1. 2. Derive the least squares estimator of ẞo for the regression model Y₁ = Po +εi- points Given the data (X) and (Y), we will assume that a regression model Y₁ = B₁Xi + &; is appropriate with normally distributed independent error terms and variance σ² = 16. i 1 2 3 4 Xi 7 12 25 30 Yi 128 213 446 540 (a) State the likelihood function for the four Y observations. (b) Evaluate the likelihood function for ẞ₁ = 17 and B₁ = 19. For which of these is the likelihood function the largest? (c) Find the maximum likelihood estimates for ẞ₁ and ẞo and using Sxx, Sxy, and the means for Xi and Yi, respectively, as demonstrated in the instructional videos.
1. 2. Derive the least squares estimator of ẞo for the regression model Y₁ = Po +εi- points Given the data (X) and (Y), we will assume that a regression model Y₁ = B₁Xi + &; is appropriate with normally distributed independent error terms and variance σ² = 16. i 1 2 3 4 Xi 7 12 25 30 Yi 128 213 446 540 (a) State the likelihood function for the four Y observations. (b) Evaluate the likelihood function for ẞ₁ = 17 and B₁ = 19. For which of these is the likelihood function the largest? (c) Find the maximum likelihood estimates for ẞ₁ and ẞo and using Sxx, Sxy, and the means for Xi and Yi, respectively, as demonstrated in the instructional videos.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Question using the least square
Transcribed Image Text:1.
Derive the least squares estimator of Bo for the regression model
Y = Bo + Ei.
2.
point
Given the data (Xi) and (Y), we will assume that a regression
model Y; = B1X; + E¡ is appropriate with normally distributed independent error
terms and variance o2 = 16.
%3D
i
1
4
7
12
25
30
Yi
128
213
446
540
(a) State the likelihood function for the four Y observations.
(b) Evaluate the likelihood function for B, = 17 and B, = 19. For which of
these is the likelihood function the largest?
(c) Find the maximum likelihood estimates for B, and Bo and using Sx, Sxy,
and the means for Xi and Yi, respectively, as demonstrated in the
instructional videos.
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