PBAF 528 Week Theory Is the variable s place in the equation certain and theoretically sound? Most important! 2. T-test
|
|
- Edmund Singleton
- 5 years ago
- Views:
Transcription
1 PBAF 528 Week 6 How do we choose our model? How do you decde whch ndependent varables? If you want to read more about ths, try Studenmund, A.H. Usng Econometrcs Chapter 7. (ether 3 rd or 4 th Edtons) 1. Theory Is the varable s place n the equaton certan and theoretcally sound? Most mportant! 2. T-test 3. Is the varable s estmated coeffcent sgnfcant n the expected drecton (one-sded test)? 2 R Does the overall ft of the equaton mprove when then varable s added to the equaton? 4. Bas Do other varables coeffcents change sgnfcantly when the varable s added to the equaton? If all of these are true, then the varable belongs n the equaton. Dummy Varables 1. Intercept Dummy Varables A dummy varable that changes the constant or ntercept term Y = β 0 + β 1 X + β 2 D + ε 2. Seasonal Dummes (Mult-alternatve Dummes) Dummy varables used to represent qualtatve varables that take on more than two alternatves Use one less dummy varable than there are alternatves. Each dummy wll represent one condton.
2 3. Slope Dummes A dummy varable that changes the slope of the relatonshp between x and y 4. Dummy Dependent Varables Dummy varable s used as the dependent varable Example #1: More than 2 categores (more than one dummy varable) Educaton can be thought of as: (1) not havng earned a hgh school dploma, (2) havng earned only a hgh school dploma, and (3) havng more educaton than a hgh school dploma. Then we use two dummes. We ll call them D 1 and D 2. D 1 =1 f you have only a hgh school dploma 0 otherwse D 2 =1 f you have more educaton than a hgh school dploma 0 otherwse. What are all the possbltes? you have more than a hgh school degree you have a hgh school dploma and nothng beyond that you have not earned any dploma D 1 = and D 2 = D 1 = and D 2 = D 1 = and D 2 = CAUTION: Don t nclude too many dummes or you ll have to explan each data pont! CAUTION: Don t nclude a dummy that only takes a value of 1 for one data pont and zero for all other observatons. Ths one-tme dummy acts to elmnate that observaton from the data set, mprovng the ft artfcally. 2
3 Some deas for usng dummy varables: Could use dummy for seasonal changes f you have data where each case s at a dfferent tme pont. Illustraton #1: If the data has been recorded quarterly, you wll need 3 dummy varables. D 1 = { 1 n Quarter 1 0 otherwse D 2 = { 1 n Quarter 2 0 otherwse D 3 = { 1 n Quarter 3 0 otherwse Quarter 1 Quarter 2 Quarter 3 Quarter 4 D 1 D 2 D 3 Illustraton #2: Dummy for Tme Seres Data If you were nterested to study the mpact of a partcular event on a gven varable, a dummy varable could be used for ths. For example, the mpact of Sept 11 on arlne travel could be modeled wth a dummy varable. D = 0 for D = 1 for 2002 to present The sgn of the coeffcent of D wll gve the drecton of any shft n Interacton Terms Interacton terms are products of two or more ndependent varables. Allow for dfferences n effect of an explanatory factor across categores or levels of another factor Used when the change n Y wth respect to one ndependent varable depends on the level of another ndependent varable. Can nteract wth dummes or contnuous varables. 3
4 For a contnuous(ndependent) and a dummy: Allows the slope between the dependent and ndependent varable to be dfferent dependng on whether the condton specfed by the dummy s met. Used whenever the mpact of an ndependent varable on the dependent varable s hypotheszed to change f some qualtatve condton s met. 1. What does the regresson equaton look lke wth an nteracton n t? Ths s called a slope dummy varable Y = β 0 + β 1 X + β 2 D +β 3 X D + ε I Ths one has an nteracton between an ndependent varable, X, and a dummy varable, D. What effect does the nteracton have on the slope (that s, the change n Y brought about by a change n X)? When D=0, Y/ X=β 1 Ths s the slope for the reference group When D=1, Y/ X=β 1 +β 3 Ths s the slope for the ndcated group The slope (or the coeffcent of X) changes when the condton specfed by D s met. 4
5 from AH Studenmund Usng Econometrcs: A Practcal Gude p You need both the slope dummy and the ntercept dummy n the equaton. The above regresson lne has both a slope dummy and an ntercept dummy (a dummy that does not get multpled by anythng). Ths s necessary n most cases snce just ncludng a slope dummy would bas the slope by forcng t to explan more than t should, for example, changes n the mean between two groups. An ntercept dummy best explans ths sort of change. So, the model should nclude an ntercept dummy (plan dummy term) where there s a slope dummy (a dummy multpled by a predctor). Thnk carefully about your hypotheses about the drecton of the relatonshp between the dummes and the outcomes snce these terms make the model very flexble. 3. How do you test for sgnfcance of nteracton terms? To test for dfferences n slopes between the categores, use the t-test on the nteracton term. To test overall dfferences n the regresson relatonshp wth and wthout the ncluson of an nteracton use an F-test (#2). 5
6 Example #2: Dummy Varable Interactng wth a Contnuous (Independent) Varable Does extensve meda coverage of a mltary crss nfluence publc opnon on how to respond to the crss? Poltcal scentsts at UCLA came up wth a model concernng the 1990 Persan Gulf War, precptated by Iraq leader Saddam Hussen s nvason of Kuwat. They developed a model to analyze the level of support Amercans had for mltary (rather than dplomatc) response to the crss. The dependent varable ranges from 0 (preference for a dplomatc response) to 4 (preference for mltary response. Here s the model they developed based on data from 1,763 U.S. Ctzens. E(y)=β 0 + β 1 x 1 + β 2 x 2 +β 3 x 3 +β 4 x 4 +β 5 x 5 +β 6 x 6 +β 7 x 7 +β 8 x 2 x 3 +β 9 x 2 x 4 where: x 1 = Level of TV news exposure n a selected week (number of days) x 2 = Knowledge of seven poltcal fgures (1 pont for each correct answer) x 3 = Dummy varable for Gender (1 f male, 0 f female) x 4 = Dummy varable for Race (1 f nonwhte, 0 f whte) x 5 = Partsanshp (0-6 scale, where 0 = strong Democrat and 6 = strong Republcan) x 6 = Defense spendng atttude (1-7 scale, where 1 = greatly decrease spendng and 7 = greatly ncreased spendng) x 7 = Educaton The regresson results: Varable β estmate Standard Error Two-Taled p-value TV news exposure (x 1 ) Poltcal knowledge (x 2 ) Gender (x 3 ) <.001 Race (x 4 ) <.001 Partsanshp (x 5 ) <.001 Defense spendng (x 6 ) <.001 Educaton (x 7 ) <.001 Knowledge X Gender (x 2 x 3 ) Knowledge X Race (x 2 x 4 ) R 2 =.194, F=46.88 (p<.001) Source: Iyengar, S. and Smon, A News coverage of the Gulf Crss and publc opnon. Communcaton Research 20,: 380 (Table 2) 6
7 1) Interpret the β estmates for TV news exposure. 2) Is there enough support to say that TV news exposure s assocated wth support for a mltary resoluton of the crss? 3) Is there suffcent evdence to say that the relatonshp between support for a mltary resoluton and gender depends on poltcal knowledge? 4) What s the effect of knowledge on support for mltary resoluton for men? E(y)=β 0 + β 1 x 1 + β 2 x 2 +β 3 (1) +β 4 x 4 +β 5 x 5 +β 6 x 6 +β 7 x 7 +β 8 x 2 (1) +β 9 x 2 x 4 5) What s the effect of knowledge on support for mltary resoluton for women? E(y)=β 0 + β 1 x 1 + β 2 x 2 +β 3 (0) +β 4 x 4 +β 5 x 5 +β 6 x 6 +β 7 x 7 +β 8 x 2 (0) +β 9 x 2 x 4 6) What test would you use to answer the followng queston: Overall, does gender affect support for a mltary resoluton? 7
8 Example #3: Interactng 2 contnuous varables Fowles and Loeb hypotheszed that drunk drvng fataltes are more lkely at hgh alttude because hgher elevatons dmnsh the oxygen ntake of the bran, whch ncreases the mpact of a gven amount of alcohol. F = Traffc fataltes per vehcle mle (by state) B = per capta consumpton of beer S = average hghway drvng speed D = dummy (1=state has a vehcle nspecton program, 0=no nspecton program) A = average alttude of metro areas (1000s of feet) Fˆ = B S 0.24D 0.35A B A (t-statstcs) (-0.8) (1.53) (-0.96) (-1.07) (1.97) Hypotheszed relatonshp ? n=48 adjusted R 2 =.499 The nteracton n ths model s between two contnuous varables, consumpton rate of beer and alttude. The effect on the outcome of each the two varables nvolved n the nteracton depends on the nteracton coeffcent and the coeffcent on the orgnal varable. 1) Does the average alttude of metropoltan areas n the state affect the relatonshp between per capta beer consumpton and the rate of traffc fataltes? 2) How much hgher a fatalty rate do we expect for an average alttude of metro area ncrease by 1000 feet? 3) Does the alttude affect the overall regresson relatonshp explanng fatalty rate? (How would you approach ths?) 8
Chapter 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 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 informationDummy variables in multiple variable regression model
WESS Econometrcs (Handout ) Dummy varables n multple varable regresson model. Addtve dummy varables In the prevous handout we consdered the followng regresson model: y x 2x2 k xk,, 2,, n and we nterpreted
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 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 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 8 Indicator Variables
Chapter 8 Indcator Varables In general, e explanatory varables n any regresson analyss are assumed to be quanttatve n nature. For example, e varables lke temperature, dstance, age etc. are quanttatve n
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 informationBasically, if you have a dummy dependent variable you will be estimating a probability.
ECON 497: Lecture Notes 13 Page 1 of 1 Metropoltan State Unversty ECON 497: Research and Forecastng Lecture Notes 13 Dummy Dependent Varable Technques Studenmund Chapter 13 Bascally, f you have a dummy
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 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 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 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 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 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 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 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 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 informationDepartment of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution
Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable
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 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 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 informationLinear Regression Analysis: Terminology and Notation
ECON 35* -- Secton : Basc Concepts of Regresson Analyss (Page ) Lnear Regresson Analyss: Termnology and Notaton Consder the generc verson of the smple (two-varable) lnear regresson model. It s represented
More informationChapter 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 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 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 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 informationECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE)
ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE) June 7, 016 15:30 Frst famly name: Name: DNI/ID: Moble: Second famly Name: GECO/GADE: Instructor: E-mal: Queston 1 A B C Blank Queston A B C Blank Queston
More informationProperties of Least Squares
Week 3 3.1 Smple Lnear Regresson Model 3. Propertes of Least Squares Estmators Y Y β 1 + β X + u weekly famly expendtures X weekly famly ncome For a gven level of x, the expected level of food expendtures
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 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 informationBIO Lab 2: TWO-LEVEL NORMAL MODELS with school children popularity data
Lab : TWO-LEVEL NORMAL MODELS wth school chldren popularty data Purpose: Introduce basc two-level models for normally dstrbuted responses usng STATA. In partcular, we dscuss Random ntercept models wthout
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 informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have
More informationEcon107 Applied Econometrics Topic 9: Heteroskedasticity (Studenmund, Chapter 10)
I. Defnton and Problems Econ7 Appled Econometrcs Topc 9: Heteroskedastcty (Studenmund, Chapter ) We now relax another classcal assumpton. Ths s a problem that arses often wth cross sectons of ndvduals,
More informationTests of Exclusion Restrictions on Regression Coefficients: Formulation and Interpretation
ECONOMICS 5* -- NOTE 6 ECON 5* -- NOTE 6 Tests of Excluson Restrctons on Regresson Coeffcents: Formulaton and Interpretaton The populaton regresson equaton (PRE) for the general multple lnear regresson
More informationA dummy variable equal to 1 if the nearby school is in regular session and 0 otherwise;
Lehrstuhl für Betrebswrtschaftslehre, Emprsche Wrtschaftsforschung Otto-von-Guercke-Unverstät Magdeburg, Postfach 410, 39016 Magdeburg Prof. Dr. Dr. Bodo Vogt Otto-von-Guercke-Unverstät Magdeburg Fakultät
More informationChapter 8 Multivariate Regression Analysis
Chapter 8 Multvarate Regresson Analyss 8.3 Multple Regresson wth K Independent Varables 8.4 Sgnfcance tests of Parameters Populaton Regresson Model For K ndependent varables, the populaton regresson and
More informationIII. Econometric Methodology Regression Analysis
Page Econ07 Appled Econometrcs Topc : An Overvew of Regresson Analyss (Studenmund, Chapter ) I. The Nature and Scope of Econometrcs. Lot s of defntons of econometrcs. Nobel Prze Commttee Paul Samuelson,
More informationExam. Econometrics - Exam 1
Econometrcs - Exam 1 Exam Problem 1: (15 ponts) Suppose that the classcal regresson model apples but that the true value of the constant s zero. In order to answer the followng questons assume just one
More informationFinancing Innovation: Evidence from R&D Grants
Fnancng Innovaton: Evdence from R&D Grants Sabrna T. Howell Onlne Appendx Fgure 1: Number of Applcants Note: Ths fgure shows the number of losng and wnnng Phase 1 grant applcants over tme by offce (Energy
More informationChapter 5 Multilevel Models
Chapter 5 Multlevel Models 5.1 Cross-sectonal multlevel models 5.1.1 Two-level models 5.1.2 Multple level models 5.1.3 Multple level modelng n other felds 5.2 Longtudnal multlevel models 5.2.1 Two-level
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 informationCHAPTER 8 SOLUTIONS TO PROBLEMS
CHAPTER 8 SOLUTIONS TO PROBLEMS 8.1 Parts () and (). The homoskedastcty assumpton played no role n Chapter 5 n showng that OLS s consstent. But we know that heteroskedastcty causes statstcal nference based
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 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 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 informationIntroduction to Dummy Variable Regressors. 1. An Example of Dummy Variable Regressors
ECONOMICS 5* -- Introducton to Dummy Varable Regressors ECON 5* -- Introducton to NOTE Introducton to Dummy Varable Regressors. An Example of Dummy Varable Regressors A model of North Amercan car prces
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 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 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 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 informationSoc 3811 Basic Social Statistics Third Midterm Exam Spring 2010
Soc 3811 Basc Socal Statstcs Thrd Mdterm Exam Sprng 2010 Your Name [50 ponts]: ID #: Your TA: Kyungmn Baek Meghan Zacher Frank Zhang INSTRUCTIONS: (A) Wrte your name on the lne at top front of every sheet.
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 informationANSWERS CHAPTER 9. TIO 9.2: If the values are the same, the difference is 0, therefore the null hypothesis cannot be rejected.
ANSWERS CHAPTER 9 THINK IT OVER thnk t over TIO 9.: χ 2 k = ( f e ) = 0 e Breakng the equaton down: the test statstc for the ch-squared dstrbuton s equal to the sum over all categores of the expected frequency
More information( )( ) [ ] [ ] ( ) 1 = [ ] = ( ) 1. H = X X X X is called the hat matrix ( it puts the hats on the Y s) and is of order n n H = X X X X.
( ) ( ) where ( ) 1 ˆ β = X X X X β + ε = β + Aε A = X X 1 X [ ] E ˆ β β AE ε β so ˆ = + = β s unbased ( )( ) [ ] ˆ Cov β = E ˆ β β ˆ β β = E Aεε A AE ε ε A Aσ IA = σ AA = σ X X = [ ] = ( ) 1 Ftted values
More informationPredictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore
Sesson Outlne Introducton to classfcaton problems and dscrete choce models. Introducton to Logstcs Regresson. Logstc functon and Logt functon. Maxmum Lkelhood Estmator (MLE) for estmaton of LR parameters.
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 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 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 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 informationMidterm Examination. Regression and Forecasting Models
IOMS Department Regresson and Forecastng Models Professor Wllam Greene Phone: 22.998.0876 Offce: KMC 7-90 Home page: people.stern.nyu.edu/wgreene Emal: wgreene@stern.nyu.edu Course web page: people.stern.nyu.edu/wgreene/regresson/outlne.htm
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(c) Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University
Transform a bnary qualtatve varable (wth non-numercal values) to a dummy varable. For example, GENDER = f the observaton s male = f t s female (c) Pongsa Pornchawseskul, Faculty of Economcs, Chulalongkorn
More informationEconometrics: What's It All About, Alfie?
ECON 351* -- Introducton (Page 1) Econometrcs: What's It All About, Ale? Usng sample data on observable varables to learn about economc relatonshps, the unctonal relatonshps among economc varables. Econometrcs
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 informationECON 351* -- Note 23: Tests for Coefficient Differences: Examples Introduction. Sample data: A random sample of 534 paid employees.
Model and Data ECON 35* -- NOTE 3 Tests for Coeffcent Dfferences: Examples. Introducton Sample data: A random sample of 534 pad employees. Varable defntons: W hourly wage rate of employee ; lnw the natural
More informationANOVA. The Observations y ij
ANOVA Stands for ANalyss Of VArance But t s a test of dfferences n means The dea: The Observatons y j Treatment group = 1 = 2 = k y 11 y 21 y k,1 y 12 y 22 y k,2 y 1, n1 y 2, n2 y k, nk means: m 1 m 2
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 informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationMeasuring the Strength of Association
Stat 3000 Statstcs for Scentsts and Engneers Measurng the Strength of Assocaton Note that the slope s one measure of the lnear assocaton between two contnuous varables t tells ou how much the average of
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 informationMarginal Effects in Probit Models: Interpretation and Testing. 1. Interpreting Probit Coefficients
ECON 5 -- NOE 15 Margnal Effects n Probt Models: Interpretaton and estng hs note ntroduces you to the two types of margnal effects n probt models: margnal ndex effects, and margnal probablty effects. It
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 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 informationChapter 3. Two-Variable Regression Model: The Problem of Estimation
Chapter 3. Two-Varable Regresson Model: The Problem of Estmaton Ordnary Least Squares Method (OLS) Recall that, PRF: Y = β 1 + β X + u Thus, snce PRF s not drectly observable, t s estmated by SRF; that
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationSociology 301. Bivariate Regression II: Testing Slope and Coefficient of Determination. Bivariate Regression. Calculating Expected Values
Socology 30 Bvarate Regresson II: Testng Slope and Coeffcent of Determnaton Lyng Luo 05.03 Bvarate Regresson F.ed regresson model for sample ntercept slope Learnng objec;ves Understand the basc dea of
More informationMultinomial logit regression
07/0/6 Multnomal logt regresson Introducton We now turn our attenton to regresson models for the analyss of categorcal dependent varables wth more than two response categores: Y car owned (many possble
More informationSTAT 511 FINAL EXAM NAME Spring 2001
STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
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 informationUsing T.O.M to Estimate Parameter of distributions that have not Single Exponential Family
IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran
More informationNumber of cases Number of factors Number of covariates Number of levels of factor i. Value of the dependent variable for case k
ANOVA Model and Matrx Computatons Notaton The followng notaton s used throughout ths chapter unless otherwse stated: N F CN Y Z j w W Number of cases Number of factors Number of covarates Number of levels
More informationContinuous vs. Discrete Goods
CE 651 Transportaton Economcs Charsma Choudhury Lecture 3-4 Analyss of Demand Contnuous vs. Dscrete Goods Contnuous Goods Dscrete Goods x auto 1 Indfference u curves 3 u u 1 x 1 0 1 bus Outlne Data Modelng
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 informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationsince [1-( 0+ 1x1i+ 2x2 i)] [ 0+ 1x1i+ assumed to be a reasonable approximation
Econ 388 R. Butler 204 revsons Lecture 4 Dummy Dependent Varables I. Lnear Probablty Model: the Regresson model wth a dummy varables as the dependent varable assumpton, mplcaton regular multple regresson
More information3/3/2014. CDS M Phil Econometrics. Vijayamohanan Pillai N. CDS Mphil Econometrics Vijayamohan. 3-Mar-14. CDS M Phil Econometrics.
Dummy varable Models an Plla N Dummy X-varables Dummy Y-varables Dummy X-varables Dummy X-varables Dummy varable: varable assumng values 0 and to ndcate some attrbutes To classfy data nto mutually exclusve
More informationThe Geometry of Logit and Probit
The Geometry of Logt and Probt Ths short note s meant as a supplement to Chapters and 3 of Spatal Models of Parlamentary Votng and the notaton and reference to fgures n the text below s to those two chapters.
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 informationYoung Drivers and Run-Off-the-Road Crashes
Young Drvers and Run-Off-the-Road Crashes Sunanda Dssanayake Department of Cvl Engneerng Kansas State Unversty 2118 Fedler Hall Manhattan, KS 66506 sunanda@ksu.edu ABSTRACT Motor vehcle crashes are one
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 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 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 informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationUNR Joint Economics Working Paper Series Working Paper No Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?
UNR Jont Economcs Workng Paper Seres Workng Paper No. 08-005 Further Analyss of the Zpf Law: Does the Rank-Sze Rule Really Exst? Fungsa Nota and Shunfeng Song Department of Economcs /030 Unversty of Nevada,
More informationF8: Heteroscedasticity
F8: Heteroscedastcty Feng L Department of Statstcs, Stockholm Unversty What s so-called heteroscedastcty In a lnear regresson model, we assume the error term has a normal dstrbuton wth mean zero and varance
More information