In class, we have defined the hypothesis for univariate linear regression as he(x) = 00 + 0₁x and the mean-square cost function as 1 J(00.01) - Σ (h₂(x²) — y()) ² 2m i=1 We define the following terms: m Ex0, x, y= 1Ỷy, xy= ¹ [x®y®¸ x²= ¹ [(x0)² m m m i=1 i=1 i=1 a. Show that the optimal values of the learning parameters 00 and 01 are given by: ху-ху 00 = y-x x²-x² 0₁ = ху-ху x²-x² b. What is the advantage of expressing the learning parameters in this format? =

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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In class, we have defined the hypothesis for univariate linear regression as
he(x) = 00 + 0₁x
and the mean-square cost function as
2
J(00,01)
Σ (ho(x²) - y(i)) ²
2m
i=1
We define the following terms:
m
`x), y= 10.
;Σy"), xy = - ²
x(1) y(i) x²:
(x(1)) ²
m
a. Show that the optimal values of the learning parameters 00 and 0₁ are given by:
00 = y-x
xy−xy
x²-x²
01
=
ху-ху
x²-x²
b. What is the advantage of expressing the learning parameters in this format?
=
Transcribed Image Text:In class, we have defined the hypothesis for univariate linear regression as he(x) = 00 + 0₁x and the mean-square cost function as 2 J(00,01) Σ (ho(x²) - y(i)) ² 2m i=1 We define the following terms: m `x), y= 10. ;Σy"), xy = - ² x(1) y(i) x²: (x(1)) ² m a. Show that the optimal values of the learning parameters 00 and 0₁ are given by: 00 = y-x xy−xy x²-x² 01 = ху-ху x²-x² b. What is the advantage of expressing the learning parameters in this format? =
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