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Unformatted text preview: SUMMARY OF WEEK 1 [STAT4610 Applied Regression Analysis] CHAPTER 1 Regression Analysis : A statistical technique for exploring and modeling the relationship between variables. Relations: Functional vs. Statistical Functional relation expressed by a Statistical relation expressed by a mathematical formula: Y=f(X) formula: Y=f(X)+ε All observations fall directly on the In general, the observations for a line of functional relationship. statistical relation do not fall directly on the curve of relationship. Steps in Regression Analysis • • • • Statement of the problem Selection of potentially relevant variables Data collection (Retrospective study based on historical data, Observational study,Designed Experiment (the best!) Model specification (linear, nonlinear) The form of the function f(X1,X2,…,Xp ) can be linear or nonlinear! f linear : y = β0 + β1x1 + ε (Simple linear) f nonlinear : y = β0 + exp(β1 x1 + ε (Nonlinear) f linear : y = β0 + β1 logX + ε (Linearizable (re‐expressed or transformed)) f linear : y = β0 +β1X+β2X2+ ε (Linearizable (re‐expressed or transformed)) If the parameters enter the equation linearly (or nonlinearly) we call linear (or nonlinear). Choice of fitting method (Least squares, ML), Model fitting (Estimation of parameters), Model Adequacy Checking. • • • INPUTS
Model Data Statistical methods Calculate OUTPUTS
Parameter estimates Confidence intervals ( i ) Criticism, validation, 1 FALL 10, DR. NEDRET BILLOR| Auburn University SUMMARY OF WEEK 1 [STAT4610 Applied Regression Analysis] Types of variables in data collection Predictors: quantitative ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Response: quantitative All predictors: qualitative ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Analysis of Variance Response: quantitative Predictors: mixture of quantitative and qualitative ‐‐‐‐ Analysis of Covariance Response: quantitative Predictors: quantitative or mixed ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Logistic Regression Response: qualitative (e.g. binary) Simple Linear Regression (SLR) : Modelling y with one predictor Y=β0 + β1X1 + ε Multiple Linear Regression (MLR) : Modelling y with more than one predictor: Y=β0 + β1X1 + β2X2 + … + βkXk + ε Ordinary Regression Analysis 2 FALL 10, DR. NEDRET BILLOR| Auburn University ...
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This note was uploaded on 10/12/2010 for the course STAT 4630 taught by Professor Billor during the Spring '10 term at Auburn University.
- Spring '10