Question: For the simple regression with a constant Yi = + Xi + ui, given in equation (3.1) verify the following numerical properties of the

For the simple regression with a constant Yi = α + βXi + ui, given in equation (3.1) verify the following numerical properties of the OLS estimators:

n i=1 ei = 0,

n i=1 eiXi = 0,

n i=1 ei Yi = 0,

n i=1

Yi =

n i=1 Yi

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 Econometrics Questions!

Q:

,.kindly solve please 1. Consider the simple regression model: V/i = Po+ Piri +ui, for i = 1, ..., n, with E(ur,) 7 0 and let z be a dummy instrumental variable for a, such that we can write: with...

Q:

Optimal Weighting of Unbiased Estimators. This is based on Baltagi (1995). For the simple regression without a constant Yi = Xi +ui, i = 1, 2, . . .,N; where is a scalar and ui IID(0, 2)...

Q:

For the simple regression without a constant Yi = Xi + ui, with ui IID(0, 2). (a) Derive the OLS estimator of and find its variance. (b) What numerical properties of the OLS estimators described in...

Q:

Set #2 Economics 141 Fall 2016 Due September 29 Review Exercises (not to turn in): Exercises 2.2, 2.4, 2.5, and 2.7 from Wooldridge's text. 1. Suppose you are given the following (semi-fabricated)...

Q:

. Provide detailed explanations to the attachments. Class 1 OLS estimators, properties, Gauss-Markov theorem, simple regression 1. A regression of average weekly earnings (AW E, measured in dollars)...

Q:

1. Consider the simple regression model: V/i = Po+ Piri +ui, for i = 1, ..., n, with E(ur,) 7 0 and let z be a dummy instrumental variable for a, such that we can write: with E(uilz;) = 0 and...

Q:

,. I NEED YOUR EFFORT HERE PLEASE 1. The simple linear regression model Y, = Bo + Bir; +;, &; " N(0, 0'), i = 1, ..., n, can also be written as a general linear model Y = XB+E, where Y = (Y1, . . .,...

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:

All questions pertain to the simple (two-variable) linear regression model for which the population regression equation can be written in conventional notation as: Y += + uX ii10i (1) where Yi and Xi...

Q:

@ kindly solve the following EXERCISE 4.36. In Example 4.20, use Eq. 4.16 to verify that the fake spheres with a = 2 and a = , have no umbilical points. (4.16) T. EXAMPLE 4.20 (Fake Spheres). We wish...

Q:

(Multiple choice) 1. The primary objective of financial reporting is to provide information a. on the cash flows of the company. b. to the federal government. c. useful for making investment and...

Q:

A $10,000, five-year bond redeemable at par and bearing interest at 6.5% payable semi-annually is purchased at a market price of $10,000 four years and 10 months before maturity. a). Determine the...

Q:

Marks & Spencer should look at each of the management accounting reports it produces with an eye toward how it helps managers make better decisions. Does it provide needed scorekeeping? Does it...

Q:

A bar of rectangular cross section is loaded and supported as shown in the figure. The distance between supports is L = 1.5m and the height of the bar is h = 120mm. The deflection at the midpoint is...