Question 4: Consider a data set with the response vector Y = (y₁,..., yn) and the datamatrix-1X12(EB)1Inl=We model the relationship between X and Y using the linear regression model: y =00+0₁₁+0₂x₁2 + €₁, i 1,...,n, where ~ N(0,02). Let the parameter vector bedenoted as (00, 01,02). We wish to minimize the sum of squared residuals: SSE =Σ(yi (00+0₁₁+0₂2))². Let the fitted value be denoted as ĝi = 0 + 0₁x₁1 + 0₂x₁2,and let the fitted value vector be denoted as Ŷ.=2a) Show that SSE = Σ-1(yi - ŷi)².b) Show that SSE = (Y – Ŷ)¹(Y – Ý).c) Show that Ŷ = XO.d) Simplify the derivative equationasse20e) Find the solution of which solves the equation in part d.: 0.

Given a data set with the response vector, and the data matrix .

Answered: Question 4: Consider a data set with…

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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Derive the least squares estimates of a and ß for the centred form of the simple linear regression model given by Yi = a + B(x; – I) + €; i= 1,2,..,n. Check that the estimates do give a minimum in the same way as we saw for the standard form of the simple linear regression model.
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