设随机变量^6x)的分布律为^6x)则关于X，Y的关系下列说法中正确的是（）A.不相关，相互独立B.相关，相互独立C.不相关，不相互独立D.相关，不相互独立

我国老年人口规模为()亿人。A. 2.64B. 3.75C. 1.33D. 4.86

设总体X~N(μ，σ^2)(σ^2已知)则在给定样本容量n及置信度1-α的情况下，未知参数μ的置信区间长度随着样本均值widehat(X)的增加而(      )A. 增加B. 减少C. 不变D. 不能确定增或减

等级相关系数计算时，要求指标变量（）。A. 均为离散型变量B. 均为连续型变量C. 一个是离散型变量，一个是连续型变量D. 以上都可以

体育统计工作的基本过程包括统计资料的( )。A. 收集B. 分类C. 整理D. 审核E. 分析

调换X和Y之后(1)建立回归模型,回归结果如下:Dependent Variable: YMethod: Least SquaresDate: 12/04/10 Time: 11:21Sample: 1970 1994Included observations: 25CoefficientStd. Errort-StatisticProb. X0.6374370.02124230.008460.0000C50.874548.2910586.1360730.0000R-squared0.975095 Mean dependent var298.2000Adjusted R-squared0.974012 S.D. dependent var27.97320S.E. of regression4.509491 Akaike info criterion5.926864Sum squared resid467.7167 Schwarz criterion6.024374Log likelihood-72.08580 Hannan-Quinn cr.ter.5.953909F-statistic90..5078 Durbin-Watson stat0.352762Prob(F-statistic)0.000000给定n=25,,在的显著水平下,查DW统计表可知,。模型中,所以可以判断模型中存在正自相关。(2)对模型的修正1)采广义差分法修正自相关:使用普通最小二乘法估计的估计值,得由上式可知=0.850961,对原模型进行广义差分,得到广义差分方程:回归结果如下:Dependent Variable: Y-0.850961*Y(-1)Method: Least SquaresDate: 12/04/10 Time: 11:17Sample (adjusted): 1971 1994Included observations: 24 after adjustmentsCoefficientStd. Errort-StatisticProb. X-0.850961*X(-1)0.5351250.0747937.1547960.0000C13.973344.7894362.9175330.0080R-squared0.699417 Mean dependent var48.03762Adjusted R-squared0.685754 S.D. dependent var4.550930S.E. of regression2.551144 Akaike info criterion4.790616Sum squared resid143.1833 Schwarz criterion4.888787Log likelihood-5..48739 Hannan-Quinn cr.ter.4.816661F-statistic51.19110 Durbin-Watson stat2.377660Prob(F-statistic)0.000000给定n=24,,在的显著水平下,查DW统计表可知,。模型中,因此可以判断模型不存在自相关。所以修正后的模型为:6.5参考解答:(1)建立回归模型,回归结果如下:Dependent Variable: LOG(Y)Method: Least SquaresDate: 05/07/10 Time: 00:17Sample: 1980 2000Included observations: 21CoefficientStd. Errort-StatisticProb. C2.1710410.2410259.0075290.0000LOG(X)0.9510900.03889724.451230.0000R-squared0.969199 Mean dependent var8.039307Adjusted R-squared0.967578 S.D. dependent var0.565486S.E. of regression0.101822 Akaike info criterion-1.640785Sum squared resid0.196987 Schwarz criterion-1.541307Log likelihood19.22825 Hannan-Quinn cr.ter.-1.619196F-statistic597.8626 Durbin-Watson stat1.159788Prob(F-statistic)0.000000给定n=21,,在的显著水平下,查DW统计表可知,。模型中,所以可以判断模型中存在正自相关。(2)采用广义差分法修正自相关:使用普通最小二乘法估计的估计值,得由上式可知=0.400234,对原模型进行广义差分,得到广义差分方程:回归结果如下:Dependent Variable: LOG(Y)-0.400234*LOG(Y(-1))Method: Least SquaresDate: 05/07/10 Time: 00:21Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsCoefficientStd. Errort-StatisticProb. C1.4770950.2256366.5463720.0000LOG(X)-0.400234*LOG(X(-1))0.9059890.05976715.158710.0000R-squared0.927357 Mean dependent var4.882162Adjusted R-squared0.923321 S.D. dependent var0.344052S.E. of regression0.095271 Akaike info criterion-1.769534Sum squared resid0.163380 Schwarz criterion-1.669961Log likelihood19.69534 Hannan-Quinn cr.ter.-1.750096F-statistic229.7864 Durbin-Watson stat1.441543Prob(F-statistic)0.000000给定n=20,,在的显著水平下,查DW统计表可知,。模型中,所以可以判断广义差分模型中不存在自相关。由差分方程式可以得出:所以修正后的模型为:(3)变换数据后的回归结果如下:Dependent Variable: LOG(Y/Y(-1))Method: Least SquaresDate: 05/07/10 Time: 00:23Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsCoefficientStd. Errort-StatisticProb. C0.0540470.0133224.0568960.0007LOG(X/X(-1))0.4422240.0660246.6979010.0000R-squared0.713658 Mean dependent var0.091592Adjusted R-squared0.697750 S.D. dependent var0.098311S.E. of regression0.054049 Akaike info criterion-2.903219Sum squared resid0.052583 Schwarz criterion-2.803646Log likelihood31.03219 Hannan-Quinn cr.ter.-2.883781F-statistic4..86188 Durbin-Watson stat1.590363Prob(F-statistic)0.000003给定n=20,,在的显著水平下,查DW统计表可知,。模型中,所以可以判断变化数据后的模型中不存在自相关。Prob(F-statistic)0.000000估计结果如下Se = (2.50.3) (0.0075)t = (-3.765.) (125.3411)R2 = 0.9978,F = 15710.39,d f = 34,DW = 0.5234(2)对样本量为36、一个解释变量的模型、5%显著水平,查DW统计表可知,dL=1.411,dU= 1.525,模型中DW<dL,显然消费模型中有自相关。(3)采用广义差分法由上式可知,对原模型进行广义差分,得到广义差分方程:回归结果如下:Dependent Variable: Y-0.72855*Y(-1)Method: Least SquaresDate: 05/06/10 Time: 23:11Sample (adjusted): 1961 1995Included observations: 35 after adjustmentsCoefficientStd. Errort-StatisticProb. C-3.7830591.870964-2.0219840.0513X-0.72855*X(-1)0.9484060.01890550.168200.0000R-squared0.987058 Mean dependent var86.40203Adjusted R-squared0.986666 S.D. dependent var26.56943S.E. of regression3.068065 Akaike info criterion5.135417Sum squared resid310.6298 Schwarz criterion5.224294Log likelihood-87.86979 Hannan-Quinn cr.ter.5.166097F-statistic2516.848 Durbin-Watson stat2.097157Prob(F-statistic)0.000000样本容量减少1.,为35,查5%显著水平的DW统计表可知dL = 1.402.dU = 1.519,模型中DW = 2.0972> dU,说明广义差分模型中已无自相关。同时,判定系数R2、t、F统计量均达到理想水平。由差分方程式可以得出:所以最终的消费模型为:由上述模型可知,美国个人实际可支配收入每增加1元,个人实际消费支出平均增加0.9484元。练习题6.2参考解答:(1)模型1中存在自相关,模型2中不存在自相关。(2)通过DW检验可以判定自相关的存在;在模型1.,DW=0.8252,查5%显著水平的DW统计表可知,,,因此模型1存在正自相关;而在模型2中,DW=1.82, 查5%显著水平的DW统计表可知,,,因此模型2不存在自相关。(3)虚假自相关是由模型设定失误所造成的自相关,主要包括遗漏某些重要的解释变量或者模型函数形式不正确,因此在区分虚假自相关和真正自相关是主要从这两个方面来判断,即根据经济意义检查解释变量是否遗漏了重要的变量,或者根据数据的数字特征检验模型形式的设定是否恰当。练习题6.3参考解答:(1)先对数据进行处理,收入-消费模型(个人实际收入与个人实际消费支出)个人实际消费支出=人均生活消费支出/商品零售物价指数*100建立回归模型,回归结果如下:Dependent Variable: YMethod: Least SquaresDate: 05/06/10 Time: 23:20Sample: 2001 2019Included observations: 19CoefficientStd. Errort-StatisticProb. X0.6904880.01287753.620680.0000C79.9300412.399196.4463900.0000R-squared0.994122 Mean dependent var70..2747Adjusted R-squared0.993776 S.D. dependent var246.4491S.E. of regression19.44245 Akaike info criterion8.872095Sum squared resid6.26.149 Schwarz criterion8.971510Log likelihood-82.28490 Hannan-Quinn cr.ter.8.888920F-statistic2875.178 Durbin-Watson stat0.574663Prob(F-statistic)0.000000估计结果如下(2)DW=0.575,对样本量为36、一个解释变量的模型、5%显著水平的DW统计表可知,说明误差项存在正自相关。(3)采用广义差分法使用普通最小二乘法估计的估计值,得由上式可知=0.657352,对原模型进行广义差分,得到广义差分方程:回归结果如下:Dependent Variable: Y-0.657352*Y(-1)Method: Least SquaresDate: 05/06/10 Time: 23:25Sample (adjusted): 2002 2019Included observations: 18 after adjustmentsCoefficientStd. Errort-StatisticProb. C35.977618.1035464.4397370.0004X-0.657352*X(-1)0.6686950.02064232.395120.0000R-squared0.984983 Mean dependent var278.1002Adjusted R-squared0.984044 S.D. dependent var105.1781S.E. of regression13.28570 Akaike info criterion8.115693Sum squared resid2824.158 Schwarz criterion8.214623Log likelihood-71.04124 Hannan-Quinn cr.ter.8.129334F-statistic1049.444 Durbin-Watson stat1.830746Prob(F-statistic)0.000000估计结果如下DW=1.830,已知,模型中因此,在广义差分模型中已无自相关。由差分方程式可以得出:(错误)( )

频数分布表是整理资料时最常用的方法。A. 对B. 错

10. 对于给定的正数α，0A. u_(alpha)=-u_(1-alpha)B. x_(1-alpha)^2(n)=-x_(alpha)^2(n)C. t_(alpha)(n)=-t_(1-alpha)(n)D. F_(1-alpha)(n_(1),n_(2))=(1)/(F_(alpha)(n_{2),n_(1))}

设总体 X sim E(lambda)，(X_1, X_2, ... X_n)为来自总体 X 的简单随机样本，则下列结论不正确的是(）。A. E(overline(X))= lambda；B. D(overline(X))= (1)/(nlambda^2)；C. E(overline(X))= (1)/(lambda)；D. X_i sim E(lambda)。

统计研究的根本目的是( )。A. 由样本特征来推断总体情况B. 用样本统计量来估计总体参数C. 通过样本的统计指标来判定总体参数是否相等的问题D. 减小抽样误差