hwk1 - STAT 8260 Theory of Linear Models Homework 1 Due...

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STAT 8260 — Theory of Linear Models Homework 1 – Due Tuesday, Jan. 29 Homework Guidelines: Homework is due by 4:30 on the due date specified above. You may turn it in at the beginning of class or place it in my mailbox in the Statistics Building. No late homeworks will be accepted without permission granted prior to the due date. Use only standard (8 . 5 × 11 inch) paper and use only one side of each sheet. Homework should show enough detail so that the reader can clearly understand the procedures of the solutions. This is absolutely essential for you to receive full credit for your answer since the answers to most of the problems in Rencher appear in the back of the book. Problems should appear in the order that they were assigned. Assignment: 1. Consider the following vectors in R 5 : x = (2 , 1 , 1 , 1 , 4) T , and y = (3 , 6 , 1 , 5 , 7) T . a. Find h x , y i , || x || 2 , || y || 2 , ˆ y = p ( y | x ), and y - ˆ y . Show that x ( y - ˆ y ), and || y || 2 = || ˆ y || 2 + || y - ˆ y || 2 . b. Let w = ( - 1 , 2 , 4 , - 4 , 0) T and z = 3 x + 2 w . Show that h w , x i = 0 and that || z || 2 = 9 || x || 2 + 4 || w || 2 . (Why must this be true?) c. Let A 1 = { 1 , 2 } ,A 2 = { 3 , 4 } ,A 3 = { 5 } . Find p ( y | i A i ), i = 1 , 2 , 3. 2. Is projection a linear transformation in the sense that p ( c y | x ) = cp ( y | x ) for any real number c ? Prove or disprove. What is the relationship between p ( y | x ) and p ( y | c x ) for c 6 = 0? 3. Suppose
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This note was uploaded on 11/13/2011 for the course STAT 8260 taught by Professor Hall during the Summer '10 term at UGA.

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hwk1 - STAT 8260 Theory of Linear Models Homework 1 Due...

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