Regression. The Simple Linear Regression Model
|
|
- Kellie Robinson
- 6 years ago
- Views:
Transcription
1 Regresson Smple Lnear Regresson Model Least Squares Method Coeffcent of Determnaton Model Assumptons Testng for Sgnfcance Usng the Estmated Regresson Equaton for Estmaton and Predcton Resdual Analss: Valdatng Model Assumptons Outlers and Influental Oservatons The Smple Lnear Regresson Model Smple Lnear Regresson Model β 0 + β x + ε Smple Lnear Regresson Equaton E( β 0 + β x ^ Estmated Smple Lnear Regresson Equaton 0 + x
2 Least Squares Method Least Squares Crteron mn ( $ oserved value of the dependent varale ^ for the th oservaton estmated value of the dependent varale for the th oservaton The Least Squares Method Slope for the Estmated Regresson Equaton x ( x / n x ( x / n -Intercept for the Estmated Regresson Equaton 0 - x x value of ndependent varale for th oservaton value of dependent varale for th oservaton _ x mean value for ndependent varale _ mean value for dependent varale n total numer of oservatons
3 The Coeffcent of Determnaton Relatonshp Among SST, SSR, SSE SST SSR + SSE ( ( ^ + ( ^ Coeffcent of Determnaton r SSR/SST SST total sum of squares SSR sum of squares due to regresson SSE sum of squares due to error Model Assumptons Assumptons Aout the Error Term ε The error ε s a random varale wth mean of zero. The varance of ε, denoted σ, s the same for all values of the ndependent varale. The values of ε are ndependent. The error ε s a normall dstruted random varale.
4 Testng for Sgnfcance To test for a sgnfcant regresson relatonshp, we must conduct a hpothess test to determne whether the value of β s zero. Two tests are commonl used t Test F Test Both tests requre an estmate of σ, the varance of ε n the regresson model. An Estmate of σ Testng for Sgnfcance The mean square error (MSE provdes the estmate of σ, and the notaton s s also used. s MSE SSE/(n- SSE ( ˆ ( 0 x An Estmate of σ To estmate σ we take the square root of σ. The resultng s s called the standard error of the estmate. SSE s MSE n
5 Testng for Sgnfcance: t Test Hpotheses Test Statstc Rejecton Rule H 0 : β 0 H a : β 0 t s Reject H 0 f t < -t α/ or t > t α/ where t α/ s ased on a t dstruton wth n - degrees of freedom. Confdence Interval for β We can use a 95% confdence nterval for β to test the hpotheses just used n the t test. H 0 s rejected f the hpotheszed value of β s not ncluded n the confdence nterval for β. The form of a confdence nterval for β s: ± t α / where s the pont estmate t α / s s the margn of error t α / s the t value provdng an area of α/ n the upper tal of a t dstruton wth n - degrees of freedom s
6 Testng for Sgnfcance: F Test Hpotheses Test Statstc Rejecton Rule H 0 : β 0 H a : β 0 F MSR/MSE Reject H 0 f F > F α where F α s ased on an F dstruton wth d.f. n the numerator and n - d.f. n the denomnator. Some Cautons aout the Interpretaton of Sgnfcance Tests Rejectng H 0 : β 0 and concludng that the relatonshp etween x and s sgnfcant does not enale us to conclude that a cause-and-effect relatonshp s present etween x and. Just ecause we are ale to reject H 0 : β 0 and demonstrate statstcal sgnfcance does not enale us to conclude that there s a lnear relatonshp etween x and.
7 Usng the Estmated Regresson Equaton for Estmaton and Predcton Confdence Interval Estmate of E( p $ p ± t α / s $ p Predcton Interval Estmate of p p + t α/ s nd where the confdence coeffcent s - α and t α/ s ased on a t dstruton wth n - d.f. Resdual Analss If the assumptons aout the error term ε appear questonale, the hpothess tests aout the sgnfcance of the regresson relatonshp and the nterval estmaton results ma not e vald. The resduals provde the est nformaton aout ε. Much of the resdual analss s ased on an examnaton of graphcal plots.
8 Resdual Plot Aganst x If the assumpton that the varance of ε s the same for all values of x s vald, and the assumed regresson model s an adequate representaton of the relatonshp etween the varales: The resdual plot should gve an overall mpresson of a horzontal and of ponts Standardzed Resdual for Oservaton Standardzed Resduals ˆ s ˆ ˆ s s h ˆ ( x x h + n ( x x The standardzed resdual plot can provde nsght aout the assumpton that the error term ε has a normal dstruton. If ths assumpton s satsfed, the dstruton of the standardzed resduals should appear to come from a standard normal proalt dstruton.
9 Outlers and Influental Oservatons Detectng Outlers An outler s an oservaton that s unusual n comparson wth the other data. Mnta classfes an oservaton as an outler f ts standardzed resdual value s < - or > +. Ths standardzed resdual rule sometmes fals to dentf an unusuall large oservaton as eng an outler. Ths rule s shortcomng can e crcumvented usng studentzed deleted resduals. The th studentzed deleted resdual wll e larger than the th standardzed resdual.
Chapter 14 Simple Linear Regression
Chapter 4 Smple Lnear Regresson Chapter 4 - Smple Lnear Regresson Manageral decsons often are based on the relatonshp between two or more varables. Regresson analss can be used to develop an equaton showng
More informationChapter 15 - Multiple Regression
Chapter - Multple Regresson Chapter - Multple Regresson Multple Regresson Model The equaton that descrbes how the dependent varable y s related to the ndependent varables x, x,... x p and an error term
More informationDepartment of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6
Department of Quanttatve Methods & Informaton Systems Tme Seres and Ther Components QMIS 30 Chapter 6 Fall 00 Dr. Mohammad Zanal These sldes were modfed from ther orgnal source for educatonal purpose only.
More informationx yi In chapter 14, we want to perform inference (i.e. calculate confidence intervals and perform tests of significance) in this setting.
The Practce of Statstcs, nd ed. Chapter 14 Inference for Regresson Introducton In chapter 3 we used a least-squares regresson lne (LSRL) to represent a lnear relatonshp etween two quanttatve explanator
More informationStatistics for Business and Economics
Statstcs for Busness and Economcs Chapter 11 Smple Regresson Copyrght 010 Pearson Educaton, Inc. Publshng as Prentce Hall Ch. 11-1 11.1 Overvew of Lnear Models n An equaton can be ft to show the best lnear
More informationStatistics for Managers Using Microsoft Excel/SPSS Chapter 13 The Simple Linear Regression Model and Correlation
Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 13 The Smple Lnear Regresson Model and Correlaton 1999 Prentce-Hall, Inc. Chap. 13-1 Chapter Topcs Types of Regresson Models Determnng the Smple Lnear
More informationStatistics for Economics & Business
Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable
More informationLecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 212. Chapters 14, 15 & 16. Professor Ahmadi, Ph.D. Department of Management
Lecture Notes for STATISTICAL METHODS FOR BUSINESS II BMGT 1 Chapters 14, 15 & 16 Professor Ahmad, Ph.D. Department of Management Revsed August 005 Chapter 14 Formulas Smple Lnear Regresson Model: y =
More informationChapter 11: Simple Linear Regression and Correlation
Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests
More informationCorrelation and Regression. Correlation 9.1. Correlation. Chapter 9
Chapter 9 Correlaton and Regresson 9. Correlaton Correlaton A correlaton s a relatonshp between two varables. The data can be represented b the ordered pars (, ) where s the ndependent (or eplanator) varable,
More informationwhere I = (n x n) diagonal identity matrix with diagonal elements = 1 and off-diagonal elements = 0; and σ 2 e = variance of (Y X).
11.4.1 Estmaton of Multple Regresson Coeffcents In multple lnear regresson, we essentally solve n equatons for the p unnown parameters. hus n must e equal to or greater than p and n practce n should e
More informationComparison of Regression Lines
STATGRAPHICS Rev. 9/13/2013 Comparson of Regresson Lnes Summary... 1 Data Input... 3 Analyss Summary... 4 Plot of Ftted Model... 6 Condtonal Sums of Squares... 6 Analyss Optons... 7 Forecasts... 8 Confdence
More informationChapter 13: Multiple Regression
Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to
More informationStatistics II Final Exam 26/6/18
Statstcs II Fnal Exam 26/6/18 Academc Year 2017/18 Solutons Exam duraton: 2 h 30 mn 1. (3 ponts) A town hall s conductng a study to determne the amount of leftover food produced by the restaurants n the
More informationY = β 0 + β 1 X 1 + β 2 X β k X k + ε
Chapter 3 Secton 3.1 Model Assumptons: Multple Regresson Model Predcton Equaton Std. Devaton of Error Correlaton Matrx Smple Lnear Regresson: 1.) Lnearty.) Constant Varance 3.) Independent Errors 4.) Normalty
More informationBasic Business Statistics, 10/e
Chapter 13 13-1 Basc Busness Statstcs 11 th Edton Chapter 13 Smple Lnear Regresson Basc Busness Statstcs, 11e 009 Prentce-Hall, Inc. Chap 13-1 Learnng Objectves In ths chapter, you learn: How to use regresson
More informationLearning Objectives for Chapter 11
Chapter : Lnear Regresson and Correlaton Methods Hldebrand, Ott and Gray Basc Statstcal Ideas for Managers Second Edton Learnng Objectves for Chapter Usng the scatterplot n regresson analyss Usng the method
More informationa. (All your answers should be in the letter!
Econ 301 Blkent Unversty Taskn Econometrcs Department of Economcs Md Term Exam I November 8, 015 Name For each hypothess testng n the exam complete the followng steps: Indcate the test statstc, ts crtcal
More informationChapter 15 Student Lecture Notes 15-1
Chapter 15 Student Lecture Notes 15-1 Basc Busness Statstcs (9 th Edton) Chapter 15 Multple Regresson Model Buldng 004 Prentce-Hall, Inc. Chap 15-1 Chapter Topcs The Quadratc Regresson Model Usng Transformatons
More informationSTAT 3008 Applied Regression Analysis
STAT 3008 Appled Regresson Analyss Tutoral : Smple Lnear Regresson LAI Chun He Department of Statstcs, The Chnese Unversty of Hong Kong 1 Model Assumpton To quantfy the relatonshp between two factors,
More information[The following data appear in Wooldridge Q2.3.] The table below contains the ACT score and college GPA for eight college students.
PPOL 59-3 Problem Set Exercses n Smple Regresson Due n class /8/7 In ths problem set, you are asked to compute varous statstcs by hand to gve you a better sense of the mechancs of the Pearson correlaton
More informationCorrelation and Regression
Correlaton and Regresson otes prepared by Pamela Peterson Drake Index Basc terms and concepts... Smple regresson...5 Multple Regresson...3 Regresson termnology...0 Regresson formulas... Basc terms and
More informationBiostatistics 360 F&t Tests and Intervals in Regression 1
Bostatstcs 360 F&t Tests and Intervals n Regresson ORIGIN Model: Y = X + Corrected Sums of Squares: X X bar where: s the y ntercept of the regresson lne (translaton) s the slope of the regresson lne (scalng
More information1. Inference on Regression Parameters a. Finding Mean, s.d and covariance amongst estimates. 2. Confidence Intervals and Working Hotelling Bands
Content. Inference on Regresson Parameters a. Fndng Mean, s.d and covarance amongst estmates.. Confdence Intervals and Workng Hotellng Bands 3. Cochran s Theorem 4. General Lnear Testng 5. Measures of
More informationECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics
ECOOMICS 35*-A Md-Term Exam -- Fall Term 000 Page of 3 pages QUEE'S UIVERSITY AT KIGSTO Department of Economcs ECOOMICS 35* - Secton A Introductory Econometrcs Fall Term 000 MID-TERM EAM ASWERS MG Abbott
More informationLecture 6: Introduction to Linear Regression
Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6
More informationScatter Plot x
Construct a scatter plot usng excel for the gven data. Determne whether there s a postve lnear correlaton, negatve lnear correlaton, or no lnear correlaton. Complete the table and fnd the correlaton coeffcent
More informationPsychology 282 Lecture #24 Outline Regression Diagnostics: Outliers
Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.
More informationMultiple Regression Analysis
Multle Regresson Analss Roland Szlág Ph.D. Assocate rofessor Correlaton descres the strength of a relatonsh, the degree to whch one varale s lnearl related to another Regresson shows us how to determne
More information2016 Wiley. Study Session 2: Ethical and Professional Standards Application
6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton
More informationNANYANG TECHNOLOGICAL UNIVERSITY SEMESTER I EXAMINATION MTH352/MH3510 Regression Analysis
NANYANG TECHNOLOGICAL UNIVERSITY SEMESTER I EXAMINATION 014-015 MTH35/MH3510 Regresson Analyss December 014 TIME ALLOWED: HOURS INSTRUCTIONS TO CANDIDATES 1. Ths examnaton paper contans FOUR (4) questons
More informationx i1 =1 for all i (the constant ).
Chapter 5 The Multple Regresson Model Consder an economc model where the dependent varable s a functon of K explanatory varables. The economc model has the form: y = f ( x,x,..., ) xk Approxmate ths by
More informationStatistics for Managers Using Microsoft Excel/SPSS Chapter 14 Multiple Regression Models
Statstcs for Managers Usng Mcrosoft Excel/SPSS Chapter 14 Multple Regresson Models 1999 Prentce-Hall, Inc. Chap. 14-1 Chapter Topcs The Multple Regresson Model Contrbuton of Indvdual Independent Varables
More informationEconomics 130. Lecture 4 Simple Linear Regression Continued
Economcs 130 Lecture 4 Contnued Readngs for Week 4 Text, Chapter and 3. We contnue wth addressng our second ssue + add n how we evaluate these relatonshps: Where do we get data to do ths analyss? How do
More informationNegative Binomial Regression
STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...
More informationSTATISTICS QUESTIONS. Step by Step Solutions.
STATISTICS QUESTIONS Step by Step Solutons www.mathcracker.com 9//016 Problem 1: A researcher s nterested n the effects of famly sze on delnquency for a group of offenders and examnes famles wth one to
More informationRegression Analysis. Regression Analysis
Regresson Analyss Smple Regresson Multvarate Regresson Stepwse Regresson Replcaton and Predcton Error 1 Regresson Analyss In general, we "ft" a model by mnmzng a metrc that represents the error. n mn (y
More informationSIMPLE LINEAR REGRESSION and CORRELATION
Expermental Desgn and Statstcal Methods Workshop SIMPLE LINEAR REGRESSION and CORRELATION Jesús Pedrafta Arlla jesus.pedrafta@uab.cat Departament de Cènca Anmal dels Alments Items Correlaton: degree of
More information18. SIMPLE LINEAR REGRESSION III
8. SIMPLE LINEAR REGRESSION III US Domestc Beers: Calores vs. % Alcohol Ftted Values and Resduals To each observed x, there corresponds a y-value on the ftted lne, y ˆ ˆ = α + x. The are called ftted values.
More informationLecture 4 Hypothesis Testing
Lecture 4 Hypothess Testng We may wsh to test pror hypotheses about the coeffcents we estmate. We can use the estmates to test whether the data rejects our hypothess. An example mght be that we wsh to
More informationInterval Estimation in the Classical Normal Linear Regression Model. 1. Introduction
ECONOMICS 35* -- NOTE 7 ECON 35* -- NOTE 7 Interval Estmaton n the Classcal Normal Lnear Regresson Model Ths note outlnes the basc elements of nterval estmaton n the Classcal Normal Lnear Regresson Model
More informationSystematic Error Illustration of Bias. Sources of Systematic Errors. Effects of Systematic Errors 9/23/2009. Instrument Errors Method Errors Personal
9/3/009 Sstematc Error Illustraton of Bas Sources of Sstematc Errors Instrument Errors Method Errors Personal Prejudce Preconceved noton of true value umber bas Prefer 0/5 Small over large Even over odd
More informationSTAT 3340 Assignment 1 solutions. 1. Find the equation of the line which passes through the points (1,1) and (4,5).
(out of 15 ponts) STAT 3340 Assgnment 1 solutons (10) (10) 1. Fnd the equaton of the lne whch passes through the ponts (1,1) and (4,5). β 1 = (5 1)/(4 1) = 4/3 equaton for the lne s y y 0 = β 1 (x x 0
More information28. SIMPLE LINEAR REGRESSION III
8. SIMPLE LINEAR REGRESSION III Ftted Values and Resduals US Domestc Beers: Calores vs. % Alcohol To each observed x, there corresponds a y-value on the ftted lne, y ˆ = βˆ + βˆ x. The are called ftted
More information17 - LINEAR REGRESSION II
Topc 7 Lnear Regresson II 7- Topc 7 - LINEAR REGRESSION II Testng and Estmaton Inferences about β Recall that we estmate Yˆ ˆ β + ˆ βx. 0 μ Y X x β0 + βx usng To estmate σ σ squared error Y X x ε s ε we
More informationLecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding
Recall: man dea of lnear regresson Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 8 Lnear regresson can be used to study an
More informationLecture 9: Linear regression: centering, hypothesis testing, multiple covariates, and confounding
Lecture 9: Lnear regresson: centerng, hypothess testng, multple covarates, and confoundng Sandy Eckel seckel@jhsph.edu 6 May 008 Recall: man dea of lnear regresson Lnear regresson can be used to study
More informationReminder: Nested models. Lecture 9: Interactions, Quadratic terms and Splines. Effect Modification. Model 1
Lecture 9: Interactons, Quadratc terms and Splnes An Manchakul amancha@jhsph.edu 3 Aprl 7 Remnder: Nested models Parent model contans one set of varables Extended model adds one or more new varables to
More informationUnit 10: Simple Linear Regression and Correlation
Unt 10: Smple Lnear Regresson and Correlaton Statstcs 571: Statstcal Methods Ramón V. León 6/28/2004 Unt 10 - Stat 571 - Ramón V. León 1 Introductory Remarks Regresson analyss s a method for studyng the
More informationResource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Regression Analysis
Resource Allocaton and Decson Analss (ECON 800) Sprng 04 Foundatons of Regresson Analss Readng: Regresson Analss (ECON 800 Coursepak, Page 3) Defntons and Concepts: Regresson Analss statstcal technques
More informationThe SAS program I used to obtain the analyses for my answers is given below.
Homework 1 Answer sheet Page 1 The SAS program I used to obtan the analyses for my answers s gven below. dm'log;clear;output;clear'; *************************************************************; *** EXST7034
More informationUNIVERSITY OF TORONTO. Faculty of Arts and Science JUNE EXAMINATIONS STA 302 H1F / STA 1001 H1F Duration - 3 hours Aids Allowed: Calculator
UNIVERSITY OF TORONTO Faculty of Arts and Scence JUNE EXAMINATIONS 008 STA 30 HF / STA 00 HF Duraton - 3 hours Ads Allowed: Calculator LAST NAME: FIRST NAME: STUDENT NUMBER: Enrolled n (Crcle one): STA30
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More informationTopic- 11 The Analysis of Variance
Topc- 11 The Analyss of Varance Expermental Desgn The samplng plan or expermental desgn determnes the way that a sample s selected. In an observatonal study, the expermenter observes data that already
More informationChapter 14 Simple Linear Regression Page 1. Introduction to regression analysis 14-2
Chapter 4 Smple Lnear Regresson Page. Introducton to regresson analyss 4- The Regresson Equaton. Lnear Functons 4-4 3. Estmaton and nterpretaton of model parameters 4-6 4. Inference on the model parameters
More informationStatistics MINITAB - Lab 2
Statstcs 20080 MINITAB - Lab 2 1. Smple Lnear Regresson In smple lnear regresson we attempt to model a lnear relatonshp between two varables wth a straght lne and make statstcal nferences concernng that
More informationDurban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications
Durban Watson for Testng the Lack-of-Ft of Polynomal Regresson Models wthout Replcatons Ruba A. Alyaf, Maha A. Omar, Abdullah A. Al-Shha ralyaf@ksu.edu.sa, maomar@ksu.edu.sa, aalshha@ksu.edu.sa Department
More informationIntroduction to Regression
Introducton to Regresson Dr Tom Ilvento Department of Food and Resource Economcs Overvew The last part of the course wll focus on Regresson Analyss Ths s one of the more powerful statstcal technques Provdes
More informationHere is the rationale: If X and y have a strong positive relationship to one another, then ( x x) will tend to be positive when ( y y)
Secton 1.5 Correlaton In the prevous sectons, we looked at regresson and the value r was a measurement of how much of the varaton n y can be attrbuted to the lnear relatonshp between y and x. In ths secton,
More informationChapter 2 - The Simple Linear Regression Model S =0. e i is a random error. S β2 β. This is a minimization problem. Solution is a calculus exercise.
Chapter - The Smple Lnear Regresson Model The lnear regresson equaton s: where y + = β + β e for =,..., y and are observable varables e s a random error How can an estmaton rule be constructed for the
More informatione i is a random error
Chapter - The Smple Lnear Regresson Model The lnear regresson equaton s: where + β + β e for,..., and are observable varables e s a random error How can an estmaton rule be constructed for the unknown
More informationChapter 9: Statistical Inference and the Relationship between Two Variables
Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,
More informationexperimenteel en correlationeel onderzoek
expermenteel en correlatoneel onderzoek lecture 6: one-way analyss of varance Leary. Introducton to Behavoral Research Methods. pages 246 271 (chapters 10 and 11): conceptual statstcs Moore, McCabe, and
More informationTopic 7: Analysis of Variance
Topc 7: Analyss of Varance Outlne Parttonng sums of squares Breakdown the degrees of freedom Expected mean squares (EMS) F test ANOVA table General lnear test Pearson Correlaton / R 2 Analyss of Varance
More informationβ0 + β1xi and want to estimate the unknown
SLR Models Estmaton Those OLS Estmates Estmators (e ante) v. estmates (e post) The Smple Lnear Regresson (SLR) Condtons -4 An Asde: The Populaton Regresson Functon B and B are Lnear Estmators (condtonal
More informationLinear regression. Regression Models. Chapter 11 Student Lecture Notes Regression Analysis is the
Chapter 11 Student Lecture Notes 11-1 Lnear regresson Wenl lu Dept. Health statstcs School of publc health Tanjn medcal unversty 1 Regresson Models 1. Answer What Is the Relatonshp Between the Varables?.
More informationPubH 7405: REGRESSION ANALYSIS SLR: PARAMETER ESTIMATION
PuH 745: REGRESSION ANALYSIS SLR: PARAMETER ESTIMATION REGRESSION MODEL Model: Y + + ε where and are two new parameters called regresson coeffcents, the Intercept and the Slope, respectvel. The last term,
More informationJanuary Examinations 2015
24/5 Canddates Only January Examnatons 25 DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR STUDENT CANDIDATE NO.. Department Module Code Module Ttle Exam Duraton (n words)
More informationPubH 7405: REGRESSION ANALYSIS. SLR: INFERENCES, Part II
PubH 7405: REGRESSION ANALSIS SLR: INFERENCES, Part II We cover te topc of nference n two sessons; te frst sesson focused on nferences concernng te slope and te ntercept; ts s a contnuaton on estmatng
More informationBiostatistics. Chapter 11 Simple Linear Correlation and Regression. Jing Li
Bostatstcs Chapter 11 Smple Lnear Correlaton and Regresson Jng L jng.l@sjtu.edu.cn http://cbb.sjtu.edu.cn/~jngl/courses/2018fall/b372/ Dept of Bonformatcs & Bostatstcs, SJTU Recall eat chocolate Cell 175,
More informationThe Ordinary Least Squares (OLS) Estimator
The Ordnary Least Squares (OLS) Estmator 1 Regresson Analyss Regresson Analyss: a statstcal technque for nvestgatng and modelng the relatonshp between varables. Applcatons: Engneerng, the physcal and chemcal
More informationPolynomial Regression Models
LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance
More informationTests of Single Linear Coefficient Restrictions: t-tests and F-tests. 1. Basic Rules. 2. Testing Single Linear Coefficient Restrictions
ECONOMICS 35* -- NOTE ECON 35* -- NOTE Tests of Sngle Lnear Coeffcent Restrctons: t-tests and -tests Basc Rules Tests of a sngle lnear coeffcent restrcton can be performed usng ether a two-taled t-test
More informationProfessor Chris Murray. Midterm Exam
Econ 7 Econometrcs Sprng 4 Professor Chrs Murray McElhnney D cjmurray@uh.edu Mdterm Exam Wrte your answers on one sde of the blank whte paper that I have gven you.. Do not wrte your answers on ths exam.
More informationStatistics Chapter 4
Statstcs Chapter 4 "There are three knds of les: les, damned les, and statstcs." Benjamn Dsrael, 1895 (Brtsh statesman) Gaussan Dstrbuton, 4-1 If a measurement s repeated many tmes a statstcal treatment
More informationx = , so that calculated
Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to
More informationDiagnostics in Poisson Regression. Models - Residual Analysis
Dagnostcs n Posson Regresson Models - Resdual Analyss 1 Outlne Dagnostcs n Posson Regresson Models - Resdual Analyss Example 3: Recall of Stressful Events contnued 2 Resdual Analyss Resduals represent
More informationChap 10: Diagnostics, p384
Chap 10: Dagnostcs, p384 Multcollnearty 10.5 p406 Defnton Multcollnearty exsts when two or more ndependent varables used n regresson are moderately or hghly correlated. - when multcollnearty exsts, regresson
More information/ n ) are compared. The logic is: if the two
STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence
More informationChapter 5: Hypothesis Tests, Confidence Intervals & Gauss-Markov Result
Chapter 5: Hypothess Tests, Confdence Intervals & Gauss-Markov Result 1-1 Outlne 1. The standard error of 2. Hypothess tests concernng β 1 3. Confdence ntervals for β 1 4. Regresson when X s bnary 5. Heteroskedastcty
More informationSIMPLE LINEAR REGRESSION
Smple Lnear Regresson and Correlaton Introducton Prevousl, our attenton has been focused on one varable whch we desgnated b x. Frequentl, t s desrable to learn somethng about the relatonshp between two
More informationFirst Year Examination Department of Statistics, University of Florida
Frst Year Examnaton Department of Statstcs, Unversty of Florda May 7, 010, 8:00 am - 1:00 noon Instructons: 1. You have four hours to answer questons n ths examnaton.. You must show your work to receve
More informationProblem of Estimation. Ordinary Least Squares (OLS) Ordinary Least Squares Method. Basic Econometrics in Transportation. Bivariate Regression Analysis
1/60 Problem of Estmaton Basc Econometrcs n Transportaton Bvarate Regresson Analyss Amr Samm Cvl Engneerng Department Sharf Unversty of Technology Ordnary Least Squares (OLS) Maxmum Lkelhood (ML) Generally,
More informationUniversity of California at Berkeley Fall Introductory Applied Econometrics Final examination
SID: EEP 118 / IAS 118 Elsabeth Sadoulet and Daley Kutzman Unversty of Calforna at Berkeley Fall 01 Introductory Appled Econometrcs Fnal examnaton Scores add up to 10 ponts Your name: SID: 1. (15 ponts)
More informationis the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors
Multple Lnear and Polynomal Regresson wth Statstcal Analyss Gven a set of data of measured (or observed) values of a dependent varable: y versus n ndependent varables x 1, x, x n, multple lnear regresson
More informationCHAPTER 8. Exercise Solutions
CHAPTER 8 Exercse Solutons 77 Chapter 8, Exercse Solutons, Prncples of Econometrcs, 3e 78 EXERCISE 8. When = N N N ( x x) ( x x) ( x x) = = = N = = = N N N ( x ) ( ) ( ) ( x x ) x x x x x = = = = Chapter
More informationChapter 10. What is Regression Analysis? Simple Linear Regression Analysis. Examples
Chapter 10 Smple Lnear Regresson Analyss What s Regresson Analyss? A statstcal technque that descrbes the relatonshp between a dependent varable and one or more ndependent varables. Examples Consder the
More informationDO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR. Introductory Econometrics 1 hour 30 minutes
25/6 Canddates Only January Examnatons 26 Student Number: Desk Number:...... DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR Department Module Code Module Ttle Exam Duraton
More informationSee Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition)
Count Data Models See Book Chapter 11 2 nd Edton (Chapter 10 1 st Edton) Count data consst of non-negatve nteger values Examples: number of drver route changes per week, the number of trp departure changes
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationMD. LUTFOR RAHMAN 1 AND KALIPADA SEN 2 Abstract
ISSN 058-71 Bangladesh J. Agrl. Res. 34(3) : 395-401, September 009 PROBLEMS OF USUAL EIGHTED ANALYSIS OF VARIANCE (ANOVA) IN RANDOMIZED BLOCK DESIGN (RBD) ITH MORE THAN ONE OBSERVATIONS PER CELL HEN ERROR
More informationA Comparative Study for Estimation Parameters in Panel Data Model
A Comparatve Study for Estmaton Parameters n Panel Data Model Ahmed H. Youssef and Mohamed R. Abonazel hs paper examnes the panel data models when the regresson coeffcents are fxed random and mxed and
More informationEcon Statistical Properties of the OLS estimator. Sanjaya DeSilva
Econ 39 - Statstcal Propertes of the OLS estmator Sanjaya DeSlva September, 008 1 Overvew Recall that the true regresson model s Y = β 0 + β 1 X + u (1) Applyng the OLS method to a sample of data, we estmate
More informationAnalysis of Variance and Design of Experiments-II
Analyss of Varance and Desgn of Experments-II MODULE - III LECTURE - 8 PARTIALLY BALANCED INCOMPLETE BLOCK DESIGN (PBIBD) Dr Shalah Department of Mathematcs & Statstcs Indan Insttute of Technology Kanpur
More informationA METHOD FOR DETECTING OUTLIERS IN FUZZY REGRESSION
OPERATIONS RESEARCH AND DECISIONS No. 2 21 Barbara GŁADYSZ* A METHOD FOR DETECTING OUTLIERS IN FUZZY REGRESSION In ths artcle we propose a method for dentfyng outlers n fuzzy regresson. Outlers n a sample
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed
More informationUnbalanced Nested ANOVA - Sokal & Rohlf Example
8 Lnear Models 3 SR Box.6 Nested ANOVA ORIGIN Unbalanced Nested ANOVA - Sokal & Rohlf Example prepared by Wm Sten Ths sheet offers prototyped example of "Full Sb" nested ANOVA appearng n Sokal & Rohlf
More informationMethods of Detecting Outliers in A Regression Analysis Model.
Methods of Detectng Outlers n A Regresson Analyss Model. Ogu, A. I. *, Inyama, S. C+, Achugamonu, P. C++ *Department of Statstcs, Imo State Unversty,Owerr +Department of Mathematcs, Federal Unversty of
More informationNow we relax this assumption and allow that the error variance depends on the independent variables, i.e., heteroskedasticity
ECON 48 / WH Hong Heteroskedastcty. Consequences of Heteroskedastcty for OLS Assumpton MLR. 5: Homoskedastcty var ( u x ) = σ Now we relax ths assumpton and allow that the error varance depends on the
More informationAnswers Problem Set 2 Chem 314A Williamsen Spring 2000
Answers Problem Set Chem 314A Wllamsen Sprng 000 1) Gve me the followng crtcal values from the statstcal tables. a) z-statstc,-sded test, 99.7% confdence lmt ±3 b) t-statstc (Case I), 1-sded test, 95%
More information