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
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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fix or correct my answers if there is any error and give me the correct using the format
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb55c1690-4c18-4793-9129-6cd04f8390e3%2F02831af8-7c51-4d26-943d-34a9cde07dff%2Fn5tm1r_processed.png&w=3840&q=75)
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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