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Binghamton University, SUNY Department of EconomicsCourse : Econ 466 - EconometricsSection : B1Term : Spring 2019Instructor : Luis D. Chanc A. ()T.A. : Shi Zuo ()Problem Set No 2Due 02/06/2019 , 8:00 p.m.1 Estimation.1. Let, ^ = P(Xi X)(Yi Y)=P(Xi X)2. Show that ^ = P(Xi X)Yi=P(Xi X)22. Consider the following regression Yi = 0 +ui (regression without any regressor).Show that the OLS estimate ^ 0 of 0 is Y = PYi=N.3. Consider the following regression Yi = Xi +ui (there is not intercept).Show that the OLS estimator of is ^ = (PXiYi)=(PX2i ).4. Consider the linear model: Yi = 0 + 1(Xi X) +ui.Find the OLS estimators of 0 and 1. Compare with the OLS estimators of 0 and 1 in the standardmodel discussed in class (Yi = 0 + 1Xi +ui).5. Based on a sample of 10 observations the following results were obtained:PYi = 1;110 ; PXi = 1;700 ; PXiYi = 205;500 ; PX2i = 322;000 ; PY2i = 132;100Show that the OLS estimate ^ 0 and ^ 1 for the model Yi = 0 + 1Xi+ui are ^ 0 = 24:5 and ^ 1 = 0:509.2 ANOVA.1. Let, Yi = 0 + 1Xi +ui and ^ 1 = P(Xi X)(Yi Y)=P(Xi X)2.Show that SSE = P( ^Yi ^Y)2 = ^ 21(PX2i N X2).2. Consider the following regression Yi = 0 + ui (regression without any regressor), and let ^ 0 be theOLS estimate of 0. Find the variance of ^ 0 and the SSR.3. Consider the following regression Yi = Xi +ui (there is not intercept), and let ^ be the OLS estimateof . Find the variance of ^ .4. Consider the following regression Yi = Xi +ui (there is not intercept), and let ~ be the OLS estimateof . Let ^ 1 be the OLS estimate of 1 for the standard model discussed in class (Yi = 0 + 1Xi +ui).Show that Var( ~ ) Var( ^ 1).(Hint: for any sample of data, PX2i P(Xi X)2, with strict inequality unless X = 0)5. Consider the linear model: Yi = 0 + 1(Xi X) +ui. Let ^ 0 and ^ 1 be the OLS estmates. Find thevariance of ^ 0 and ^ 1. Compare with the variance of the OLS estimator of 0 and 1 in the standardmodel discussed in class (Yi = 0 + 1Xi +ui).6. Based on a sample of 10 observations the following results were obtained:PYi = 1;110 ; PXi = 1;700 ; PXiYi = 205;500 ; PX2i = 322;000 ; PY2i = 132;100Show that SSE 8549:67ECON 466 Pag. 1 out of 2 Spring 2019Binghamton University, SUNY Department of Economics7. Let r1 be the coe cient of correlation between n pairs of values (Yi;Xi) and r2 be the coe cient ofcorrelation between n pairs of values (aYi +b;cXi +d) where a, b, c, and d are constants. Show thatr1 = r2 and hence establish the principle that the coe cient of correlation is invariant with respect tothe change of scale and the change of origin.Hint:r1 = rYX = Cov(X;Y)pVar(X)Var(Y) NPXiYi PXiPYip[NPX2i (PXi)2][NPY2i (PYi)2]8. If r, the coe cient of correlation between n pairs of values (Xi;Yi), is positive, then determine whethereach of the following statements is true or false:(a) r between ( Xi; Yi) is also positive.(b) r between ( Xi;Yi) and that between (Xi; Yi) can be either positive or negative.9. Let ^ YX and ^ XY represent the slopes in the regression of Y on X (Y = 0 + YXX + u) and X onY (X = 0 + XYY +v), respectively. Show that ^ YX ^ XY = r2.ECON 466 Pag. 2 out of 2 Spring 2019本团队核心人员组成主要包括硅谷工程师、BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：[email protected] 微信：codehelp