Professor E.Z. Stuff has decided that the least squares estimator is too much trouble. Noting that two points determine a line, Dr. Stuff chooses two points from a sample of size N and draws a line between them, calling the slope of this line the EZ estimator of ẞ2 in the simple regression model. Algebraically, if the two points are (x1,y1) and (x2, y2), the EZ estimation rule is: 1 2 – 91 y2 - bEz x2 x1 x2 x1 Assuming that all the assumptions of the simple regression model hold, namely, (SR1-SR6): (a) Show that bez is a "linear" estimator. (Must show that bez can be expressed as weighted sum bEz = Σ wiYi) (b) Show that bEZ is an unbiased estimator. (Must show that E(bɛz) = ß2) 1 x2 - x1 yl
Professor E.Z. Stuff has decided that the least squares estimator is too much trouble. Noting that two points determine a line, Dr. Stuff chooses two points from a sample of size N and draws a line between them, calling the slope of this line the EZ estimator of ẞ2 in the simple regression model. Algebraically, if the two points are (x1,y1) and (x2, y2), the EZ estimation rule is: 1 2 – 91 y2 - bEz x2 x1 x2 x1 Assuming that all the assumptions of the simple regression model hold, namely, (SR1-SR6): (a) Show that bez is a "linear" estimator. (Must show that bez can be expressed as weighted sum bEz = Σ wiYi) (b) Show that bEZ is an unbiased estimator. (Must show that E(bɛz) = ß2) 1 x2 - x1 yl
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PRACTICE HOMEWORK
Transcribed Image Text:Professor E.Z. Stuff has decided that the least squares estimator is too much trouble. Noting that two points determine a line, Dr. Stuff chooses two points from a sample
of size N and draws a line between them, calling the slope of this line the EZ estimator of ẞ2 in the simple regression model.
Algebraically, if the two points are (x1,y1) and (x2, y2), the EZ estimation rule is:
1
2 – 91
y2
-
bEz
x2 x1
x2
x1
Assuming that all the assumptions of the simple regression model hold, namely, (SR1-SR6):
(a) Show that bez is a "linear" estimator.
(Must show that bez can be expressed as weighted sum bEz = Σ wiYi)
(b) Show that bEZ is an unbiased estimator.
(Must show that E(bɛz) = ß2)
1
x2
-
x1
yl
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