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Question 2. (a) Write the simple linear regression model Mi=Bot Biểi tôi i=1,2,..., where ,~ N(0, ²) as a general linear model by identifying Y, X, 3 and e. Y = XB+E (b) State the distribution of e. (c) Hence find the least squares estimators of 30 and 3₁.

Question 2. (a) Write the simple linear regression model Mi=Bot Biểi tôi i=1,2,..., where ,~ N(0, ²) as a general linear model by identifying Y, X, 3 and e. Y = XB+E (b) State the distribution of e. (c) Hence find the least squares estimators of 30 and 3₁.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 2. (a) Write the simple linear regression model Yi = Bo + B₁xi + i=1,2,...,n where ~ N(0,02) as a general linear model by identifying Y, X, B and e. (b) State the distribution of e. Y = XB+E (c) Hence find the least squares estimators of 30 and 3₁. (d) Using the result that Var (3) = ²(XTX)-¹ find Var(30), Var(8₁) and Cov(80, 8₁). (e) The hat matrix is defined as H = X(X¹X)-¹X¹ Show that it is symmetric and idempotent. (f) Show that the vector of fitted values Ŷ is given by Ý =HY. (g) Hence find the vector of fitted values for the simple linear regression model.
Transcribed Image Text:Question 2. (a) Write the simple linear regression model Yi = Bo + B₁xi + i=1,2,...,n where ~ N(0,02) as a general linear model by identifying Y, X, B and e. (b) State the distribution of e. Y = XB+E (c) Hence find the least squares estimators of 30 and 3₁. (d) Using the result that Var (3) = ²(XTX)-¹ find Var(30), Var(8₁) and Cov(80, 8₁). (e) The hat matrix is defined as H = X(X¹X)-¹X¹ Show that it is symmetric and idempotent. (f) Show that the vector of fitted values Ŷ is given by Ý =HY. (g) Hence find the vector of fitted values for the simple linear regression model.
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