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
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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