Calculating the likelihoodgive B² -2.7, B₁ = 2.9=and 5 = 0.25Ź12X Y X²81020 64 40026 100 67615 40 225 160033 86 389 26761

YiConsider a linear regression model Yi=β0+β1Xi+ϵi ∀ i=1,2,...,nhere, ϵi follows Normal(0,σ2)…

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Calculating the likelihood
give B² -2.7, B₁ = 2.9
=
and 5 = 0.25
Ź
12
X Y X²
8
10
20 64 400
26 100 676
15 40 225 1600
33 86 389 26761

Expert Solution

Step 1: Given Information

$Y_{i}$ Consider a linear regression model

$Y_{i} = β_{0} + β_{1} X_{i} + ϵ_{i} \forall i = 1, 2, . . ., n$

$h e r e, ϵ_{i} f o l l o w s N o r m a l (0, σ^{2}) d i s t r i b u t i o n$

Given the values.

$β_{0} =$ -2.7

$β_{1} = 2.9$

$σ = 0.25$

and n = 3

To compute Likelihood construct the following table for residuals $ϵ_{i}$

$X_{i}$	$Y_{i}$	$ϵ_{i} = Y_{i} - β_{0} - β_{1} X_{i}$	$ϵ_{i}^{2}$
8	20	-0.5	0.25
10	26	-0.3	0.09
15	40	-0.8	0.64

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Calculating the likelihood give B = -2.7, B₁ = 2.9 and 5 = 0.25 W XY 8 20 64 400 26 100 676 10 15 40 225 1600 33 86 389 2676