New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

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

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here


by: Mason Crist


Mason Crist
GPA 3.68


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in Epidemiology

This 5 page Class Notes was uploaded by Mason Crist on Monday September 28, 2015. The Class Notes belongs to BSTA651 at University of Pennsylvania taught by Staff in Fall. Since its upload, it has received 36 views. For similar materials see /class/215362/bsta651-university-of-pennsylvania in Epidemiology at University of Pennsylvania.




Report this Material


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: 09/28/15
Statistical Methods amp Data Analysis I BSTA630 Part 11 Fall Semester 20062007 Knashawn H Morales ScD kmorales ccebmedupennedu SLR Least Squares Estimation Modi ed mm 71112005 some notes WeirTnAg Hwang Instructor Slide 1 Scallerplol Weight and Height Weight kg HE EhHEm Estimating B1 002 I Methods of estimation MLE Moment I Least square LS estimates in SLR Basic Idea gt Find 30 and 31 st Observed data K as close to u 31X regression line as possible gt Find 30 and 31 st 5175 as small as possible I closeness Slide 3 Square 53 small Absolute value l e l small Slide 2 Least Square LS Estimates Find 30 and 31 st Minimize 211z 7 30 312 Solve for 66191 0 and 66130 0 9 67 2 gillz 30 31 0 5 Zyzi oi iz h0 11 11 then all divided by n 5 5017515 Slide 4 Estimate 72 Varei Least Square LS Estimates 3 Since 39 Minimize 27111 u 131 5512 51 N N002 and Va39r5 T2 a 11 7 2 0 ml 2 u 1 1gtgt7 1 A n A n I If 3 1 known then i Z1y17 02 17 1230 0 1 11 11 11 51 K 7 g 7 3le gt 211111 7 17 113111 9113 0 N N002 1111 11 n 11 we estimate 02 by i 2x1y17n517751237 20 1 7quot 11 A 11 211 30 319512 i 5111 7 13151111 0 11 gt The sample variance with a known 0 mean Slide 5 Slide 7 2 Estimate 0 Varei When 30131 are unknown replace 30131 by ao l 1 n A A Least Square LS Estimates 211111 7 1 0 7 1312 Since SW 221Xz 7 7 Y 271 my 7 nail n 7 2 n 2 72 I But need to reduce degrees of frfedqm df because we estimate u and 31 And SW 2171 z X 21 1 m 62 72 111 7 90 7 My n 7 We have 1 1 RSS A s 7 7 A 2 7 191 Si 1129 1quotquot 112 30 1 15 Q1 30 1 1 tted value of y 7 Residual zyz 7 11 observed yz 7 tted Value of y1 7 RSSResidual Sum of Square 27191 7 1 7 919602 27191 7 131 Slide 6 Slide 8 Adjustment for the df Estimate normal variance with 1952y We N NWJTZ 1 When mean M is known A 1 g2 2ng 7 M2 MLE unbiased 2 When mean M is unknown A2 L1 9 e 502 MLE unbiased 11 Loose df because we estimate M by a Slide 9 Inference for 3031 I Inferences based on ha I Model YL O1Xz51 EZNN0U2 i12 I LS estimates of 130131 A 7 Sxy 131 7 SW 30 1 19 I Properties of LS estimates 1 Mean Unbiasedness M51 191 and Elo u 2 Standard Errors for 3150 Slide 10 Means of Bl and Bo A 5 271X17XXY17Y SW 7 BLUE 7 XV 271 EXz 7 XYz 7Xz 7 XW 2211097 XV BLOC XV 2109 XW of le 222109 7 XV since XXX 7 X 0 0 ELIMXZAW 221X17W 7 1 E 0 u Exercise Slide 11 Mean of 6392 2 22191 7w Rss 2 7L 7 2 Since 7 A2 w M X72172 Exercise E M72 7 7L72T2 U2 Hence E72 72 More references Weisberg Appendix A Montgomery Appendix C Linear models course BSTA 651 Slide 12 Properties of LS estimates Standard Errors of 6130 I Means 131 7451 Var y Vadw 3 m m E T T VWZLAXZ 7 XYz 2 1 n XI 7 X2Va39rYz so 21 I Standard Errors SW 72 A 53x 02 SW mel gm A 1 2 Va39r 0 02 Slide 13 Slide 15 Standard Errors of 6130 A A When will we estimate Bl precisely VWWO Va 1919 VW17 izVaTlt51gt 250041151 72 U2 7 i2 7 0 Exercise A 71 Saw I Precision gt Small Va39r 1 1 22 2 7 a n SW A A I Important factors Also 31130 are correlated 7L SW A A 0292 Caz3111 7 S Exercise Slide 14 Slide 16 Sampling Distributions for 6150 31 so 2221Xz7 mg 7 Y Sm 1ltXz7 Xv 221Xr m 1ltXz7 Xv gt Weighted sum of data K Since 31 is a linear combination of K and K are Normal rv gt al also follows Normal distribution 2 91 N wag 522 m 90 N N o02s Slide 17 Sampling Distribution for 6392 7 A 2 w Exercise 7 N X3172 Slide 18


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

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

Steve Martinelli UC Los Angeles

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

Anthony Lee UC Santa Barbara

"I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund 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


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:

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

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.