Question: (10)Consider the model y i = 0 + 1 x i + u i . (a)Show that Cov ( y i .u i ) =

(10)Consider the model yi = 0 + 1xi + ui.

(a)Show that Cov(yi.ui) = 0

(b)Prove that the OLS provides an unbiased estimate of 1

(c)Prove that no other linear unbiased estimator for 1 has a smaller variance than the OLS estimator

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Consider the model: y i = ? 0 + ? 1 x i + u i , for i = 1, 2, . . . , N. Given the OLS estimator ?? 0 = y ? ?? 1 x, Show that the OLS errors have zero mean, i.e., u? = 0.

Q:

+ (10) Problem 4. Objective: To solve Poisson equation with no-flux (Neumann) boundary conditions, using finite differences and Gauss-Seidel. Consider the Poisson problem on [0, 1] x [0, 1] with...

Q:

University of California, Los Angeles Department of Statistics Statistics 100C Instructor: Nicolas Christou Homework 3 EXERCISE 1 Answer the following questions: a. Suppose y1 , y2 , . . . , yn are...

Q:

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Q:

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Q:

calculate the equations please Question 7. Point allocation: equal weights for each question. This question contains 6 short questions. I am looking for concise and specific answers and many do not...

Q:

1 MATH3075 Mathematical Finance (Normal) Due by 4 pm on Thursday, September 17, 2015 1. [10 marks] Elementary market model. Consider a single-period two-state market model M = (B, S) with the two...

Q:

. Kindly solve the following attachment. Q2. [14 points] Consider the same simple linear regression (SLR) model in Q1 which satises Gauss Markov assumptions: Y = ,80 + ,81 X + u, where the error term...

Q:

We saw in class that endogeneity leads to a violation of A1. In this question, we will work with a reduced form model to illustrate the problems. Throughout this question, we will work with the...

Q:

tt Suppose the Phillips curve equation is given as: u= 6 - 1.5 ( - e) which is equivalent to: Unemployment rate = Natural rate of unemployment - a (actual inflation - expected inflation) Based on the...

Q:

1. Tamarisk Company's unadjusted trial balance at December 31, 2020, included the following accounts. Debit $57,800 4,120 Accounts receivable Allowance for doubtful accounts Net sales Bad debt...

Q:

Describe the marketing mix for one of Disneys franchises.

Q:

Shirley, a recent college graduate, excitedly described to her older sister the $ 1 comma 8 4 0 1 , 8 4 0 sofa , table, and chairs she found today. However, when asked she could not tell her sister...

Q:

A _______ is a structured survey of the accuracy and level of completeness of the data in an information system. data overview data analysis systems audit data quality audit systems analysis

Q:

3. What values would you say are your core values?

Q:

12. Think of a situation where you felt particularly powerless. It must be a real event that you remember relatively well. Try to think back. What was it you imagined just before you felt powerless...

Q:

13. Try to imagine how you would feel if you had tackled the problem, the con-flict, the challenge, etc., that made you powerless in task 12, for example upstairs, confident, confident, calm,...