Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. consider the following regression model: yi = α

Consider the following regression model: Yi = αXi + Ui , i = 1, .., n...

90.2K

Verified Solution

Question

Basic Math

Consider the following regression model: Yi = αXi + Ui , i = 1,.., n (2)

The error terms Ui are independently and identically distributedwith E[Ui |X] = 0 and V[Ui |X] = σ^2 .

1. Write down the objective function of the method of leastsquares.

2. Write down the first order condition and derive the OLSestimator αˆ.

Suppose model (2) is estimated, although the (true) populationregression model corresponds to: Yi = β0 + β1Xi + Ui , i = 1, .., nwith β0 different to 0.

3. Derive the expectation of αˆ, E[ˆα], as a function of β0, β1and Xi . Is αˆ an unbiased estimator for β1? [Hint: Derive firstE[ˆα|X].]

4. Derive the conditional variance of αˆ, V[ˆα|X], as a functionof σ^2 and Xi .

Answer & Explanation Solved by verified expert
3.8 Ratings (672 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Physics
1.2K views

A group of students, performing the same Uniformly Accelerated Motion experiment that you did in lab,...

Physics
1.2K views

5 A small disc is projected on a horizontal floor with a speed u Coefficient...

Basic Math
1.2K views

Multiply 2 75 x 1 2 OA 0 825 OB 3 3 OC 8 25...

Calculus
1.2K views

nd the derivative x f x ex cosh x

Algebra
1.2K views

10 8 6 4 a Je 25 b 20 15 10 S 10 15 20...

Algebra
1.2K views

2x-y+z=6x-3y +z = -2x + 2y-z = 3draw a sketch of the three fields and...

Accounting
1.2K views

Which of the following accounts has a normal credit balance? a. Accounts Receivable b....

Accounting
1.2K views

Gong Badak Medical Centre (GBMC), a newly set-up hospital, leases an electronic digital scanning machine...

Finance
1.2K views

9311.73 is wrong (1 point) Suzie wants to buy a car for...

Accounting
1.2K views

Madison Corp. has a hurdle rate/required rate of return of 9%. Operating income Average Operating...

Finance
1.2K views

Razak has some property for sale and has received two offers. The first offer is...

Finance
1.2K views

use the equation Pv1-5=DIV1/rE-Gx(1-(1+g/1+rE)^n) to find value of dividend payments OVE = Homework:...