# Hw2sol - Stat 511 Homework 2 Solution(pts:20 Spring 2011 In the solution notice that you do have different choices of A and doesn’t affect the

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stat 511 Homework 2 Solution (pts:20) Spring 2011 In the solution, notice that you do have different choices of A and doesn’t affect the estimation. 1. Consider a factor effects model for a study with a balanced two-way factorial treatment design: Y ijk = μ + α i + β j + αβ ij + ijk , for i = 1 , 2, j = 1 , 2 , 3, and k = 1 , 2. The “LSMEANS” for the two row means are μ + α 1 + ( β 1 + β 2 + β 3 ) / 3 + ( αβ 11 + αβ 12 + αβ 13 ) / 3 and μ + α 2 + ( β 1 + β 2 + β 3 ) / 3 + ( αβ 21 + αβ 22 + αβ 23 ) / 3. The X matrix is: 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 Are the two LSMEANS estimable? If so, give vectors A (one for each LSMEANS) that demonstrate that each is estimable. Yes, they are estimable because they are linear function of E Y ijk . One set of possible A ’s are A 1 = (1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , , , , , , 0) A 2 = (0 , , , , , , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6) 2. I recently had to deal with a “two-way” factorial study where factor A was State: Iowa or Missouri, and factor B was a type of stream: Grazed, Buffered, or Grazed and Buffered. As it happened, the investigators could find all three types of streams in Iowa, but only two types...
View Full Document

## This note was uploaded on 02/11/2012 for the course STAT 511 taught by Professor Staff during the Spring '08 term at Iowa State.

### Page1 / 4

Hw2sol - Stat 511 Homework 2 Solution(pts:20 Spring 2011 In the solution notice that you do have different choices of A and doesn’t affect the

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

View Full Document
Ask a homework question - tutors are online