Specifically, expression of Wk from the critical point w we solve for each coefficient Wk (1

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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We would like to fit a linear regression estimate to the dataset
D =
(2)
(N)
,, (x
(i)
with x"" ER" by minimizing the ordinary least square (OLS) objective function:
N
M
J(w)
-E w; X
j =1
i=1
Specifically,
we solve for each coefficient Wk (1 <k < M) by deriving an
aJ (w.
=0. What is the expression for each Wk in terms of
(a)
expression of Wk from the critical point
the dataset (v(1)
N, yN) and w1, ·', Wk-1, Wk+1, *', WM ?
Select one:
Wi
Wk =
i =1 (Xk
M
Wk =
Wk = x)
4=1
Wk =
(b)
How many coefficients do you need to estimate? When solving for these coef-
ficients, how many equations do you have?
Select one:
N coefficients, M equations
M coefficients, N equations
M coefficients, M equations
N coefficients, N equations
Transcribed Image Text:We would like to fit a linear regression estimate to the dataset D = (2) (N) ,, (x (i) with x"" ER" by minimizing the ordinary least square (OLS) objective function: N M J(w) -E w; X j =1 i=1 Specifically, we solve for each coefficient Wk (1 <k < M) by deriving an aJ (w. =0. What is the expression for each Wk in terms of (a) expression of Wk from the critical point the dataset (v(1) N, yN) and w1, ·', Wk-1, Wk+1, *', WM ? Select one: Wi Wk = i =1 (Xk M Wk = Wk = x) 4=1 Wk = (b) How many coefficients do you need to estimate? When solving for these coef- ficients, how many equations do you have? Select one: N coefficients, M equations M coefficients, N equations M coefficients, M equations N coefficients, N equations
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