统计预测与决策——徐国祥第三章参考答案

第三章⑴解：代码：y=c(12.5,13.8,14,25,14,25,14.5,13,14,15,15,75,16.5)xl=c(0.41,0.5410.63,0.54,0.48,0.46,0.62,0.61,0.64,0.71)cor(y,xl)>cor(yFxl)截图：[1]0.8479618由R语言运算结果可知，广告费支出与销售额的相关系数约为0.8479,有显著的相关关系。(2)代码:cc<-data.frame(y,xl)model<-lm(y-xl?data=cc)summary(model)截图：Call:Im(formula=y~xl,data=cc)Residuals:MinIQMedian3QMax-0.95582-0.28293-0.025640.472061.04622Coefficients:EstimateScd.(Intercept)8.304xl10.729Errortvalue1.3546.1330.000279***2.3714.5250.001938**20.050.1Signif.codes:0'食食*'0.0010.01Residualstandarderror;0.6683on8degreesoffreedomMultipleR-squared:0.719,AdjustedR-squared:0.6839F-statistic:20.47on1and8DF,p-value:0.001938由R语言运算结果知回归模型为y=8.304-H0.729xo(3)由上 题 快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题 运算结果可知，MultipleR-squared的值为0.719,即可决系数， 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 明回归模型能解释的销售额变动的比例为7L9%。代码:install.packages("installr")#更新R版本require(installr)updateR0library(lmtest)#安装DW检验函数dwtest(model)截图：>dwcest(model)Durbin-Watsontestdata:modelDW=1.562,p-value=0.1678alternativehypothesis:trueautocorrelationisgreaterthan0DW统计量的值为L562,无显著自相关性。代码:new<-data.frame(xl=0.67)ypred<-predict(modelInew,interval="prediction",level=0.95)ypred#预测区间截图：>ypred*预测区间fitIwrupr115.4922613.7751517.20937>1在置信度为0.05的情况下,广告费支出为0.67万元时,预测下周销售额区间约为(13.77,o7、代码：7=0(150,140,160,170150,162,185,165190,185)xl=c(40,42,48,55,65,79,88,100,120,140)cor(y,xl)model<-lm(y-xl!data=cc)summary(model)截图：>cor(yrxi)[1]0.8077659>x»odel<-lm(y~xlrdata=cc)>suTOnary(model)Call:Im(formula-y*•xl,data-cc)Residuals:MinIQMedian3QMax-11-498-8.5S0-2.4607.13315.202Coefficients:EstimateStd.ErrorzvaluePr(>|r|)(Intercept)134.78938.643215.5952.85e-07«**xl0.39780.10263.8760.0047Signif.codes:0'***'0.0010.010.05'・'0.1Resxdualstandarderror:10.53on8degreesoffreedomMultipleR-squared:O.€525,AdjuscedR-squared:0.609F-sxzatiscic:15.02on1and8DF,p-value:0.004704由上题运算结果可知，MultipleR-squared即可决系数的值为0.6525,相关系数值约为0.8078o由R语言运算结果知回归模型为y=134,7893+0.3978Xo回归系数的检验的t值为3.876。，当显著性水平为0.05时，自由度为8的t检验的临界值为2.306,3.876>2,306,因此回归系数显著，回归方程的检验的F值为1502。，当显著性水平为0.05时，FQ,8)的临界值为5.3215,02>5.32,因此回归方程显著口8、(1)代码:7=0(61.6,53.2,65.5,64.9,72.7,52.2,50.2,44,53.8,53.5)xl=c(6,44,9.1,8,1,97,4.8,7,6,4,4,9,1,67)x2=c(6,3,5,5,3,6,5.8,6,8,7,9,4,2,6,0,2,8,67)cc<-data.frame(y,xl,x2)model<-lm(y-xl+x2,data=cc)summary(model)截图：Call:Im(formula=y**xl*x2,data=cc)Residuals:MinIQMedian3QMax-S.7005-4.0547-0.78744.68336.6122Coefficients••EscxmateStd.ErrortvaluePrOltn(Intercept)13.44913.2321.0160.34325xl4.0171.0713.7490.00718一x22.8121.3792.0400.08076.Signif.codes:00.0010.010.05工'0.1Residualstandarderror:5•66€on7degreesoffreedomMultipleR-squared:0.6682,AdjustedR-squared:0.5734F-scatiscic:7.049on2and7DF,p-value:0.02104由R语言运算结果知回归模型y=13.449+4.017xl+2,812x2o(2)由运算结果可知可决系数即MultipleR-squared的值为0.6682。(3)代码与结果:dwtest(model)>dwtest(model)Durbin-Watsontestdata:modelDW=0.1776,p-value=1.678e-05alternativehypothesis:trueautocorrelationisgreaterthan0因此，D-W统计量的值为0.1776。(3)代码与结果：new<-data.frame(xl=5,x2=6)ypred<-predict(model,newjnterval=Mprediction",level=0.95)fixIwxupr150.4037435.6483165.15318>1因此，在显著性水平为0.05的水平下，xl=5,x2=6时Y的预测区间约为(35.64831,65.15918)(1)代码与结果：y二c(15,15,21,28,30,35,40,35,30,45,50,60,45,60,50)xl=c(0,0,0,1,1,1,1,222,334,4,5)x2=c(21,18,22,24,25,25,26,34,25,38,44,51,39,54,55)cc<-data.frame(y,xl,x2)ccmodel<-lm(y-xl+x2,data=cc)summary(model)Residuals:MinIQMedian3QMax-10.122-3.5431.5422.31710.557Coefficients:EstimateScd.Errorz(Incercept)2.085720.056591.050026.739312.61310u.32621value0.3090.0223.21S0.762260.982960.00737««Signif.codes:0.001……0.05)'0.1Residualstandarderror:6.059on12degreesoffreedomMulcipleR-squared:0.8503rAdjustedR-squared:0.8254F-scacisclc:34.08on2and12DFrp-value:1.125e-05多元回归方程为：y=2.08572+0.05699xl+1,05002x2⑵代码与结果：new<-data.frame(xl=2,x2=25)ypred<-predict(model,newjnterval=Mprediction",level=0.95)>ypred*预测区间fitIwrupr128.4502713.4217643.47878在显著性水平为0.05情况下，xl=2,x2=25时,Y的置信区间约为(13.42,43.48)(4)多重共线性检脸代码和结果：>x：L=c(。，0,0,工，1,1,1,2,2,2,3,3,4,4,5)x2-c(21r18r22r24r25r25r26r34r25r38r44r51r39r5*55)cor(xlfx2)[1]0.919834>I多重共线性检验自变量之间的相关关系，本题有xl,x2两个自变量，计算其相关系数即可判断多重共线性。计算得相关系数约为0.92,xl和x2间可能存在多重共线性。