### Write this model in the general linear model form

Assignment Help Mathematics
##### Reference no: EM131034896

1. Consider the following data set,

 B 1 2 3 A 1 74 71 99 64 68 104 2 99 108 114 98 110 111

and the Balanced Factor- effects model with interactions

Yijk = μ + αi + βj + γij + εijk

i = 1,2 ,j= 1,2,3, k = 1,2

where  εijk ∼ N (0, σ2).

(a) Write this model in the General Linear Model form Y = Xβ + ε.

(b) Find  PX , P1, PAPB.

(c) Use the decomposition

PX = P1 + PA + PB + PAB,

to construct the ANOVA table for this model.

(d)Verify your results in (c) using R.

2. Consider the following data set, and Factor- effects model with interactions

Yijk = µ + αi + βj + γij + εijk

i = 1, 2,  j = 1, 3   k = 1, . . . , nij

 B 1 2 3 A 1 74 71 99 64 68 104 60 75 93 2 99 108 114 98 110 111

(a) Write this model in the General Linear Model form Y = Xβ + ε.

(b) Consider Yijk = µ + βj + γij + εijk as the reduced model and test H0: α1 = α2.

(c) Now consider Yijk = µ + βj + εijk as the reduced model and test H0: α1 = α2.

(d) Is there any discrepancy between your conclusions in (b) and (c)? Explain why.

3. For the balanced one-Factor random effects model discussed in class show

E[SSB] =   (A - 1)σ2 + (N - (Σini2/N)) σa2

E[SSW] =  σ2(N - A)

4. Consider the two-factor balanced additive random-effects model without interaction

Yijk  = µ + ai + bj  + εijk

i = 1, 2,  j = 1, 2,  k = 1, 2.

Suppose εijk are iid N (0, σ2) variables, ai are iid N (0, σa2) variables, bi are iid N (0, σb2) variables, Cov(εijk, ai) = 0, Cov(εijk, bj ) = 0, and Cov(ai, bj) = 0.

i. Write this model in the General Linear Mixed Model form Y = Xβ + Zu + ε.

ii. Find an expression for V = Cov(Y).

Attachment:- Notes.rar

#### Questions Cloud

 Element of the business case presentation : Identify the project scope, and create aims and objectives for the scenario, and include these in a section titled, ‘Project Scope, Aims and Objectives' Explain how each was affected by the events : Explain how each was affected by the events. With power, urgency, and legitimacy in mind, what were possible effects of Enron’s corporate culture on stakeholders? All of the executives in this case believed they were not guilty of the charges levied .. When a verb is written in the passive voice : When a verb is written in the passive voice, the following is true: Provision of ultrasound services : 1. Estimate the base case cost of each alternative regarding the provision of ultrasound services. (For now, ignore the discount if three units are purchased.) Write this model in the general linear model form : Write this model in the General Linear Model form Y = Xβ + ε. Consider Yijk = µ + βj + γij + εijk as the reduced model and test H0: α1 = α2. Now consider Yijk = µ + βj + εijk as the reduced model and test H0: α1 = α2 Product life-cycle is an important marketing concept : What challenges does Blu Dot face in selling consumer products (as opposed to business products)? Do you think the product life-cycle is an important marketing concept in developing and managing Blu Dot products? Why or why not? Describe the product .. Evaluating capital budgeting decisions : When you want to learn something, even something as complicated as how to make capital budgeting decisions, never rule out the value of simple observation. Observing and analyzing the past and present decisions of others can help you make present .. Is raleigh using the marketing concept : Is Raleigh using the marketing concept? Explain. What type of approach does Raleigh use to select target markets? Of the four categories of segmentation variables, which is most important to Raleigh’s segmentation strategy, and why? Compare the lean service system of southwest airlines : Compare the lean service system of Southwest Airlines to a full service airline such as United Airlines or British Airways on the following: (a) airplane boarding process, (b) cabin service, (c) ticket transfer to other Southwest flights, (d) frequen..

### Write a Review

#### Determine the heading of the boat required for the boat

A person who can row 2.6mph in still water wants to row due east across a river. The river is flowing from the north at a rate of 0.8mph. Determine the heading of the boat required for the boat to travel due east across the river.

#### Discuss the type of study the sampling method the parameter

daniel needs to study a possible link between anti-inflammatory drugs and kidney disease. help daniel design a study

#### Find an equation of a rational function f that satisfies

Find an equation of a rational function f that satisfies the given conditions.

#### What was the average annual increase

The average price of a house in England was 106,000 in the year 2000, and 211,000 in the year 2006. What was the average annual increase (in percent) of house prices in England between 2000 and 2006?

#### What are the dimensions of the block

a new fence is constructed on three sides of a housing block with area 240m^2 the fourth side facing the road is left open. if 52 of fencing is used, what are the dimensions of the block?

#### How would i maximize the firm using lagrange multipliers

Imagine a representative rm with the following production function. How would i maximize the following firm, using LaGrange Multipliers?

#### How to get ax(x-1)+b(x-1)+cx^2

How to get Ax(x-1)+B(x-1)+Cx^2 instead of is A(x-1)*x^2+Bx*(x-1)+C*x^3

#### How fast does x change with respect to theta

If the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta = pi/3

#### At a level of 1% which variables are significant

Using what you know about t-scores, identify which of the variables have a significant influence on the LISTPRICE.

#### Find the rate of increase in revenue

Find the rate of increase in revenue when production is 1000 switches per day. Find the rate of increase in profit when production is 1000 switches per day. dollars/day.

#### Show the correct concave structure and indicate the behavior

Apply the second derivative test at each critical point. Show the correct concave structure and indicate the behavior of f(x) as x →±∞, for f(x) = 4x5 - 5x4.

#### Separable differential equation

Could someone please show me how to solve this separable differential equation?