Consider the simple linear model Y = Bo + B1 + €, e are independent, iden- tically distributed with mean 0 and variance o?. Note: Must use the Linear combination of Y method! See Example 12 of 3 - Simple Linear Regression (Inference). a) Show that the least square estimator Bo =Ỹ – Bjữ is an unbiased of Bo. I Er?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
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please help with sub part c

Consider the simple linear model Y =
tically distributed with mean 0 and variance o?. Note: Must use the Linear
combination of Y method! See Example 12 of 3 - Simple Linear Regression
(Inference).
Bo + B1 + €, e are independent, iden-
a) Show that the least square estimator Bo
Ỹ - Bī is an unbiased of B-
b) Show that (1) Varl&] = i
o? (ii) and attains the minimum
n Σ, (τ- )>.
variance among all estimates that are linear combination of the response
variable Y.
c) Show that the test statistic
t =
is equivalent to t=
where S.E(B)) =
%3D
S.E(§)'
VE (; – #)²
1-r2
-
п-2
Transcribed Image Text:Consider the simple linear model Y = tically distributed with mean 0 and variance o?. Note: Must use the Linear combination of Y method! See Example 12 of 3 - Simple Linear Regression (Inference). Bo + B1 + €, e are independent, iden- a) Show that the least square estimator Bo Ỹ - Bī is an unbiased of B- b) Show that (1) Varl&] = i o? (ii) and attains the minimum n Σ, (τ- )>. variance among all estimates that are linear combination of the response variable Y. c) Show that the test statistic t = is equivalent to t= where S.E(B)) = %3D S.E(§)' VE (; – #)² 1-r2 - п-2
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