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Consider the regression model Y₁ = ẞX; +u; 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,..., Y. ☑' where Y and X are the sample means of Y; and X;, respectively. 1 +Yn) Show that ẞ is conditionally unbiased. 1. E(YX1, X2 Xn) = BX (@K}6, +Yn) +X₂+...+Xn) = B 2. E(BIX1, X2,..., Xn) = E || (x₁₁ X 2...., Xn) D

Consider the regression model Y₁ = ẞX; +u; 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,..., Y. ☑' where Y and X are the sample means of Y; and X;, respectively. 1 +Yn) Show that ẞ is conditionally unbiased. 1. E(YX1, X2 Xn) = BX (@K}6, +Yn) +X₂+...+Xn) = B 2. E(BIX1, X2,..., Xn) = E || (x₁₁ X 2...., Xn) D

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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 4PPS
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Consider the regression model Y₁ = ẞX; +u; 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,..., Y. ☑' where Y and X are the sample means of Y; and X;, respectively. 1 +Yn) Show that ẞ is conditionally unbiased. 1. E(YX1, X2 Xn) = BX (@K}6, +Yn) +X₂+...+Xn) = B 2. E(BIX1, X2,..., Xn) = E || (x₁₁ X 2...., Xn) D
Transcribed Image Text:Consider the regression model Y₁ = ẞX; +u; 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,..., Y. ☑' where Y and X are the sample means of Y; and X;, respectively. 1 +Yn) Show that ẞ is conditionally unbiased. 1. E(YX1, X2 Xn) = BX (@K}6, +Yn) +X₂+...+Xn) = B 2. E(BIX1, X2,..., Xn) = E || (x₁₁ X 2...., Xn) D
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