hw2 - Winter 2010 STAT 331/SYDE 334 Zhu, M University of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Winter 2010 STAT 331/SYDE 334 Zhu, M University of Waterloo STAT 331/SYDE 334 Problem Set 2 Due: F, Feb 12, 2010 or Tu, Feb 16, 2010 Hand in this assignment into a box labelled “STAT 331” in MC 6028. If you are leaving Waterloo for the reading week, please do so on F, Feb 12 by 3:00 pm. If you are not leaving Waterloo for the reading week, you can do so on Tu, Feb 16 by 12:00 noon. All data sets are available in a directory called “Data Sets” on the course web site hosted by the ANGEL system, http://uwace.uwaterloo.ca/ . Once logged onto the system, click on the “Content” tab. 1. (12 pts) Consider the linear model y = X β + ǫ under the Gauss-Markov condition, i.e., E ( ǫ ) = 0 and Var( ǫ ) = σ 2 I . (a) (8 pts) Let ˆ β = ( X T X )- 1 X T y be the usual least-squares estimate. Use the formula Cov( Ay , By ) = A Var( y ) B T to show Cov( y − ˆ y , ˆ β ) = O , where O is a matrix of all zeros. (b) (2 pts) What extra condition, if any, is needed if you want to conclude that y − ˆ y and ˆ β are statistically independent? (c) (2 pts) In the general context of the study of linear models, briefly comment why it is sometimes important for y −...
View Full Document

This note was uploaded on 05/25/2010 for the course STAT 331 taught by Professor Sning during the Spring '10 term at University of Warsaw.

Page1 / 2

hw2 - Winter 2010 STAT 331/SYDE 334 Zhu, M University of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online