sociology 362 regression
|
|
- Edwin Wiggins
- 6 years ago
- Views:
Transcription
1 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, X). The feature of the response variable distribution that has attracted the most interest in the past is the mean. The response variable is frequently quantitative and measured on a true metric, but it doesn t have to be; similarly, the independent variables are frequently quantitative, but they don t have to be. For the time being we ll work exclusively with regression models in which the dependent variable and the independent variables are both quantitative. Below we use data from respondents to the current population survey (cps) to look at how the mean of the sample conditional distribution of hourly wage varies across distinct values of. Let s begin by graphing Y against X, i.e., wages (vertical axis) against schooling (horizontal axis) figure 1. conditional distributions of wage by schooling Model 1 We ll start with a model for the mean of wages that totally ignores schooling. Write this model as M ( y ) a 1 a where 8 18 is a schooling value and is a constant that is calculated from sample data. Let the calculated value of a be written as â. Then the predicted or fitted value of wage for the ith person at the th value of schooling can be written as ˆ aˆ y
2 So the equation for the observed value of wage for the i th person at the th year of schooling can be written as y aˆ + ˆ e where the term on the end is the residual, the difference between the observed value of the response variable and the fitted value from the model. To render all this operational, the constant a must be calculated from sample data. For that purpose we use the function of sample data that minimizes the sum of the squared residuals: The value of â 1. regress hrwage e ˆ ˆ ( y yˆ ) eˆ ( y can be found by running aˆ) Source SS df MS Number of obs F(, 14). Model.. Prob > F. Residual R-squared Ad R-squared. Total Root MSE hrwage Coef. Std. Err. t P> t [9% Conf. Interval] _cons which yields the least-squares value of a y 889. This will be our predicted or fitted value of wage for everyone in the sample, no matter how many they have, since the model ignores schooling. ˆ $9. Here s the graph of the fitted line against. hrwage grand figure. fitting constant function
3 Model Now let s fit a model in which the fitted values of y are equal to the mean wage at each distinct value of. In contrast to the previous model, in which there was the same mean wage at every value of schooling, this model accommodates a possibly different value of the mean at every value of X. Hence, there will be as many different, distinct predictions as there are different values of schooling, in this case, eleven. You can see from the scatter diagram that this makes more sense. So the second model for the mean of y is Then the predicted or fitted value of wage for the ith person at the th value of schooling can be written as where the value of the â M ( y ) a yˆ aˆ that minimizes the sum of squared residuals are the conditional sample means at each value of schooling, i.e., y. equation for the i th observation at the th is Then the y aˆ + eˆ To find the eleven fitted wage values, I issue the following Stata command:. oneway hrwage edyrs, tab Summary of hrwage edyrs Mean Std. Dev. Freq Total Analysis of Variance Source SS df MS F Prob > F Between groups Within groups Total Here s the graph of this sample fitted conditional mean function:
4 hrwage mean_ y figure 3. conditional mean function Model 3 Instead of a sample conditional mean function that fits exactly the mean of wage for every distinct value of schooling, perhaps we would prefer, or be satisfied with, a linear approximation to it. To get the best linear predictor of wage given schooling, we do a linear regression on schooling. The model for the mean wage is then M ( y ) a + 3 bx which yields the equation for the fitted line: yˆ aˆ + bˆ x So the equation for the observation is y aˆ + bx ˆ + eˆ To render all this operational, the constants â and must be calculated from sample data. For that purpose we again use the function of sample data that minimizes the sum of the squared residuals: e ˆ ( y yˆ ) ˆb eˆ ( y aˆ bx ˆ ) â bˆ The values of and can be found by running
5 3. regress hrwage edyrs Source SS df MS Number of obs F( 1, 13) 97.7 Model Prob > F. Residual R-squared Ad R-squared.84 Total Root MSE 4.14 hrwage Coef. Std. Err. t P> t [9% Conf. Interval] edyrs _cons Here s the graph of the fitted values of wage from the linear regression. hrwage blp figure 4. best linear predictor Below is the graph of all the fitted models. The linear regression does a good ob of tracking the exact fitted conditional mean function. To see how good, compare the mean square residuals from the different models as given in the table.
6 grand mean_y blp figure. constant, mean, and blp functions model comparisons constant model conditional mean linear regression SST total sum of squares SSresidual residual sum of squares SSregression Regression sum of squares df residual degrees of freedom (n-1) 14 (n-11) 4 (n-) 13 MSres mean square residual (1374.9/14)4.7 (17.98/4).18 (394.9/13).6 Root MSres sqrt(4.7) 4.9 sqrt(.18) 4.49 sqrt(.6) 4.
7 Other statistics for wages and schooling total variation in y: standard deviation of y: ( y y) s y / mean of y: y 9.88 total variation in x: ( x ) x standard deviation of x: s x / mean of x: x covariation of y and x: ( x x)( y y) covariance of y and x: s xy 44.8/ correlation of x and y: r xy s / s s 4.68/(.38)(4.91).4 xy x y
sociology 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 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 informationIntroductory Econometrics. Lecture 13: Hypothesis testing in the multiple regression model, Part 1
Introductory Econometrics Lecture 13: Hypothesis testing in the multiple regression model, Part 1 Jun Ma School of Economics Renmin University of China October 19, 2016 The model I We consider the classical
More informationAcknowledgements. Outline. Marie Diener-West. ICTR Leadership / Team INTRODUCTION TO CLINICAL RESEARCH. Introduction to Linear Regression
INTRODUCTION TO CLINICAL RESEARCH Introduction to Linear Regression Karen Bandeen-Roche, Ph.D. July 17, 2012 Acknowledgements Marie Diener-West Rick Thompson ICTR Leadership / Team JHU Intro to Clinical
More informationsociology sociology Scatterplots Quantitative Research Methods: Introduction to correlation and regression Age vs Income
Scatterplots Quantitative Research Methods: Introduction to correlation and regression Scatterplots can be considered as interval/ratio analogue of cross-tabs: arbitrarily many values mapped out in -dimensions
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 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 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 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 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 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 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 informationECON Introductory Econometrics. Lecture 5: OLS with One Regressor: Hypothesis Tests
ECON4150 - Introductory Econometrics Lecture 5: OLS with One Regressor: Hypothesis Tests Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 5 Lecture outline 2 Testing Hypotheses about one
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 informationMultiple Regression: Inference
Multiple Regression: Inference The t-test: is ˆ j big and precise enough? We test the null hypothesis: H 0 : β j =0; i.e. test that x j has no effect on y once the other explanatory variables are controlled
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 information1 Independent Practice: Hypothesis tests for one parameter:
1 Independent Practice: Hypothesis tests for one parameter: Data from the Indian DHS survey from 2006 includes a measure of autonomy of the women surveyed (a scale from 0-10, 10 being the most autonomous)
More informationECON3150/4150 Spring 2015
ECON3150/4150 Spring 2015 Lecture 3&4 - The linear regression model Siv-Elisabeth Skjelbred University of Oslo January 29, 2015 1 / 67 Chapter 4 in S&W Section 17.1 in S&W (extended OLS assumptions) 2
More informationMonday 7 th Febraury 2005
Monday 7 th Febraury 2 Analysis of Pigs data Data: Body weights of 48 pigs at 9 successive follow-up visits. This is an equally spaced data. It is always a good habit to reshape the data, so we can easily
More informationAnswer all questions from part I. Answer two question from part II.a, and one question from part II.b.
B203: Quantitative Methods Answer all questions from part I. Answer two question from part II.a, and one question from part II.b. Part I: Compulsory Questions. Answer all questions. Each question carries
More informationLecture 4: Multivariate Regression, Part 2
Lecture 4: Multivariate Regression, Part 2 Gauss-Markov Assumptions 1) Linear in Parameters: Y X X X i 0 1 1 2 2 k k 2) Random Sampling: we have a random sample from the population that follows the above
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 4: Multivariate Regression, Part 2
Lecture 4: Multivariate Regression, Part 2 Gauss-Markov Assumptions 1) Linear in Parameters: Y X X X i 0 1 1 2 2 k k 2) Random Sampling: we have a random sample from the population that follows the above
More informationProblem Set 1 ANSWERS
Economics 20 Prof. Patricia M. Anderson Problem Set 1 ANSWERS Part I. Multiple Choice Problems 1. If X and Z are two random variables, then E[X-Z] is d. E[X] E[Z] This is just a simple application of one
More informationLINEAR REGRESSION ANALYSIS. MODULE XVI Lecture Exercises
LINEAR REGRESSION ANALYSIS MODULE XVI Lecture - 44 Exercises Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Exercise 1 The following data has been obtained on
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 information2.1. Consider the following production function, known in the literature as the transcendental production function (TPF).
CHAPTER Functional Forms of Regression Models.1. Consider the following production function, known in the literature as the transcendental production function (TPF). Q i B 1 L B i K i B 3 e B L B K 4 i
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 informationTHE MULTIVARIATE LINEAR REGRESSION MODEL
THE MULTIVARIATE LINEAR REGRESSION MODEL Why multiple regression analysis? Model with more than 1 independent variable: y 0 1x1 2x2 u It allows : -Controlling for other factors, and get a ceteris paribus
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 informationECON3150/4150 Spring 2016
ECON3150/4150 Spring 2016 Lecture 4 - The linear regression model Siv-Elisabeth Skjelbred University of Oslo Last updated: January 26, 2016 1 / 49 Overview These lecture slides covers: The linear regression
More informationLecture 5. In the last lecture, we covered. This lecture introduces you to
Lecture 5 In the last lecture, we covered. homework 2. The linear regression model (4.) 3. Estimating the coefficients (4.2) This lecture introduces you to. Measures of Fit (4.3) 2. The Least Square Assumptions
More information1 The basics of panel data
Introductory Applied Econometrics EEP/IAS 118 Spring 2015 Related materials: Steven Buck Notes to accompany fixed effects material 4-16-14 ˆ Wooldridge 5e, Ch. 1.3: The Structure of Economic Data ˆ Wooldridge
More informationUnemployment Rate Example
Unemployment Rate Example Find unemployment rates for men and women in your age bracket Go to FRED Categories/Population/Current Population Survey/Unemployment Rate Release Tables/Selected unemployment
More informationLab 6 - Simple Regression
Lab 6 - Simple Regression Spring 2017 Contents 1 Thinking About Regression 2 2 Regression Output 3 3 Fitted Values 5 4 Residuals 6 5 Functional Forms 8 Updated from Stata tutorials provided by Prof. Cichello
More informationLecture 7: OLS with qualitative information
Lecture 7: OLS with qualitative information Dummy variables Dummy variable: an indicator that says whether a particular observation is in a category or not Like a light switch: on or off Most useful values:
More information9. Linear Regression and Correlation
9. Linear Regression and Correlation Data: y a quantitative response variable x a quantitative explanatory variable (Chap. 8: Recall that both variables were categorical) For example, y = annual income,
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 informationStatistical Inference with Regression Analysis
Introductory Applied Econometrics EEP/IAS 118 Spring 2015 Steven Buck Lecture #13 Statistical Inference with Regression Analysis Next we turn to calculating confidence intervals and hypothesis testing
More information1. The shoe size of five randomly selected men in the class is 7, 7.5, 6, 6.5 the shoe size of 4 randomly selected women is 6, 5.
Economics 3 Introduction to Econometrics Winter 2004 Professor Dobkin Name Final Exam (Sample) You must answer all the questions. The exam is closed book and closed notes you may use calculators. You must
More informationQuestion 1a 1b 1c 1d 1e 2a 2b 2c 2d 2e 2f 3a 3b 3c 3d 3e 3f M ult: choice Points
Economics 102: Analysis of Economic Data Cameron Spring 2016 May 12 Department of Economics, U.C.-Davis Second Midterm Exam (Version A) Compulsory. Closed book. Total of 30 points and worth 22.5% of course
More informationThe Regression Tool. Yona Rubinstein. July Yona Rubinstein (LSE) The Regression Tool 07/16 1 / 35
The Regression Tool Yona Rubinstein July 2016 Yona Rubinstein (LSE) The Regression Tool 07/16 1 / 35 Regressions Regression analysis is one of the most commonly used statistical techniques in social and
More information1 A Review of Correlation and Regression
1 A Review of Correlation and Regression SW, Chapter 12 Suppose we select n = 10 persons from the population of college seniors who plan to take the MCAT exam. Each takes the test, is coached, and then
More informationSociology 63993, Exam 2 Answer Key [DRAFT] March 27, 2015 Richard Williams, University of Notre Dame,
Sociology 63993, Exam 2 Answer Key [DRAFT] March 27, 2015 Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ I. True-False. (20 points) Indicate whether the following statements
More informationRegression Models. Chapter 4
Chapter 4 Regression Models To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Introduction Regression analysis
More informationLecture 3: Multivariate Regression
Lecture 3: Multivariate Regression Rates, cont. Two weeks ago, we modeled state homicide rates as being dependent on one variable: poverty. In reality, we know that state homicide rates depend on numerous
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 informationOrdinary Least Squares (OLS): Multiple Linear Regression (MLR) Analytics What s New? Not Much!
Ordinary Least Squares (OLS): Multiple Linear Regression (MLR) Analytics What s New? Not Much! OLS: Comparison of SLR and MLR Analysis Interpreting Coefficients I (SRF): Marginal effects ceteris paribus
More informationAnalysis of Bivariate Data
Analysis of Bivariate Data Data Two Quantitative variables GPA and GAES Interest rates and indices Tax and fund allocation Population size and prison population Bivariate data (x,y) Case corr® 2 Independent
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 informationCorrelation and regression. Correlation and regression analysis. Measures of association. Why bother? Positive linear relationship
1 Correlation and regression analsis 12 Januar 2009 Monda, 14.00-16.00 (C1058) Frank Haege Department of Politics and Public Administration Universit of Limerick frank.haege@ul.ie www.frankhaege.eu Correlation
More information8. Nonstandard standard error issues 8.1. The bias of robust standard errors
8.1. The bias of robust standard errors Bias Robust standard errors are now easily obtained using e.g. Stata option robust Robust standard errors are preferable to normal standard errors when residuals
More informationWeek 3: Simple Linear Regression
Week 3: Simple Linear Regression Marcelo Coca Perraillon University of Colorado Anschutz Medical Campus Health Services Research Methods I HSMP 7607 2017 c 2017 PERRAILLON ALL RIGHTS RESERVED 1 Outline
More informationChapter 4. Regression Models. Learning Objectives
Chapter 4 Regression Models To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing
More informationWarwick Economics Summer School Topics in Microeconometrics Instrumental Variables Estimation
Warwick Economics Summer School Topics in Microeconometrics Instrumental Variables Estimation Michele Aquaro University of Warwick This version: July 21, 2016 1 / 31 Reading material Textbook: Introductory
More informationApplied Statistics and Econometrics
Applied Statistics and Econometrics Lecture 5 Saul Lach September 2017 Saul Lach () Applied Statistics and Econometrics September 2017 1 / 44 Outline of Lecture 5 Now that we know the sampling distribution
More informationLongitudinal Data Analysis Using Stata Paul D. Allison, Ph.D. Upcoming Seminar: May 18-19, 2017, Chicago, Illinois
Longitudinal Data Analysis Using Stata Paul D. Allison, Ph.D. Upcoming Seminar: May 18-19, 217, Chicago, Illinois Outline 1. Opportunities and challenges of panel data. a. Data requirements b. Control
More informationEconometrics. 8) Instrumental variables
30C00200 Econometrics 8) Instrumental variables Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Thery of IV regression Overidentification Two-stage least squates
More informationComputer Exercise 3 Answers Hypothesis Testing
Computer Exercise 3 Answers Hypothesis Testing. reg lnhpay xper yearsed tenure ---------+------------------------------ F( 3, 6221) = 512.58 Model 457.732594 3 152.577531 Residual 1851.79026 6221.297667619
More informationEssential of Simple regression
Essential of Simple regression We use simple regression when we are interested in the relationship between two variables (e.g., x is class size, and y is student s GPA). For simplicity we assume the relationship
More informationF Tests and F statistics
F Tests and F statistics Testing Linear estrictions F Stats and F Tests F Distributions F stats (w/ ) F Stats and tstat s eported F Stat's in OLS Output Example I: Bodyfat Babies and Bathwater F Stats,
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 informationEmpirical Application of Simple Regression (Chapter 2)
Empirical Application of Simple Regression (Chapter 2) 1. The data file is House Data, which can be downloaded from my webpage. 2. Use stata menu File Import Excel Spreadsheet to read the data. Don t forget
More informationLecture (chapter 13): Association between variables measured at the interval-ratio level
Lecture (chapter 13): Association between variables measured at the interval-ratio level Ernesto F. L. Amaral April 9 11, 2018 Advanced Methods of Social Research (SOCI 420) Source: Healey, Joseph F. 2015.
More informationECON3150/4150 Spring 2016
ECON3150/4150 Spring 2016 Lecture 6 Multiple regression model Siv-Elisabeth Skjelbred University of Oslo February 5th Last updated: February 3, 2016 1 / 49 Outline Multiple linear regression model and
More informationEconometrics II Censoring & Truncation. May 5, 2011
Econometrics II Censoring & Truncation Måns Söderbom May 5, 2011 1 Censored and Truncated Models Recall that a corner solution is an actual economic outcome, e.g. zero expenditure on health by a household
More informationRegression Models. Chapter 4. Introduction. Introduction. Introduction
Chapter 4 Regression Models Quantitative Analysis for Management, Tenth Edition, by Render, Stair, and Hanna 008 Prentice-Hall, Inc. Introduction Regression analysis is a very valuable tool for a manager
More informationInference for the Regression Coefficient
Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression line. We can shows that b 0 and b 1 are the unbiased estimates
More informationLecture 12: Interactions and Splines
Lecture 12: Interactions and Splines Sandy Eckel seckel@jhsph.edu 12 May 2007 1 Definition Effect Modification The phenomenon in which the relationship between the primary predictor and outcome varies
More informationBusiness Statistics. Lecture 9: Simple Regression
Business Statistics Lecture 9: Simple Regression 1 On to Model Building! Up to now, class was about descriptive and inferential statistics Numerical and graphical summaries of data Confidence intervals
More information1: a b c d e 2: a b c d e 3: a b c d e 4: a b c d e 5: a b c d e. 6: a b c d e 7: a b c d e 8: a b c d e 9: a b c d e 10: a b c d e
Economics 102: Analysis of Economic Data Cameron Spring 2016 Department of Economics, U.C.-Davis Final Exam (A) Tuesday June 7 Compulsory. Closed book. Total of 58 points and worth 45% of course grade.
More informationECON Introductory Econometrics. Lecture 4: Linear Regression with One Regressor
ECON4150 - Introductory Econometrics Lecture 4: Linear Regression with One Regressor Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 4 Lecture outline 2 The OLS estimators The effect of
More informationLab 07 Introduction to Econometrics
Lab 07 Introduction to Econometrics Learning outcomes for this lab: Introduce the different typologies of data and the econometric models that can be used Understand the rationale behind econometrics Understand
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 informationFunctional Form. So far considered models written in linear form. Y = b 0 + b 1 X + u (1) Implies a straight line relationship between y and X
Functional Form So far considered models written in linear form Y = b 0 + b 1 X + u (1) Implies a straight line relationship between y and X Functional Form So far considered models written in linear form
More informationECON2228 Notes 2. Christopher F Baum. Boston College Economics. cfb (BC Econ) ECON2228 Notes / 47
ECON2228 Notes 2 Christopher F Baum Boston College Economics 2014 2015 cfb (BC Econ) ECON2228 Notes 2 2014 2015 1 / 47 Chapter 2: The simple regression model Most of this course will be concerned with
More information10) Time series econometrics
30C00200 Econometrics 10) Time series econometrics Timo Kuosmanen Professor, Ph.D. 1 Topics today Static vs. dynamic time series model Suprious regression Stationary and nonstationary time series Unit
More informationNonrecursive Models Highlights Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised April 6, 2015
Nonrecursive Models Highlights Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised April 6, 2015 This lecture borrows heavily from Duncan s Introduction to Structural
More informationy response variable x 1, x 2,, x k -- a set of explanatory variables
11. Multiple Regression and Correlation y response variable x 1, x 2,, x k -- a set of explanatory variables In this chapter, all variables are assumed to be quantitative. Chapters 12-14 show how to incorporate
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 informationSection I. Define or explain the following terms (3 points each) 1. centered vs. uncentered 2 R - 2. Frisch theorem -
First Exam: Economics 388, Econometrics Spring 006 in R. Butler s class YOUR NAME: Section I (30 points) Questions 1-10 (3 points each) Section II (40 points) Questions 11-15 (10 points each) Section III
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 informationMeasurement Error. Often a data set will contain imperfect measures of the data we would ideally like.
Measurement Error Often a data set will contain imperfect measures of the data we would ideally like. Aggregate Data: (GDP, Consumption, Investment are only best guesses of theoretical counterparts and
More informationBusiness Statistics. Lecture 10: Correlation and Linear Regression
Business Statistics Lecture 10: Correlation and Linear Regression Scatterplot A scatterplot shows the relationship between two quantitative variables measured on the same individuals. It displays the Form
More informationStatistical Techniques II EXST7015 Simple Linear Regression
Statistical Techniques II EXST7015 Simple Linear Regression 03a_SLR 1 Y - the dependent variable 35 30 25 The objective Given points plotted on two coordinates, Y and X, find the best line to fit the data.
More informationLecture 3: Inference in SLR
Lecture 3: Inference in SLR STAT 51 Spring 011 Background Reading KNNL:.1.6 3-1 Topic Overview This topic will cover: Review of hypothesis testing Inference about 1 Inference about 0 Confidence Intervals
More informationHandout 12. Endogeneity & Simultaneous Equation Models
Handout 12. Endogeneity & Simultaneous Equation Models In which you learn about another potential source of endogeneity caused by the simultaneous determination of economic variables, and learn how to
More informationHomework Solutions Applied Logistic Regression
Homework Solutions Applied Logistic Regression WEEK 6 Exercise 1 From the ICU data, use as the outcome variable vital status (STA) and CPR prior to ICU admission (CPR) as a covariate. (a) Demonstrate that
More informationLecture 12: Effect modification, and confounding in logistic regression
Lecture 12: Effect modification, and confounding in logistic regression Ani Manichaikul amanicha@jhsph.edu 4 May 2007 Today Categorical predictor create dummy variables just like for linear regression
More informationRegression #8: Loose Ends
Regression #8: Loose Ends Econ 671 Purdue University Justin L. Tobias (Purdue) Regression #8 1 / 30 In this lecture we investigate a variety of topics that you are probably familiar with, but need to touch
More informationSociology Exam 2 Answer Key March 30, 2012
Sociology 63993 Exam 2 Answer Key March 30, 2012 I. True-False. (20 points) Indicate whether the following statements are true or false. If false, briefly explain why. 1. A researcher has constructed scales
More information1 Linear Regression Analysis The Mincer Wage Equation Data Econometric Model Estimation... 11
Econ 495 - Econometric Review 1 Contents 1 Linear Regression Analysis 4 1.1 The Mincer Wage Equation................. 4 1.2 Data............................. 6 1.3 Econometric Model.....................
More informationBIOSTATS 640 Spring 2018 Unit 2. Regression and Correlation (Part 1 of 2) STATA Users
Unit Regression and Correlation 1 of - Practice Problems Solutions Stata Users 1. In this exercise, you will gain some practice doing a simple linear regression using a Stata data set called week0.dta.
More informationA discussion on multiple regression models
A discussion on multiple regression models In our previous discussion of simple linear regression, we focused on a model in which one independent or explanatory variable X was used to predict the value
More informationLecture 2 Simple Linear Regression STAT 512 Spring 2011 Background Reading KNNL: Chapter 1
Lecture Simple Linear Regression STAT 51 Spring 011 Background Reading KNNL: Chapter 1-1 Topic Overview This topic we will cover: Regression Terminology Simple Linear Regression with a single predictor
More informationSimple Linear Regression Using Ordinary Least Squares
Simple Linear Regression Using Ordinary Least Squares Purpose: To approximate a linear relationship with a line. Reason: We want to be able to predict Y using X. Definition: The Least Squares Regression
More informationNonrecursive models (Extended Version) Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised April 6, 2015
Nonrecursive models (Extended Version) Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised April 6, 2015 NOTE: This lecture borrows heavily from Duncan s Introduction
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 informationInference for Regression Simple Linear Regression
Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression p Statistical model for linear regression p Estimating
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 information