Math 644: Regression Analysis Methods

1 math 644: Regression Analysis MethodsWenge GuoSeptember 4, 2013 Wenge GuoMath 644: Regression Analysis MethodsGeneral InformationIIntroductionIGo through the syllabus and other important informationabout the courseIBig picture of the courseIOffice: 210B Cullimore HallIContact information: most convenient way is emailIOffice hours: W and F 4:00 pm - 5:00 pm or by appointmentWenge GuoMath 644: Regression Analysis MethodsTextbookITextbook: (Required)Applied Linear Regression Models4thEd., by Kutner, Nachtsheim, and Neter. McGraw-Hill, book: (Recommended):Linear models with R, byJulian J. Faraway. Boca Raton: Chapman & Hall/CRC, GuoMath 644: Regression Analysis MethodsClass Webpage and Email ListIClass webpage and email list are used to deliver syllabus,lecture slides/notes, homework/solutions, exam/solutions,project and some important :Rwill be used throughout the course and talk more about computing when we need GuoMath 644: Regression Analysis MethodsBig Picture of the CourseIPart I: Simple Linear RegressionILinear Regression with One Predictor VariableIInferences in Regression and Correlation AnalysisIDiagnostics and Remedial MeasuresISimultaneous Inferences and Other Topics in RegressionAnalysisIPart II.

2 Multiple Linear RegressionIMatrix Approach to Simple Linear Regression AnalysisIMultiple Linear Regression I and IIIR egression Models for Quantitative and Qualitative PredictorsIBuilding the Regression Model IIPart III: Nonlinear RegressionINonlinear RegressionILogistic Regression , Poisson Regression and Generalized LinearModelsIMidterm (Parts I II)IProject (Parts I III)IFinal (Parts I III)Wenge GuoMath 644: Regression Analysis MethodsCourse EvaluationILetter grade will be given based on Homework(25%)+Midterm(25%)+Project(20%)+ Final(30%)IHomework: generally bi-weekly and about 8 homework : one and a half hours, in-class, closed scheduled at 10/23 IFinal: two hours, in-class, closed book. Will be on 12 GuoMath 644: Regression Analysis MethodsHomeworkIContain a mix of paper and computer in the homeworks in class in due day.

3 As a penalty, latehomework is deducted 15% from total score per every dayafter due receive credit on homework, you should show all workneatly, clearly label each problem, and staple the entireassignment together in correct order with your name are allowed to work with other students on the homeworkproblems, however, verbatim copying of homework GuoMath 644: Regression Analysis MethodsProjectIFind an interesting dataset yourself, real dataIInteresting and a little complicated to some extentIAnalyze the data by using Regression Analysis methodsIWrite a report, 8-10 pagesIA group of 3 people is recommendedAny questions/comments?Wenge GuoMath 644: Regression Analysis MethodsSoftwareRwill be used throughout the forR:ICompletely free software. Can be downloaded on various systems, PC, MAC, Linux, and evenIphone and Ipad!IAdvanced yet easy to Introduction to R: GuoMath 644: Regression Analysis MethodsWhy Regression ?

4 IWant to model a functional relationship between an predictor variable (input, independent variable, etc.) and a response variable (output, dependent variable, etc.)IExamples?IBut real world is noisy, nof=maIObservation noiseIProcess noiseITwo distinct goalsI(Estimation) Understanding the relationship between predictorvariables and response variablesI(Prediction) Predicting the future response given the newobserved Francis Galton, 19thcenturyIStudied the relation between heights of parents and childrenand noted that the children regressed to the populationmeanI Regression stuck as the term to describe statistical relationsbetween variablesExample ApplicationsTrend lines, eg. Google over 6 lifespan to obesity or smoking habits and engineeringIRelating physical inputs to physical outputs in complex systemsIBrainAims for the courseIGiven something you would like to predict and some numberof covariatesIWhat kind of model should you use?

5 IWhich variables should you include?IWhich transformations of variables and interaction termsshould you use?IGiven a model and some dataIHow do you fit the model to the data?IHow do you express confidence in the values of the modelparameters?IHow do you regularize the model to avoid over-fitting andother related issues?Data for Regression AnalysisIObservational DataExample: relation between age of employee (X) and numberof days of illness last year (Y)Cannot be controlled!IExperimental DataExample: an insurance company wishes to study the relationbetween productivity of its analysts in processing claims (Y)and length of : the length of trainingIExperimental Units: the analysts included in the Randomized Design: Most basic type of statisticaldesignExample: same example, but every experimental unit has anequal chance to receive any one of the Picture of the CourseIPart I: Simple Linear RegressionILinear Regression with One Predictor VariableIInferences in Regression and Correlation AnalysisIDiagnostics and Remedial MeasuresISimultaneous Inferences and Other Topics in RegressionAnalysisIPart II.

6 Multiple Linear RegressionIMatrix Approach to Simple Linear Regression AnalysisIMultiple Linear Regression I and IIIR egression Models for Quantitative and Qualitative PredictorsIBuilding the Regression Model IIPart III: Nonlinear RegressionINonlinear RegressionILogistic Regression , Poisson Regression and Generalized LinearModelsIMidterm (Parts I II)IProject (Parts I III)IFinal (Parts I III)Wenge GuoMath 644: Regression Analysis Methods