Political Science 552
|
|
- Eleanor Stevens
- 6 years ago
- Views:
Transcription
1 Dagnostcs and Smple Remedaton February 9, 4 Poltcal Scence 55 Volatng Assumptons Key Assumptons E { Y; X } β + β X E (, ) ε ~ nor σ { ε,ε } for j j X s measured wthout error Small Sample Plot Feelng Thermometer-Bush Party ID
2 Dagnostcs and Smple Remedaton February 9, 4 Large Sample Plots FT-Bush PartyID Plots wth Jtterng FT-Bush PartyID Resduals as Dagnostc Tool e Y Y $ e* e MSE
3 Dagnostcs and Smple Remedaton February 9, 4 Prototypcal Resdual Plots Data Ambguty Data Set Varable Obs. (a)-(c) X (a) Y (b) Y (c) Y (d) X (d) Y Y X Seeng Is Recognzng
4 Dagnostcs and Smple Remedaton February 9, 4 Polynomal Relatonshp Testng for Lnearty SSTO SSE r SSTO SSTO SSE E SSTO SSR SSTO SSG SSTO Nonlnear Relatonshp FT-Bush PartyID 4
5 Dagnostcs and Smple Remedaton February 9, 4 ANOVA for Nonlnearty Source SS df MS F Total SSTO n- Lnear r*ssto SSR/ Nonlnear E*SSTO k- SSG/k- Addtonal (E-r)*SSTO k- SSad/k- (E-r)/(k-) Error (-E)*SSTO n-k- SSE/n-k- (-E)/(n-k- SOURCE DF SS MS F p Regresson Nonlnear Improvement >. Error Total 48. E-sq.954 (E-sq - R-sq).3 df 5 R-sq.93 ( - E-sq).46 df 4 F (.3/5)/(.46/4.46/4).6/.5.54 Lnearty Test n Stata. generate pdv53. anova v36 pd v53, contnuous(pd) sequental anova Number of obs 496 R-squared.344 Root MSE.53 Adj R-squared.345 Source Seq. SS df MS F Prob > F Model pd v Resdual Total Grad GPA Outlers y.7x.4x.5x r GRE-Total 5
6 Dagnostcs and Smple Remedaton February 9, 4 Heteroscedastcty Modfed Levene Test e~ and ~ e d ~e e d e ~e t d s d { d d } Modfed Levene: Stata Commands * Modfed Levene Test drop _all use "D:\COURSES\PS55\EXAMPLES\grades.dta", clear * get medan for predctor and create splt for sample summarze gre_total, detal generate splt(gre_tot>) * do regresson, get resdual, and get medans regress grad_gpa gre_tot predct resd,r bysort splt: summarze resd, detal * get devatons separately for the two groups gen dabs(resd-.3335) f splt gen dabs(resd-.65) f splt ttest d d, unpared 6
7 Dagnostcs and Smple Remedaton February 9, 4 Modfed Levene: Stata Output. ttest d d, unpared Two-sample t test wth equal varances Varable Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] d d combned dff Degrees of freedom: 38 Ho: mean(d) - mean(d) dff Ha: dff < Ha: dff! Ha: dff > t t t P < t.37 P > t.64 P > t.6993 Breusch-Pagan Test log eσ γ + γ X SSE usual regresson SSE SSR * SSR from regresson on squared resduals SSR SSE χ * BP n Breusch-Pagan n Stata. regress grad_gpa gre_tot grad_gpa Coef. Std. Err. t P>t [95% Conf.Interval] gre_total _cons hettest Breusch-Pagan / Cook-Wesberg test for heteroskedastcty Ho: Constant varance Varables: ftted values of grad_gpa ch().8 Prob > ch
8 Dagnostcs and Smple Remedaton February 9, 4 Normalty Test/Normalty Plots E.375 { e } MSE z th of n STATA COMMANDS regress grad_gpa gre_total predct resd pnorm resd sort resd gen pctle(_n-.375)/(_n+.5) gen eresde(rmse)*nvnorm(pctle) correlate eresd resd (obs4) eresd resd eresd. resd.943. Normal F[(resd-m)/s] n Emprcal P[] /(N+) The Correlaton Test (obs4) eresd resd eresd. resd.943. TABLE B.6 n Shapro Wlk test for Normalty W ( ) ( X X ) a X (). swlk resd Shapro-Wlk W test for normal data Varable Obs W V z Prob>z resd
9 Dagnostcs and Smple Remedaton February 9, 4 Error n Varables (Y). drop _all. use "D:\krtzervlle.DTA".. drop f v53>6 (9 observatons deleted). regress v36 v53 Number of obs 496 R-squared.379 Adj R-squared.374 Root MSE.468 v36 Coef. Std. Err. v _cons gen FTv36+*nvnorm(unform()) (3 mssng values generated). regress FT v53 Number of obs 496 R-squared.699 Adj R-squared.694 Root MSE.43 FT Coef. Std. Err. v _cons Error n Varables (X). drop _all. use "D:\krtzervlle.DTA".. drop f v53>6 (9 observatons deleted). regress v36 v53 Number of obs 496 R-squared.379 Adj R-squared.374 Root MSE.468 v36 Coef. Std. Err. v _cons gen PIDv53+nvnorm(unform()). regress v36 PID Number of obs 496 R-squared.64 Adj R-squared.599 Root MSE.47 v36 Coef. Std. Err. PID _cons x Error n X Y x b where x X X b Y ( x + k ) Y x + Y k ( x + ) x + x k + k k b x Y x + k 9
10 Dagnostcs and Smple Remedaton February 9, 4 Transformng X Transformng Y Box-Cox λ Y ' Y Y ' log Y when λ λ Y Y β + βx n L( β, β, σ ) n exp ( Y β β X) ( πσ ) σ n λ L( β, β, σ, λ) n exp ( Y β β X) ( πσ ) σ e
11 Dagnostcs and Smple Remedaton February 9, 4 Generalzed Box-Cox n Stata θ Y β + β X λ use "D:\COURSES\PS55\EXAMPLES\clrp.dta", clear regress lhours stakes gen sqstakessqrt(stakes) regress lhours sqstakes replace lhours. f lhours boxcox lhours stakes boxcox lhours stakes,model(rhs) boxcox lhours stakes,model(theta) Nonlnear Example. regress lhours stakes Number of obs 34 R-squared.974 Root MSE Lhours Coef. Std. Err. t stakes _cons gen sqstakessqrt(stakes). regress lhours sqstakes Number of obs 34 R-squared.3443 Root MSE 3.8 lhours Coef. Std. Err. t sqstakes _cons Box Cox Example. boxcox lhours stakes,model(rhs) Number of obs 34 LR ch() 47.5 Prob > ch. lhours Coef. Std. Err. z /lambda Estmates of scale-varant parameters Coef. Notrans _cons Trans stakes.795 /sgma boxcox lhours stakes,model(theta) Number of obs 34 LR ch() Prob > ch. lhours Coef. Std. Err. z /lambda /theta Estmates of scale-varant parameters Coef. Notrans _cons Trans stakes.695 /sgma
12 Dagnostcs and Smple Remedaton February 9, 4 Lowess lowess lhours stakes lowess lhours stakes, f stakes<5 lowess lhours stakes, f stakes< lhours 5 5 Lowess smoother stakes bandwdth.8 Lowess smoother lhours 3 Lowess smoother lhours stakes bandwdth stakes bandwdth.8
Y = 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 informationIf we apply least squares to the transformed data we obtain. which yields the generalized least squares estimator of β, i.e.,
Econ 388 R. Butler 04 revsons lecture 6 WLS I. The Matrx Verson of Heteroskedastcty To llustrate ths n general, consder an error term wth varance-covarance matrx a n-by-n, nxn, matrx denoted as, nstead
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 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 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 information) is violated, so that V( instead. That is, the variance changes for at least some observations.
Econ 388 R. Butler 014 revsons Lecture 15 I. HETEROSKEDASTICITY: both pure and mpure (the mpure verson s due to an omtted regressor that s correlated wth the ncluded regressors n the model) A. heteroskedastcty=when
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 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 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 informationAddressing Alternative Explanations: Multiple Regression
Addressng Alternatve Explanatons: Multple Regresson 7.87 Dd Clnton hurt Gore example Dd Clnton hurt Gore n the 000 electon? Treatment s not lkng Bll Clnton How would you test ths? Bvarate regresson of
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 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 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 informationAddressing Alternative. Multiple Regression Spring 2012
Addressng Alternatve Explanatons: Multple Regresson 7.87 Sprng 0 Dd Clnton hurt Gore example Dd Clnton hurt Gore n the 000 electon? Treatment s not lkng Bll Clnton How would you test ths? Bvarate regresson
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 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 informationLab 4: Two-level Random Intercept Model
BIO 656 Lab4 009 Lab 4: Two-level Random Intercept Model Data: Peak expratory flow rate (pefr) measured twce, usng two dfferent nstruments, for 17 subjects. (from Chapter 1 of Multlevel and Longtudnal
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 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 informationβ0 + β1xi. You are interested in estimating the unknown parameters β
Revsed: v3 Ordnar Least Squares (OLS): Smple Lnear Regresson (SLR) Analtcs The SLR Setup Sample Statstcs Ordnar Least Squares (OLS): FOCs and SOCs Back to OLS and Sample Statstcs Predctons (and Resduals)
More informationβ0 + β1xi. You are interested in estimating the unknown parameters β
Ordnary Least Squares (OLS): Smple Lnear Regresson (SLR) Analytcs The SLR Setup Sample Statstcs Ordnary Least Squares (OLS): FOCs and SOCs Back to OLS and Sample Statstcs Predctons (and Resduals) wth OLS
More informationSystems of Equations (SUR, GMM, and 3SLS)
Lecture otes on Advanced Econometrcs Takash Yamano Fall Semester 4 Lecture 4: Sstems of Equatons (SUR, MM, and 3SLS) Seemngl Unrelated Regresson (SUR) Model Consder a set of lnear equatons: $ + ɛ $ + ɛ
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 information. *DEFINITIONS OF ARTIFICIAL DATA SET. mat m=(12,20,0) /*matrix of means of RHS vars: edu, exp, error*/
. DEFINITIONS OF ARTIFICIAL DATA SET. mat m=(,,) /matrix of means of RHS vars: edu, exp, error/. mat c=(5,-.6, \ -.6,9, \,,.) /covariance matrix of RHS vars /. mat l m /displays matrix of means / c c c3
More informationSOCY5601 Handout 8, Fall DETECTING CURVILINEARITY (continued) CONDITIONAL EFFECTS PLOTS
SOCY5601 DETECTING CURVILINEARITY (continued) CONDITIONAL EFFECTS PLOTS More on use of X 2 terms to detect curvilinearity: As we have said, a quick way to detect curvilinearity in the relationship between
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 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 informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression Sasivimol Rattanasiri, Ph.D Section for Clinical Epidemiology and Biostatistics Ramathibodi Hospital, Mahidol University E-mail: sasivimol.rat@mahidol.ac.th 1 Outline
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 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 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 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 informationModule Contact: Dr Susan Long, ECO Copyright of the University of East Anglia Version 1
UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton 016-17 ECONOMETRIC METHODS ECO-7000A Tme allowed: hours Answer ALL FOUR Questons. Queston 1 carres a weght of 5%; Queston carres 0%;
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 informationHeteroskedasticity Example
ECON 761: Heteroskedasticity Example L Magee November, 2007 This example uses the fertility data set from assignment 2 The observations are based on the responses of 4361 women in Botswana s 1988 Demographic
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 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 informationRegression. The Simple Linear Regression Model
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
More informationEconomics 326 Methods of Empirical Research in Economics. Lecture 14: Hypothesis testing in the multiple regression model, Part 2
Economics 326 Methods of Empirical Research in Economics Lecture 14: Hypothesis testing in the multiple regression model, Part 2 Vadim Marmer University of British Columbia May 5, 2010 Multiple restrictions
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 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 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 informationLab 11 - Heteroskedasticity
Lab 11 - Heteroskedasticity Spring 2017 Contents 1 Introduction 2 2 Heteroskedasticity 2 3 Addressing heteroskedasticity in Stata 3 4 Testing for heteroskedasticity 4 5 A simple example 5 1 1 Introduction
More informationLinear Modelling in Stata Session 6: Further Topics in Linear Modelling
Linear Modelling in Stata Session 6: Further Topics in Linear Modelling Mark Lunt Arthritis Research UK Epidemiology Unit University of Manchester 14/11/2017 This Week Categorical Variables Categorical
More informationLecture#12. Instrumental variables regression Causal parameters III
Lecture#12 Instrumental variables regression Causal parameters III 1 Demand experiment, market data analysis & simultaneous causality 2 Simultaneous causality Your task is to estimate the demand function
More informationGroup Comparisons: Differences in Composition Versus Differences in Models and Effects
Group Comparisons: Differences in Composition Versus Differences in Models and Effects Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 15, 2015 Overview.
More informationApplied regression. Dr. Nitiphong Songsrirote
Appled regresson Dr. Ntphong Songsrrote econ555@gmal.com www.ntphong.com 553 of 84 of 84 Page of 7 Avery robust statstcalmethodologythat tradtonally hasusedexstngrelatonshps exstng betweenvarablestoallowpredctonofthe
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 informationQuestion 1 carries a weight of 25%; question 2 carries 20%; question 3 carries 25%; and question 4 carries 30%.
UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PGT Examnaton 017-18 FINANCIAL ECONOMETRICS ECO-7009A Tme allowed: HOURS Answer ALL FOUR questons. Queston 1 carres a weght of 5%; queston carres
More informationConfidence Interval for the mean response
Week 3: Prediction and Confidence Intervals at specified x. Testing lack of fit with replicates at some x's. Inference for the correlation. Introduction to regression with several explanatory variables.
More informationSTATISTICS 110/201 PRACTICE FINAL EXAM
STATISTICS 110/201 PRACTICE FINAL EXAM Questions 1 to 5: There is a downloadable Stata package that produces sequential sums of squares for regression. In other words, the SS is built up as each variable
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 informationGeneral Linear Model (Chapter 4)
General Linear Model (Chapter 4) Outcome variable is considered continuous Simple linear regression Scatterplots OLS is BLUE under basic assumptions MSE estimates residual variance testing regression coefficients
More information****Lab 4, Feb 4: EDA and OLS and WLS
****Lab 4, Feb 4: EDA and OLS and WLS ------- log: C:\Documents and Settings\Default\Desktop\LDA\Data\cows_Lab4.log log type: text opened on: 4 Feb 2004, 09:26:19. use use "Z:\LDA\DataLDA\cowsP.dta", clear.
More informationSection Least Squares Regression
Section 2.3 - Least Squares Regression Statistics 104 Autumn 2004 Copyright c 2004 by Mark E. Irwin Regression Correlation gives us a strength of a linear relationship is, but it doesn t tell us what it
More informationPractice 2SLS with Artificial Data Part 1
Practice 2SLS with Artificial Data Part 1 Yona Rubinstein July 2016 Yona Rubinstein (LSE) Practice 2SLS with Artificial Data Part 1 07/16 1 / 16 Practice with Artificial Data In this note we use artificial
More informationLab 10 - Binary Variables
Lab 10 - Binary Variables Spring 2017 Contents 1 Introduction 1 2 SLR on a Dummy 2 3 MLR with binary independent variables 3 3.1 MLR with a Dummy: different intercepts, same slope................. 4 3.2
More informationStatistical Modelling in Stata 5: Linear Models
Statistical Modelling in Stata 5: Linear Models Mark Lunt Arthritis Research UK Epidemiology Unit University of Manchester 07/11/2017 Structure This Week What is a linear model? How good is my model? Does
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 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 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 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 informationProblem Set #5-Key Sonoma State University Dr. Cuellar Economics 317- Introduction to Econometrics
Problem Set #5-Key Sonoma State University Dr. Cuellar Economics 317- Introduction to Econometrics C1.1 Use the data set Wage1.dta to answer the following questions. Estimate regression equation wage =
More informationsociology 362 regression
sociology 36 regression Regression is a means of modeling how the conditional distribution of a response variable (say, Y) varies for different values of one or more independent explanatory variables (say,
More informationECO220Y Simple Regression: Testing the Slope
ECO220Y Simple Regression: Testing the Slope Readings: Chapter 18 (Sections 18.3-18.5) Winter 2012 Lecture 19 (Winter 2012) Simple Regression Lecture 19 1 / 32 Simple Regression Model y i = β 0 + β 1 x
More informationBinary Dependent Variables
Binary Dependent Variables In some cases the outcome of interest rather than one of the right hand side variables - is discrete rather than continuous Binary Dependent Variables In some cases the outcome
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 information7.1. Single classification analysis of variance (ANOVA) Why not use multiple 2-sample 2. When to use ANOVA
Sngle classfcaton analyss of varance (ANOVA) When to use ANOVA ANOVA models and parttonng sums of squares ANOVA: hypothess testng ANOVA: assumptons A non-parametrc alternatve: Kruskal-Walls ANOVA Power
More informationECON2228 Notes 7. Christopher F Baum. Boston College Economics. cfb (BC Econ) ECON2228 Notes / 41
ECON2228 Notes 7 Christopher F Baum Boston College Economics 2014 2015 cfb (BC Econ) ECON2228 Notes 6 2014 2015 1 / 41 Chapter 8: Heteroskedasticity In laying out the standard regression model, we made
More informationEconometrics. 9) Heteroscedasticity and autocorrelation
30C00200 Econometrics 9) Heteroscedasticity and autocorrelation Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Heteroscedasticity Possible causes Testing for
More informationSpecification Error: Omitted and Extraneous Variables
Specification Error: Omitted and Extraneous Variables Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 5, 05 Omitted variable bias. Suppose that the correct
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 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 informationProblem Set #3-Key. wage Coef. Std. Err. t P> t [95% Conf. Interval]
Problem Set #3-Key Sonoma State University Economics 317- Introduction to Econometrics Dr. Cuellar 1. Use the data set Wage1.dta to answer the following questions. a. For the regression model Wage i =
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 informationSTA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #6
STA 8 Applied Linear Models: Regression Analysis Spring 011 Solution for Homework #6 6. a) = 11 1 31 41 51 1 3 4 5 11 1 31 41 51 β = β1 β β 3 b) = 1 1 1 1 1 11 1 31 41 51 1 3 4 5 β = β 0 β1 β 6.15 a) Stem-and-leaf
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 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 informationProblem 3.1: Error autotocorrelation and heteroskedasticity Standard variance components model:
ECON 510: Panel data econometrcs Semnar 3: October., 007 Problem 3.1: Error autotocorrelaton and heteroskedastcy Standard varance components model: (0.1) y = k+ x β + + u, ε = + u, IID(0, ), u Rewrng the
More informationExercices for Applied Econometrics A
QEM F. Gardes-C. Starzec-M.A. Diaye Exercices for Applied Econometrics A I. Exercice: The panel of households expenditures in Poland, for years 1997 to 2000, gives the following statistics for the whole
More informationYarine Fawaz ECONOMETRICS I
Yarne Fawaz ECONOMETRICS I Organzaton of the course Classes: Classes to 0: -Introducton -Bvarate model -Multvarate model -Inference and tests -Advanced topcs: Lmted dependent varables; Interactons; etc.
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 informationLecture 8: Heteroskedasticity. Causes Consequences Detection Fixes
Lecture 8: Heteroskedasticity Causes Consequences Detection Fixes Assumption MLR5: Homoskedasticity 2 var( u x, x,..., x ) 1 2 In the multivariate case, this means that the variance of the error term does
More informationsociology 362 regression
sociology 36 regression Regression is a means of studying how the conditional distribution of a response variable (say, Y) varies for different values of one or more independent explanatory variables (say,
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 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 informationScientific Question Determine whether the breastfeeding of Nepalese children varies with child age and/or sex of child.
Longtudnal Logstc Regresson: Breastfeedng of Nepalese Chldren PART II GEE models (margnal, populaton average) covered last lab Random Intercept models (subject specfc) Transton models Scentfc Queston Determne
More informationProblem Set 10: Panel Data
Problem Set 10: Panel Data 1. Read in the data set, e11panel1.dta from the course website. This contains data on a sample or 1252 men and women who were asked about their hourly wage in two years, 2005
More informationRockefeller College University at Albany
Rockefeller College University at Albany PAD 705 Handout: Polynomial Distributed Lags In the Handouts section of the web site you will find the data sets (GrangerPoly.dta) I constructed for the example
More informationIV. Modeling a Mean: Simple Linear Regression
IV. Modelng a Mean: Smple Lnear Regresson We have talked about nference for a sngle mean, for comparng two means, and for comparng several means. What f the mean of one varable depends on the value of
More informationIntroduction to Analysis of Variance (ANOVA) Part 1
Introducton to Analss of Varance (ANOVA) Part 1 Sngle factor The logc of Analss of Varance Is the varance explaned b the model >> than the resdual varance In regresson models Varance explaned b regresson
More informationCHAPER 11: HETEROSCEDASTICITY: WHAT HAPPENS WHEN ERROR VARIANCE IS NONCONSTANT?
Basc Econometrcs, Gujarat and Porter CHAPER 11: HETEROSCEDASTICITY: WHAT HAPPENS WHEN ERROR VARIANCE IS NONCONSTANT? 11.1 (a) False. The estmators are unbased but are neffcent. (b) True. See Sec. 11.4
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 informationData Considerations and Ordinary Least Squares Estimation of Single-Equation Econometric Models
Chapter Data Consderatons and Ordnary Least Squares Estmaton of Sngle-Equaton Econometrc Models Secton. Data Crtcal Ingredent n All Appled Econometrc Models Suffcently large amount of hstorcal data. Ask
More informationApplied Statistics and Probability for Engineers, 6 th edition Xy
Aled Statstcs and Probablty or Engneers, 6 th edton CHAPTER Sectons - 3 553 -. a) XX 3 5.9 35 553 35 379 96. Xy 4355.8 4736.8 7.55 b) ˆ 3.73 7.55 3.74.6.6 c) 7.55 3.74(8).6(43) 89.49 -. a) ˆ (XX) X y.9
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 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 informationReduced slides. Introduction to Analysis of Variance (ANOVA) Part 1. Single factor
Reduced sldes Introducton to Analss of Varance (ANOVA) Part 1 Sngle factor 1 The logc of Analss of Varance Is the varance explaned b the model >> than the resdual varance In regresson models Varance explaned
More informationInterpreting coefficients for transformed variables
Interpreting coefficients for transformed variables! Recall that when both independent and dependent variables are untransformed, an estimated coefficient represents the change in the dependent variable
More informationInterpreting Slope Coefficients in Multiple Linear Regression Models: An Example
CONOMICS 5* -- Introducton to NOT CON 5* -- Introducton to NOT : Multple Lnear Regresson Models Interpretng Slope Coeffcents n Multple Lnear Regresson Models: An xample Consder the followng smple lnear
More information