERSQUARED09378,ADJUSTEDRSQUARED09327FSTATISTIC181ON2AND24DF,PVALUE333E15回归诊断INFLUENCEMEASURESLMSOLINFLUENCEMEASURESOFLMFORMULAYX1X2,DATATOOTHPASTEDFB1_DFBX1DFBX2DFFITCOVRCOOKDHATINF1000908000260000847001211366511E05016812006277004467006785012441159532E03005373002809007724002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