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1、1、下表给出了每周家庭的消费支出Y（美元）与每周的家庭的收入X（美元）的数据。每周收入（X）80100120140160180200220240260每周消费支出（Y）55，60，65，70，7565，70，74，80，85，8879，84，90，94，9880，93，95，103，108，113，115102，107，110，116，118，125110，115，120，130，135，140120，136，140，144，145135，137，140，152，157，160，162137，145，155，165，175，189150，152，175，178，180，185，191要求：（1
2、）对每一收入水平，计算平均的消费支出，E（YXi），即条件期望值；Xi80651007712089140101160113180125200137220149240161260173E(Y|Xi)（2）以收入为横轴、消费支出为纵轴作散点图；2001801601401201008060404080120160X200240280Y（3）在散点图中，做出（1）中的条件均值点；2001801601401201008060404080120160X200240280Y（4）你认为 X 与 Y 之间、X 与 Y 的均值之间的关系如何？如下图，表示的是家庭收入与平均消费支出的散点图，比较第（3）问的图形，
3、可知，X 与Y 之间是不完全的线性正相关关系，X 与 Y 的均值之间是完全的线性相关，即X 与 Y 的均值成正比。180160140120y10080604080120160X200240280（5）写出其总体回归函数及样本回归函数；总体回归函数是线性的还是非线性的？所取的样本如下：XiYi8055100651207914080160102180110200120220135240137260150总体回归模型：Yi170.6Xiui，根据第（4）问的散点图可知及回归模型可知，总体回归函数是线性的。样本回归模型:y 12.2730.535X ui2、根据上题中给出的数据，对每一个X 值，随机抽
4、取一个Y 值，结果如下：YX7080651009012095140110160115180120200140220155240150260要求：（1）以 Y 为纵轴、X 为横轴作图，并说明Y 与 X 之间是怎样的关系？160140120Y10080604080120160X（2）求样本回归函数，并按要求写出计算步骤；Dependent Variable:YMethod:Least SquaresDate:01/01/02Time:00:38Sample:1 10Included observations:10200240280VariableCXR-squaredCoefficient24.4
5、54550.509091Std.Error6.4138170.035743t-Statistic3.81279114.24317Prob.0.00510.0000111.000031.428936.7561846.816701202.86790.0000010.962062 Mean dependent var0.957319 S.D.dependent var6.493003 Akaike info criterion337.2727 Schwarz criterion-31.78092 F-statistic2.680127 Prob(F-statistic)Adjusted R-squa
6、redS.E.of regressionSum squared residLog likelihoodDurbin-Watson statY=24.45454545+0.5090909091*X（3）在同一个图中，做出样本回归函数及从上题中得到的总体回归函数；比较二者相同吗？为什么？3、下表给出了 19901996 年间的 CPI 指数与 S&P500 指数。年份1990199119921993199419951996CPI130.7136.2140.3144.5148.2152.4159.6S&P500 指数334.59376.18415.74451.41460.33541.64670.83
7、资料来源：总统经济报告，1997，CPI 指数见表 B-60，第 380 页；S&P 指数见表 B-93，第 406 页。要求：（1）以 CPI 指数为横轴、S&P 指数为纵轴做图；SP vs.CPI700600S&P500400300130135140145CPI150155160（3）你认为 CPI 指数与 S&P 指数之间关系如何？Dependent Variable:SPMethod:Least SquaresDate:01/01/02Time:00:59Sample:1990 1996Included observations:7VariableCCPIR-squaredCoeffi
8、cient-1137.82611.08361Std.Error177.94881.228555t-Statistic-6.3941229.021662Prob.0.00140.0003464.3886112.37289.8493609.83390681.390390.0002790.942123 Mean dependent var0.930548 S.D.dependent var29.61448 Akaike info criterion4385.086 Schwarz criterion-32.47276 F-statistic1.187041 Prob(F-statistic)Adju
9、sted R-squaredS.E.of regressionSum squared residLog likelihoodDurbin-Watson statS&P 1137.826411.0836CPI ui（-6.3941）（9.0217）R2 0.9421r 0.9305D.W.1.1870 F 81.3904RSS 4385.086该模型的经济意义表示，CPI 指数没上升 1 单位，S&P 指数上升 11.0836 单位，此数据没有明显的经济意义。（3）考虑下面的回归模型：(S&P)t B1 B2CPItut，根据表中的数据运用OLS估计上述方程，并解释你的结果；你的结果有经济意义吗
10、？SP=-1137.826376+11.08360968*CPI24、下表给出了美国 30 所知名学校的 MBA 学生 1994 年基本年薪（ASP）、GPA分数（从14 共四个等级）、GMAT 分数以及每年学费的数据。学校HarvardStanfordColumbianDartmouthWhartonNorthwesternChicagoMITVirginiaUCLABerkeleyCornellNUYDukeCarnegieMellonNorth CarolinaMichiganTexasIndianaPurdueCase WesternASP/美元10263010080010048095
11、4108993084640832108050074280740107197071970706607049059890698806782061890585205472057200GPA3.43.33.33.43.43.33.33.53.23.53.23.23.23.33.23.23.23.33.23.23.1GMAT650665640660650640650650643640647630630623635621630625615581591学费/美元23894211892140021225210502063421656216901783914496143612040020276219102060
12、01013220960858014036955617600GeorgetownMichigan StatePenn StateSouthern MethodistTulaneIllinoisLowaMinnesotaWashington6983041820491206091044080471304162048250441403.23.23.23.13.13.23.23.23.361959058060060061659060061719584160571140018034195501262893611261811436要求：（1）用双变量回归模型分析GPA是否对 ASP 有影响？Dependen
13、t Variable:ASPMethod:Least SquaresDate:01/01/02Time:01:17Sample:1 30Included observations:30VariableCGPAGMATR-squaredCoefficient-355885.915774.96597.2202Std.Error59332.1623296.78101.0962t-Statistic-5.9981950.6771305.907445Prob.0.00000.50410.000068260.0018187.7821.3412221.4813435.043310.0000000.72189
14、8 Mean dependent var0.701298 S.D.dependent var9940.289 Akaike info criterion2.67E+09 Schwarz criterion-317.1183 F-statistic1.072784 Prob(F-statistic)Adjusted R-squaredS.E.of regressionSum squared residLog likelihoodDurbin-Watson statASP=-355885.8717+15774.95992*GPA+597.2202084*GMATASP 355885.8717 15
15、774.9599GPA 597.2202GMAT u（-5.9982）（0.6771）（5.9074）9R 0.7219r 0.7013D.W.1.0728 F 35.0433RSS 2.671022Dependent Variable:ASPMethod:Least SquaresDate:01/01/02Time:01:18Sample:1 30Included observations:30VariableCGPAYR-squaredCoefficient-225517.178995.132.146033Std.Error66654.1921020.530.473281t-Statist
16、ic-3.3833893.7579994.534371Prob.0.00220.00080.000168260.0018187.7821.6047021.7448223.799250.0000010.638062 Mean dependent var0.611252 S.D.dependent var11340.02 Akaike info criterion3.47E+09 Schwarz criterion-321.0705 F-statistic1.658130 Prob(F-statistic)Adjusted R-squaredS.E.of regressionSum squared
17、 residLog likelihoodDurbin-Watson statASP=-225517.0671+78995.12961*GPA+2.146033398*YASP 225517.178995.12961GPA 2.14603Y（-6.3941）（9.0217）9R2 0.638062r 0.61125D.W.1.6581F 23.7448RSS 3.47*102（2）用合适的回归模型分析GMAT 分数是否与 ASP 有关？GMAT vs.ASP680660640GMAT620600580560400006000080000ASP100000Dependent Variable:GM
18、ATMethod:Least SquaresDate:11/05/14Time:23:10Sample:1 30Included observations:30CASPR-squaredCoefficient547.97330.001118Std.Error9.3598120.000133t-Statistic58.545338.426222Prob.0.00000.0000624.266724.004218.0308408.1242538.0607241.3595280.717175 Mean dependent var0.707074 S.D.dependent var12.99171 A
19、kaike info criterion4725.965 Schwarz criterion-118.4626 Hannan-Quinn criter.71.00122 Durbin-Watson stat0.000000Adjusted R-squaredS.E.of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)GMAT=547.973312824+0.00111768757461*ASPGMAT 547.97330.0011ASP（58.5453）（8.4262）R2 0.7171r 0.7070
20、D.W.1.3595 F 71.0012RSS 4725.965Dependent Variable:GMATMethod:Least SquaresDate:11/05/14Time:23:08Sample:1 30Included observations:30CLOG(ASP)R-squaredCoefficient-210.568875.23660Std.Error98.031998.832241t-Statistic-2.1479608.518404Prob.0.04050.0000624.266724.004218.0151868.10859920.721568 Mean depe
21、ndent var0.711624 S.D.dependent var12.89042 Akaike info criterion4652.559 Schwarz criterionAdjusted R-squaredS.E.of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)-118.2278 Hannan-Quinn criter.72.56321 Durbin-Watson stat0.0000008.0450691.435795GMAT=-210.568783815+75.2366001999*
22、LOG(ASP)GMAT -210.568875.2366log(ASP)（-2.1480）（8.5184）R2 0.7216r 0.7116D.W.1.4358 F 72.5632RSS 4652.559Dependent Variable:GMATMethod:Least SquaresDate:01/01/02Time:01:25Sample:1 30Included observations:30VariableCASPR-squaredCoefficient547.97330.001118Std.Error9.3598120.000133t-Statistic58.545338.42
23、6222Prob.0.00000.0000624.266724.004218.0308408.12425371.001220.00000020.717175 Mean dependent var0.707074 S.D.dependent var12.99171 Akaike info criterion4725.965 Schwarz criterion-118.4626 F-statistic1.359528 Prob(F-statistic)Adjusted R-squaredS.E.of regressionSum squared residLog likelihoodDurbin-Watson statGMAT=547.9733128+0.001117687575*ASP（4）每年的学费与 ASP 有关吗？你是如何知道的？如果两变量之间正相关，是否意味着进到最高费用的商业学校是有利的；Y vs.ASP280002400020000Y16000120008000400006000080000ASP100000（4）你同意高学费的商业学校意味着高质量的MBA 成绩吗？为什么？GMAT vs.Y680660640GMAT62060058056080001200016000200002400028000Y