Consider the regression model Y₁ = BX; +u; Where u; 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. where Y and X are the sample means of Y; and X;, respectively. Show that ẞ is conditionally unbiased. 1. E (Y;|X1, X2,..., Xn) = 1 -B (X ₁ + X 2 + ... + Xn) Х answer these part correctly + ... + Y) +X₂+ ... + Xn) = B 2. E (B|×₁, ×2,..., Xn) = E | (X1, X2,..., Xn) BX; ☑ BX BY
Consider the regression model Y₁ = BX; +u; Where u; 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. where Y and X are the sample means of Y; and X;, respectively. Show that ẞ is conditionally unbiased. 1. E (Y;|X1, X2,..., Xn) = 1 -B (X ₁ + X 2 + ... + Xn) Х answer these part correctly + ... + Y) +X₂+ ... + Xn) = B 2. E (B|×₁, ×2,..., Xn) = E | (X1, X2,..., Xn) BX; ☑ BX BY
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter7: Production Economics
Section: Chapter Questions
Problem 1.3CE
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Transcribed Image Text:Consider the regression model
Y₁ = BX; +u;
Where u; 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.
where Y and X are the sample means of Y; and X;, respectively.
Show that ẞ is conditionally unbiased.
1. E (Y;|X1, X2,..., Xn) =
1
-B (X ₁ + X 2 + ... + Xn)
Х
answer these part correctly
+ ... + Y)
+X₂+ ... + Xn) = B
2. E (B|×₁, ×2,..., Xn) = E
| (X1, X2,..., Xn)
BX;
☑
BX
BY
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