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Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)

Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)

Calculus For The Life Sciences
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
Problem 7E
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Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)
Transcribed Image Text:Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)
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