Consider the regression model Y₁ = BX; +u; Y Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ = Show that ẞ is a linear function of Y₁, Y2,..., Yn. Show that ẞ is conditionally unbiased. 1. E (YiX1, X2,..., Xn) = == X + +Yn) 2. E(B|×1, X2,..., Xn) = E = B Χ | (X1, X2,..., Xn) = where Y and X are the sample means of Y; and X;, respectively.
Consider the regression model Y₁ = BX; +u; Y Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ = Show that ẞ is a linear function of Y₁, Y2,..., Yn. Show that ẞ is conditionally unbiased. 1. E (YiX1, X2,..., Xn) = == X + +Yn) 2. E(B|×1, X2,..., Xn) = E = B Χ | (X1, X2,..., Xn) = where Y and X are the sample means of Y; and X;, respectively.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 5PPS
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Transcribed Image Text:Consider the regression model
Y₁ = BX; +u;
Y
Where
ui
and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ =
Show that ẞ is a linear function of Y₁, Y2,..., Yn.
Show that ẞ is conditionally unbiased.
1. E (YiX1, X2,..., Xn)
=
==
X
+
+Yn)
2. E(B|×1, X2,..., Xn) = E
= B
Χ
| (X1, X2,..., Xn)
=
where Y and X are the sample means of Y; and X;, respectively.
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