Multiple OLS Regression
|
|
- Clifton Holt
- 6 years ago
- Views:
Transcription
1 Multiple OLS Regression Ronet Bachman, Ph.D. Presented by Justice Research and Statistics Association 12/8/2016 Justice Research and Statistics Association th Street, NW, Third Floor Washington, DC 20001
2 Training and Technical Assistance Webinar Series This webinar is being audio cast via the speakers on your computer and via teleconference. To access the audio stream information, select audio and audio conference from the menu bar. This will display the call information and the button to access the audio stream. If you have speakers or headphones for your computer there is no need to call in, simply select call using computer. Justice Research and Statistics Association th Street, NW, Third Floor Washington, DC 20001
3 Training and Technical Assistance Webinar Series This webinar is being audio cast via the speakers on your computer and via teleconference. To access the audio stream information, select audio and audio conference from the menu bar. This will display the call information and the button to access the audio stream. If you have speakers or headphones for your computer there is no need to call in, simply select call using computer. Justice Research and Statistics Association th Street, NW, Third Floor Washington, DC 20001
4 Training and Technical Assistance Webinar Series All telephones have been muted. If you would like to ask a question please use the chat feature unless instructed otherwise. Please remember to select Host, Presenter or Panelists Justice Research and Statistics Association th Street, NW, Third Floor Washington, DC 20001
5 The beauty of statistical control Presented by Ronet Bachman, PhD University of Delaware To Justice Research and Statistics Association
6 Establish Relationship Between X and Y Establish Correct Time Order (X precedes Y) Establish Non-Spuriousness a spurious relationship is one that is really a false relationship caused by a third or fourth variable. Experimental Design Statistical Control Enter Multivariate Equations Multiple Regression Analyses
7
8 But we live in a Multivariate World!! Age SES Victimization Gender
9 Simple Bivariate Crosstabs Delinquency (DV) Low Medium High Gender IV Female % % % 680 Male % % %
10 Multivariate Models allow us to Statistically control for 3 rd, 4 th, kth, variables - Controlling for Parental Supervision in Partial Crosstab Table Weak Parental Supervision Female Male Delinquency Low Medium High 26% 28% 46% % 27% 49% 592 Strong Parental Supervision Delinquency 764 Female Male Low Medium High 54% 26% 20% % 30% 24%
11 Multiple OLS Regression Equations for the Population and Sample A simple extension of the bivariate model!
12 Assumptions for OLS Multiple Regression: (1) It is assumed that the data were randomly selected. (2) It is assumed that all populations are normally distributed. (3) We must assume that the data are continuous, that they are measured at the interval or ratio level. (4) We must assume that the nature of the relationship between the dependent and each of the independent variables is linear. (5) It is assumed that the error term ( ) is independent of and therefore uncorrelated with each of the independent or x variables, that it is normally distributed, and has an expected value of 0 and constant variance across all levels of x. This is referred to as the assumption of homoscedasticity. (6) The new assumption in the multivariate regression model is that the independent variables are independent of or uncorrelated with one another. Having independent variables that are highly correlated is referred to as the problem of multicollinearity.
13 Partial Regression Slopes b b 1 2 sy ryx1 ( ryx2)( rx1x2) = 2 sx1 1 r x1x2 sy ryx2 ( ryx1)( rx1x2) = 2 sx2 1 r x1x2 Notice that models control for variation between X1 and x2 as well as that between x1 and y and x2 and y Where: b 1 = the partial slope of x 1 on y b 2 = the partial slope of x 2 on y s y = the standard deviation of y s 1 = the standard deviation of the first independent variable (x 1 ) s 2 = the standard deviation of the second independent variable (x 2 ) r y1 = the bivariate correlation between y and x 1 r y2 = the bivariate correlation between y and x 2 r 12 = the bivariate correlation between x 1 and x 2
14 Model Variables Entered/Removed b Variables Entered 1 certainty of punishment a a. All requested variables entered. Variables Removed. Enter b. Dependent Variable: time 1 delinquency scale Method Model R R Square Model Summary Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), certainty of punishment ANOVA b Model Sum of Squares df Mean Square F Sig. 1 Regression a Residual Total a. Predictors: (Constant), certainty of punishment b. Dependent Variable: time 1 delinquency scale Model Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta 1 (Constant) certainty of punishment a. Dependent Variable: time 1 delinquency scale t Sig. y= (x)
15 Model Variables Entered/Removed b Variables Entered 1 sex of respondent a a. All requested variables entered. Variables Removed. Enter b. Dependent Variable: time 1 delinquency scale Method Model R R Square Model Summary Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), sex of respondent ANOVA b Model Sum of Squares df Mean Square F Sig. 1 Regression a Residual Total a. Predictors: (Constant), sex of respondent b. Dependent Variable: time 1 delinquency scale Model Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta 1 (Constant) sex of respondent a. Dependent Variable: time 1 delinquency scale y = (x) t Sig.
16 Model Variables Entered/Removed b Variables Entered 1 certainty of punishment, sex of respondent a a. All requested variables entered. Variables Removed. Enter Method b. Dependent Variable: time 1 delinquency scale Multiple r Multiple Coefficient of Determination Model R R Square Model Summary Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), certainty of punishment, sex of respondent This test is now important ANOVA b Model Sum of Squares df Mean Square F Sig. 1 Regression a Residual Total a. Predictors: (Constant), certainty of punishment, sex of respondent b. Dependent Variable: time 1 delinquency scale Model Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta 1 (Constant) sex of respondent certainty of punishment a. Dependent Variable: time 1 delinquency scale y = (x1) (x2) t Sig. Null hypothesis tests For each slope
17 What happens when both IV s are included in the model? Model Variables Entered/Removed b Variables Entered 1 certainty of punishment, gender of respondent a Variables Removed. Enter Method b. Dependent Variable: time 1 delinquency scale Multiple r Multiple Coefficient of Determination Model R R Square Model Summary Adjusted R Square Std. Error of the Estimate a H0: No relationship between any of the IVs and the DV OR ρ = 0. ANOVA b Model Sum of Squares df Mean Square F Sig. 1 Regression a Residual Total Model Coefficients a Unstandardized Coefficients Standardized Coefficients B Std. Error Beta 1 (Constant) gender of respondent certainty of punishment a. Dependent Variable: time 1 delinquency scale Null hypothesis tests For each slope Delinquency (y) = (x1) (x2) H 0 : No relationship between gender and delinquency after perceptions of risk are controlled, OR β 1 =0. H 0 : No relationship between perceptions of risk and delinquency after gender is controlled, OR β 2 =0. t Sig.
Training and Technical Assistance Webinar Series Statistical Analysis for Criminal Justice Research
Training and Technical Assistance Webinar Series Statistical Analysis for Criminal Justice Research Justice Research and Statistics Association 720 7 th Street, NW, Third Floor Washington, DC 20001 II.
More informationMultiple Regression. More Hypothesis Testing. More Hypothesis Testing The big question: What we really want to know: What we actually know: We know:
Multiple Regression Ψ320 Ainsworth More Hypothesis Testing What we really want to know: Is the relationship in the population we have selected between X & Y strong enough that we can use the relationship
More informationRegression ( Kemampuan Individu, Lingkungan kerja dan Motivasi)
Regression (, Lingkungan kerja dan ) Descriptive Statistics Mean Std. Deviation N 3.87.333 32 3.47.672 32 3.78.585 32 s Pearson Sig. (-tailed) N Kemampuan Lingkungan Individu Kerja.000.432.49.432.000.3.49.3.000..000.000.000..000.000.000.
More informationPractical Biostatistics
Practical Biostatistics Clinical Epidemiology, Biostatistics and Bioinformatics AMC Multivariable regression Day 5 Recap Describing association: Correlation Parametric technique: Pearson (PMCC) Non-parametric:
More informationESP 178 Applied Research Methods. 2/23: Quantitative Analysis
ESP 178 Applied Research Methods 2/23: Quantitative Analysis Data Preparation Data coding create codebook that defines each variable, its response scale, how it was coded Data entry for mail surveys and
More informationSociology 593 Exam 1 February 14, 1997
Sociology 9 Exam February, 997 I. True-False. ( points) Indicate whether the following statements are true or false. If false, briefly explain why.. There are IVs in a multiple regression model. If the
More informationRegression: Main Ideas Setting: Quantitative outcome with a quantitative explanatory variable. Example, cont.
TCELL 9/4/205 36-309/749 Experimental Design for Behavioral and Social Sciences Simple Regression Example Male black wheatear birds carry stones to the nest as a form of sexual display. Soler et al. wanted
More information36-309/749 Experimental Design for Behavioral and Social Sciences. Sep. 22, 2015 Lecture 4: Linear Regression
36-309/749 Experimental Design for Behavioral and Social Sciences Sep. 22, 2015 Lecture 4: Linear Regression TCELL Simple Regression Example Male black wheatear birds carry stones to the nest as a form
More informationArea1 Scaled Score (NAPLEX) .535 ** **.000 N. Sig. (2-tailed)
Institutional Assessment Report Texas Southern University College of Pharmacy and Health Sciences "An Analysis of 2013 NAPLEX, P4-Comp. Exams and P3 courses The following analysis illustrates relationships
More informationReview of Multiple Regression
Ronald H. Heck 1 Let s begin with a little review of multiple regression this week. Linear models [e.g., correlation, t-tests, analysis of variance (ANOVA), multiple regression, path analysis, multivariate
More informationChapter 9 - Correlation and Regression
Chapter 9 - Correlation and Regression 9. Scatter diagram of percentage of LBW infants (Y) and high-risk fertility rate (X ) in Vermont Health Planning Districts. 9.3 Correlation between percentage of
More informationSPSS LAB FILE 1
SPSS LAB FILE www.mcdtu.wordpress.com 1 www.mcdtu.wordpress.com 2 www.mcdtu.wordpress.com 3 OBJECTIVE 1: Transporation of Data Set to SPSS Editor INPUTS: Files: group1.xlsx, group1.txt PROCEDURE FOLLOWED:
More informationParametric Test. Multiple Linear Regression Spatial Application I: State Homicide Rates Equations taken from Zar, 1984.
Multiple Linear Regression Spatial Application I: State Homicide Rates Equations taken from Zar, 984. y ˆ = a + b x + b 2 x 2K + b n x n where n is the number of variables Example: In an earlier bivariate
More informationSimple Linear Regression
Simple Linear Regression 1 Correlation indicates the magnitude and direction of the linear relationship between two variables. Linear Regression: variable Y (criterion) is predicted by variable X (predictor)
More informationRegression. Notes. Page 1. Output Created Comments 25-JAN :29:55
REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS CI(95) BCOV R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT favorability /METHOD=ENTER Zcontemp ZAnxious6 zallcontact. Regression Notes Output
More informationAdvanced Quantitative Data Analysis
Chapter 24 Advanced Quantitative Data Analysis Daniel Muijs Doing Regression Analysis in SPSS When we want to do regression analysis in SPSS, we have to go through the following steps: 1 As usual, we choose
More informationUnivariate analysis. Simple and Multiple Regression. Univariate analysis. Simple Regression How best to summarise the data?
Univariate analysis Example - linear regression equation: y = ax + c Least squares criteria ( yobs ycalc ) = yobs ( ax + c) = minimum Simple and + = xa xc xy xa + nc = y Solve for a and c Univariate analysis
More information( ), which of the coefficients would end
Discussion Sheet 29.7.9 Qualitative Variables We have devoted most of our attention in multiple regression to quantitative or numerical variables. MR models can become more useful and complex when we consider
More informationMultiple Regression. Peerapat Wongchaiwat, Ph.D.
Peerapat Wongchaiwat, Ph.D. wongchaiwat@hotmail.com The Multiple Regression Model Examine the linear relationship between 1 dependent (Y) & 2 or more independent variables (X i ) Multiple Regression Model
More informationMANOVA is an extension of the univariate ANOVA as it involves more than one Dependent Variable (DV). The following are assumptions for using MANOVA:
MULTIVARIATE ANALYSIS OF VARIANCE MANOVA is an extension of the univariate ANOVA as it involves more than one Dependent Variable (DV). The following are assumptions for using MANOVA: 1. Cell sizes : o
More informationResearch Design - - Topic 19 Multiple regression: Applications 2009 R.C. Gardner, Ph.D.
Research Design - - Topic 19 Multiple regression: Applications 2009 R.C. Gardner, Ph.D. Curve Fitting Mediation analysis Moderation Analysis 1 Curve Fitting The investigation of non-linear functions using
More informationSPSS Output. ANOVA a b Residual Coefficients a Standardized Coefficients
SPSS Output Homework 1-1e ANOVA a Sum of Squares df Mean Square F Sig. 1 Regression 351.056 1 351.056 11.295.002 b Residual 932.412 30 31.080 Total 1283.469 31 a. Dependent Variable: Sexual Harassment
More informationMORE ON SIMPLE REGRESSION: OVERVIEW
FI=NOT0106 NOTICE. Unless otherwise indicated, all materials on this page and linked pages at the blue.temple.edu address and at the astro.temple.edu address are the sole property of Ralph B. Taylor and
More informationREVIEW 8/2/2017 陈芳华东师大英语系
REVIEW Hypothesis testing starts with a null hypothesis and a null distribution. We compare what we have to the null distribution, if the result is too extreme to belong to the null distribution (p
More informationChapter 4 Regression with Categorical Predictor Variables Page 1. Overview of regression with categorical predictors
Chapter 4 Regression with Categorical Predictor Variables Page. Overview of regression with categorical predictors 4-. Dummy coding 4-3 4-5 A. Karpinski Regression with Categorical Predictor Variables.
More informationMultivariate Correlational Analysis: An Introduction
Assignment. Multivariate Correlational Analysis: An Introduction Mertler & Vanetta, Chapter 7 Kachigan, Chapter 4, pps 180-193 Terms you should know. Multiple Regression Linear Equations Least Squares
More informationInteractions between Binary & Quantitative Predictors
Interactions between Binary & Quantitative Predictors The purpose of the study was to examine the possible joint effects of the difficulty of the practice task and the amount of practice, upon the performance
More information*************NO YOGA!!!!!!!************************************.
*************NO YOGA!!!!!!!************************************. temporary. select if human gt 1 and Q_TotalDuration gt 239 and subjectnum ne 672 and subj ectnum ne 115 and subjectnum ne 104 and subjectnum
More informationChapter 12 - Lecture 2 Inferences about regression coefficient
Chapter 12 - Lecture 2 Inferences about regression coefficient April 19th, 2010 Facts about slope Test Statistic Confidence interval Hypothesis testing Test using ANOVA Table Facts about slope In previous
More informationECON 497 Midterm Spring
ECON 497 Midterm Spring 2009 1 ECON 497: Economic Research and Forecasting Name: Spring 2009 Bellas Midterm You have three hours and twenty minutes to complete this exam. Answer all questions and explain
More informationIn Class Review Exercises Vartanian: SW 540
In Class Review Exercises Vartanian: SW 540 1. Given the following output from an OLS model looking at income, what is the slope and intercept for those who are black and those who are not black? b SE
More informationStatistics and Quantitative Analysis U4320. Segment 10 Prof. Sharyn O Halloran
Statistics and Quantitative Analysis U4320 Segment 10 Prof. Sharyn O Halloran Key Points 1. Review Univariate Regression Model 2. Introduce Multivariate Regression Model Assumptions Estimation Hypothesis
More informationSociology 593 Exam 2 March 28, 2002
Sociology 59 Exam March 8, 00 I. True-False. (0 points) Indicate whether the following statements are true or false. If false, briefly explain why.. A variable is called CATHOLIC. This probably means that
More informationWELCOME! Lecture 13 Thommy Perlinger
Quantitative Methods II WELCOME! Lecture 13 Thommy Perlinger Parametrical tests (tests for the mean) Nature and number of variables One-way vs. two-way ANOVA One-way ANOVA Y X 1 1 One dependent variable
More informationOne-Way ANOVA. Some examples of when ANOVA would be appropriate include:
One-Way ANOVA 1. Purpose Analysis of variance (ANOVA) is used when one wishes to determine whether two or more groups (e.g., classes A, B, and C) differ on some outcome of interest (e.g., an achievement
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 informationInferences for Regression
Inferences for Regression An Example: Body Fat and Waist Size Looking at the relationship between % body fat and waist size (in inches). Here is a scatterplot of our data set: Remembering Regression In
More informationItem-Total Statistics. Corrected Item- Cronbach's Item Deleted. Total
45 Lampiran 3 : Uji Validitas dan Reliabilitas Reliability Case Processing Summary N % Valid 75 00.0 Cases Excluded a 0.0 Total 75 00.0 a. Listwise deletion based on all variables in the procedure. Reliability
More informationSociology 593 Exam 1 Answer Key February 17, 1995
Sociology 593 Exam 1 Answer Key February 17, 1995 I. True-False. (5 points) Indicate whether the following statements are true or false. If false, briefly explain why. 1. A researcher regressed Y on. When
More information4/22/2010. Test 3 Review ANOVA
Test 3 Review ANOVA 1 School recruiter wants to examine if there are difference between students at different class ranks in their reported intensity of school spirit. What is the factor? How many levels
More informationCorrelation and simple linear regression S5
Basic medical statistics for clinical and eperimental research Correlation and simple linear regression S5 Katarzyna Jóźwiak k.jozwiak@nki.nl November 15, 2017 1/41 Introduction Eample: Brain size and
More informationSociology 593 Exam 2 Answer Key March 28, 2002
Sociology 59 Exam Answer Key March 8, 00 I. True-False. (0 points) Indicate whether the following statements are true or false. If false, briefly explain why.. A variable is called CATHOLIC. This probably
More information4:3 LEC - PLANNED COMPARISONS AND REGRESSION ANALYSES
4:3 LEC - PLANNED COMPARISONS AND REGRESSION ANALYSES FOR SINGLE FACTOR BETWEEN-S DESIGNS Planned or A Priori Comparisons We previously showed various ways to test all possible pairwise comparisons for
More informationBinary Logistic Regression
The coefficients of the multiple regression model are estimated using sample data with k independent variables Estimated (or predicted) value of Y Estimated intercept Estimated slope coefficients Ŷ = b
More informationVARIANCE ANALYSIS OF WOOL WOVEN FABRICS TENSILE STRENGTH USING ANCOVA MODEL
ANNALS OF THE UNIVERSITY OF ORADEA FASCICLE OF TEXTILES, LEATHERWORK VARIANCE ANALYSIS OF WOOL WOVEN FABRICS TENSILE STRENGTH USING ANCOVA MODEL VÎLCU Adrian 1, HRISTIAN Liliana 2, BORDEIANU Demetra Lăcrămioara
More informationNature vs. nurture? Lecture 18 - Regression: Inference, Outliers, and Intervals. Regression Output. Conditions for inference.
Understanding regression output from software Nature vs. nurture? Lecture 18 - Regression: Inference, Outliers, and Intervals In 1966 Cyril Burt published a paper called The genetic determination of differences
More informationMulticollinearity Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised January 13, 2015
Multicollinearity Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised January 13, 2015 Stata Example (See appendices for full example).. use http://www.nd.edu/~rwilliam/stats2/statafiles/multicoll.dta,
More informationMultiple linear regression S6
Basic medical statistics for clinical and experimental research Multiple linear regression S6 Katarzyna Jóźwiak k.jozwiak@nki.nl November 15, 2017 1/42 Introduction Two main motivations for doing multiple
More informationT-Test QUESTION T-TEST GROUPS = sex(1 2) /MISSING = ANALYSIS /VARIABLES = quiz1 quiz2 quiz3 quiz4 quiz5 final total /CRITERIA = CI(.95).
QUESTION 11.1 GROUPS = sex(1 2) /MISSING = ANALYSIS /VARIABLES = quiz2 quiz3 quiz4 quiz5 final total /CRITERIA = CI(.95). Group Statistics quiz2 quiz3 quiz4 quiz5 final total sex N Mean Std. Deviation
More informationResearch Design: Topic 18 Hierarchical Linear Modeling (Measures within Persons) 2010 R.C. Gardner, Ph.d.
Research Design: Topic 8 Hierarchical Linear Modeling (Measures within Persons) R.C. Gardner, Ph.d. General Rationale, Purpose, and Applications Linear Growth Models HLM can also be used with repeated
More informationExample. Multiple Regression. Review of ANOVA & Simple Regression /749 Experimental Design for Behavioral and Social Sciences
36-309/749 Experimental Design for Behavioral and Social Sciences Sep. 29, 2015 Lecture 5: Multiple Regression Review of ANOVA & Simple Regression Both Quantitative outcome Independent, Gaussian errors
More informationEDF 7405 Advanced Quantitative Methods in Educational Research. Data are available on IQ of the child and seven potential predictors.
EDF 7405 Advanced Quantitative Methods in Educational Research Data are available on IQ of the child and seven potential predictors. Four are medical variables available at the birth of the child: Birthweight
More informationECONOMETRIC ANALYSIS OF THE COMPANY ON STOCK EXCHANGE
ECONOMETRIC ANALYSIS OF THE COMPANY ON STOCK EXCHANGE Macovei Anamaria Geanina Ştefan cel Mare of University Suceava,Faculty of Economics and Public Administration street Universității, no. 3, city Suceava,
More information2 Prediction and Analysis of Variance
2 Prediction and Analysis of Variance Reading: Chapters and 2 of Kennedy A Guide to Econometrics Achen, Christopher H. Interpreting and Using Regression (London: Sage, 982). Chapter 4 of Andy Field, Discovering
More informationMultiple Regression Analysis
Multiple Regression Analysis Where as simple linear regression has 2 variables (1 dependent, 1 independent): y ˆ = a + bx Multiple linear regression has >2 variables (1 dependent, many independent): ˆ
More informationBivariate Regression Analysis. The most useful means of discerning causality and significance of variables
Bivariate Regression Analysis The most useful means of discerning causality and significance of variables Purpose of Regression Analysis Test causal hypotheses Make predictions from samples of data Derive
More informationHypothesis Testing for Var-Cov Components
Hypothesis Testing for Var-Cov Components When the specification of coefficients as fixed, random or non-randomly varying is considered, a null hypothesis of the form is considered, where Additional output
More informationCIVL 7012/8012. Simple Linear Regression. Lecture 3
CIVL 7012/8012 Simple Linear Regression Lecture 3 OLS assumptions - 1 Model of population Sample estimation (best-fit line) y = β 0 + β 1 x + ε y = b 0 + b 1 x We want E b 1 = β 1 ---> (1) Meaning we want
More informationISQS 5349 Final Exam, Spring 2017.
ISQS 5349 Final Exam, Spring 7. Instructions: Put all answers on paper other than this exam. If you do not have paper, some will be provided to you. The exam is OPEN BOOKS, OPEN NOTES, but NO ELECTRONIC
More informationFREC 608 Guided Exercise 9
FREC 608 Guided Eercise 9 Problem. Model of Average Annual Precipitation An article in Geography (July 980) used regression to predict average annual rainfall levels in California. Data on the following
More informationWarner, R. M. (2008). Applied Statistics: From bivariate through multivariate techniques. Thousand Oaks: Sage.
Errata for Warner, R. M. (2008). Applied Statistics: From bivariate through multivariate techniques. Thousand Oaks: Sage. Most recent update: March 4, 2009 Please send information about any errors in the
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 information1 Correlation and Inference from Regression
1 Correlation and Inference from Regression Reading: Kennedy (1998) A Guide to Econometrics, Chapters 4 and 6 Maddala, G.S. (1992) Introduction to Econometrics p. 170-177 Moore and McCabe, chapter 12 is
More informationPrepared by: Prof. Dr Bahaman Abu Samah Department of Professional Development and Continuing Education Faculty of Educational Studies Universiti
Prepared by: Prof Dr Bahaman Abu Samah Department of Professional Development and Continuing Education Faculty of Educational Studies Universiti Putra Malaysia Serdang M L Regression is an extension to
More informationTopic 1. Definitions
S Topic. Definitions. Scalar A scalar is a number. 2. Vector A vector is a column of numbers. 3. Linear combination A scalar times a vector plus a scalar times a vector, plus a scalar times a vector...
More informationEconometrics Review questions for exam
Econometrics Review questions for exam Nathaniel Higgins nhiggins@jhu.edu, 1. Suppose you have a model: y = β 0 x 1 + u You propose the model above and then estimate the model using OLS to obtain: ŷ =
More informationx3,..., Multiple Regression β q α, β 1, β 2, β 3,..., β q in the model can all be estimated by least square estimators
Multiple Regression Relating a response (dependent, input) y to a set of explanatory (independent, output, predictor) variables x, x 2, x 3,, x q. A technique for modeling the relationship between variables.
More informationModule 8: Linear Regression. The Applied Research Center
Module 8: Linear Regression The Applied Research Center Module 8 Overview } Purpose of Linear Regression } Scatter Diagrams } Regression Equation } Regression Results } Example Purpose } To predict scores
More informationA Re-Introduction to General Linear Models (GLM)
A Re-Introduction to General Linear Models (GLM) Today s Class: You do know the GLM Estimation (where the numbers in the output come from): From least squares to restricted maximum likelihood (REML) Reviewing
More informationLI EAR REGRESSIO A D CORRELATIO
CHAPTER 6 LI EAR REGRESSIO A D CORRELATIO Page Contents 6.1 Introduction 10 6. Curve Fitting 10 6.3 Fitting a Simple Linear Regression Line 103 6.4 Linear Correlation Analysis 107 6.5 Spearman s Rank Correlation
More informationMATH ASSIGNMENT 2: SOLUTIONS
MATH 204 - ASSIGNMENT 2: SOLUTIONS (a) Fitting the simple linear regression model to each of the variables in turn yields the following results: we look at t-tests for the individual coefficients, and
More informationRon Heck, Fall Week 3: Notes Building a Two-Level Model
Ron Heck, Fall 2011 1 EDEP 768E: Seminar on Multilevel Modeling rev. 9/6/2011@11:27pm Week 3: Notes Building a Two-Level Model We will build a model to explain student math achievement using student-level
More informationChapter 9 FACTORIAL ANALYSIS OF VARIANCE. When researchers have more than two groups to compare, they use analysis of variance,
09-Reinard.qxd 3/2/2006 11:21 AM Page 213 Chapter 9 FACTORIAL ANALYSIS OF VARIANCE Doing a Study That Involves More Than One Independent Variable 214 Types of Effects to Test 216 Isolating Main Effects
More informationFinal Exam - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis March 19, 2010 Instructor: John Parman Final Exam - Solutions You have until 5:30pm to complete this exam. Please remember to put your
More informationConfidence Intervals, Testing and ANOVA Summary
Confidence Intervals, Testing and ANOVA Summary 1 One Sample Tests 1.1 One Sample z test: Mean (σ known) Let X 1,, X n a r.s. from N(µ, σ) or n > 30. Let The test statistic is H 0 : µ = µ 0. z = x µ 0
More informationChapter 10-Regression
Chapter 10-Regression 10.1 Regression equation predicting infant mortality from income Y = Infant mortality X = Income Y = 6.70 s Y = 0.698 s 2 Y = 0.487 X = 46.00 s X = 6.289 s 2 X = 39.553 cov XY = 2.7245
More informationEconometrics -- Final Exam (Sample)
Econometrics -- Final Exam (Sample) 1) The sample regression line estimated by OLS A) has an intercept that is equal to zero. B) is the same as the population regression line. C) cannot have negative and
More informationEconometrics. 4) Statistical inference
30C00200 Econometrics 4) Statistical inference Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Confidence intervals of parameter estimates Student s t-distribution
More informationRetrieve and Open the Data
Retrieve and Open the Data 1. To download the data, click on the link on the class website for the SPSS syntax file for lab 1. 2. Open the file that you downloaded. 3. In the SPSS Syntax Editor, click
More informationMultiple Regression and Model Building Lecture 20 1 May 2006 R. Ryznar
Multiple Regression and Model Building 11.220 Lecture 20 1 May 2006 R. Ryznar Building Models: Making Sure the Assumptions Hold 1. There is a linear relationship between the explanatory (independent) variable(s)
More informationLAB 3 INSTRUCTIONS SIMPLE LINEAR REGRESSION
LAB 3 INSTRUCTIONS SIMPLE LINEAR REGRESSION In this lab you will first learn how to display the relationship between two quantitative variables with a scatterplot and also how to measure the strength of
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 informationInteractions and Centering in Regression: MRC09 Salaries for graduate faculty in psychology
Psychology 308c Dale Berger Interactions and Centering in Regression: MRC09 Salaries for graduate faculty in psychology This example illustrates modeling an interaction with centering and transformations.
More information(ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box.
FINAL EXAM ** Two different ways to submit your answer sheet (i) Use MS-Word and place it in a drop-box. (ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box. Deadline: December
More informationReview of the General Linear Model
Review of the General Linear Model EPSY 905: Multivariate Analysis Online Lecture #2 Learning Objectives Types of distributions: Ø Conditional distributions The General Linear Model Ø Regression Ø Analysis
More informationOrdinary Least Squares Regression Explained: Vartanian
Ordinary Least Squares Regression Eplained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent
More informationCorrelation and Regression Bangkok, 14-18, Sept. 2015
Analysing and Understanding Learning Assessment for Evidence-based Policy Making Correlation and Regression Bangkok, 14-18, Sept. 2015 Australian Council for Educational Research Correlation The strength
More informationData Analysis 1 LINEAR REGRESSION. Chapter 03
Data Analysis 1 LINEAR REGRESSION Chapter 03 Data Analysis 2 Outline The Linear Regression Model Least Squares Fit Measures of Fit Inference in Regression Other Considerations in Regression Model Qualitative
More information: The model hypothesizes a relationship between the variables. The simplest probabilistic model: or.
Chapter Simple Linear Regression : comparing means across groups : presenting relationships among numeric variables. Probabilistic Model : The model hypothesizes an relationship between the variables.
More informationRegression Analysis. BUS 735: Business Decision Making and Research
Regression Analysis BUS 735: Business Decision Making and Research 1 Goals and Agenda Goals of this section Specific goals Learn how to detect relationships between ordinal and categorical variables. Learn
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 informationCorrelation. A statistics method to measure the relationship between two variables. Three characteristics
Correlation Correlation A statistics method to measure the relationship between two variables Three characteristics Direction of the relationship Form of the relationship Strength/Consistency Direction
More informationThe inductive effect in nitridosilicates and oxysilicates and its effects on 5d energy levels of Ce 3+
The inductive effect in nitridosilicates and oxysilicates and its effects on 5d energy levels of Ce 3+ Yuwei Kong, Zhen Song, Shuxin Wang, Zhiguo Xia and Quanlin Liu* The Beijing Municipal Key Laboratory
More informationCHAPTER 10. Regression and Correlation
CHAPTER 10 Regression and Correlation In this Chapter we assess the strength of the linear relationship between two continuous variables. If a significant linear relationship is found, the next step would
More informationANCOVA. Psy 420 Andrew Ainsworth
ANCOVA Psy 420 Andrew Ainsworth What is ANCOVA? Analysis of covariance an extension of ANOVA in which main effects and interactions are assessed on DV scores after the DV has been adjusted for by the DV
More informationSimple, Marginal, and Interaction Effects in General Linear Models
Simple, Marginal, and Interaction Effects in General Linear Models PRE 905: Multivariate Analysis Lecture 3 Today s Class Centering and Coding Predictors Interpreting Parameters in the Model for the Means
More informationInter Item Correlation Matrix (R )
7 1. I have the ability to influence my child s well-being. 2. Whether my child avoids injury is just a matter of luck. 3. Luck plays a big part in determining how healthy my child is. 4. I can do a lot
More informationCorrelations. Notes. Output Created Comments 04-OCT :34:52
Correlations Output Created Comments Input Missing Value Handling Syntax Resources Notes Data Active Dataset Filter Weight Split File N of Rows in Working Data File Definition of Missing Cases Used Processor
More informationAssoc.Prof.Dr. Wolfgang Feilmayr Multivariate Methods in Regional Science: Regression and Correlation Analysis REGRESSION ANALYSIS
REGRESSION ANALYSIS Regression Analysis can be broadly defined as the analysis of statistical relationships between one dependent and one or more independent variables. Although the terms dependent and
More informationChapter Goals. To understand the methods for displaying and describing relationship among variables. Formulate Theories.
Chapter Goals To understand the methods for displaying and describing relationship among variables. Formulate Theories Interpret Results/Make Decisions Collect Data Summarize Results Chapter 7: Is There
More information