### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# LINEAR STATISTICL MODELS STAT 714

GPA 3.93

### View Full Document

## 45

## 0

## Popular in Course

## Popular in Statistics

This 2 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 714 at University of South Carolina - Columbia taught by I. Dryden in Fall. Since its upload, it has received 45 views. For similar materials see /class/229648/stat-714-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.

## Reviews for LINEAR STATISTICL MODELS

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/26/15

STAT714 LINEAR STATISTICAL MODELS Fall Session 2009 Handout 1 Result M10 Let A be an m gtlt 71 matrix with rA r If A can be partitioned as follows C D A E F v where rA rC T7 and CTXT is nonsingular7 then C 1 0 G o o is a generalized inverse of A Proof Consider CD C 10 CD C D AGAE F 0 0E FHE Em Now since the full matrix A and the subrnatrix C have the same rank7 the rows E F must be linearly dependent on C D7 so that E F KC D for some matrix K Hence E KC7 F KD and so K EC 1 and so F KD EC 1D Therefore7 we have shown AGA A7 7 and so G is a generalized inverse D PTO Result M11 Let Amxm xnxl mel7 and Imm be rnatrices7 and suppose that Ax c is consistent Then7 x is a solution to Ax c if and only if x A c I 7 A Az7 for some 2 E R Proof We know that x A c is a solution Result M9 Suppose that x A c I 7 A Az7 for some 2 E R Thus7 A AA c A 7 AA AZ AA c AXT c that is7 x A c I 7 A Az solves Ax c Conversely7 suppose that x is a solution to Ax c Now7 x A c x 7 A c A cx 7A AX A c I 7 A Ax Thus7 we can write x A c I 7 A Az7 and here we take 2 X For this part of the proof we just need to show that there exists a speci c 2 D Using this result we can vary 2 E R and generate all solutions7 and so we can generate all solutions by just knowing one of them ie7 by knowing A c Note that if A is nonsingular7 A A 1 and x A lc I 7 A lAz A lc ie7 there is just one solution NOTE Consider the general form of the solution to Ax c which is assumed to be consistent ie7 XI A c I 7 A Az We call A c a particular solution The term I 7 A Az is the general solution to the homogeneous equations Ax 07 producing vectors in

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.