PPT-Regression Analysis

In regression analysis we analyze the relationship between two or more variables The relationship between two or more variables could be linear or non linear This week first talk . isavectorofparameterstobeestimatedand x isavectorofpredictors forthe thof observationstheerrors areassumedtobenormallyandindependentlydistributedwith mean 0 and constant variance The function relating the average value of the response to the pred Professor William Greene. Stern School of Business. IOMS Department . Department of Economics. Statistics and Data Analysis. Part . 10 – Advanced Topics. Advanced topics. Nonlinear Least Squares. Nonlinear Models – ML Estimation . Linear Regression. Section 3.2. Reference Text:. The Practice of Statistics. , Fourth Edition.. Starnes, Yates, Moore. Warm up/ quiz . Draw a quick sketch of three scatterplots:. Draw a plot with r . Austin Troy. NR 245. Based primarily on material accessed from Garson, G. David 2010. . Multiple Regression. . Statnotes. : Topics in Multivariate Analysis.. http://faculty.chass.ncsu.edu/garson/PA765/statnote.htm. Professor William Greene. Stern School of Business. IOMS Department . Department of Economics. Inference and Regression. Part . 9 – Linear Model Topics. Agenda. Variable Selection – Stepwise Regression. An Application. Dr. Jerrell T. Stracener, . SAE Fellow. Leadership in Engineering. EMIS 7370/5370 STAT 5340 :. . . PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS. Systems Engineering Program. Professor William Greene. Stern School of Business. IOMS Department . Department of Economics. Inference and Regression. Perfect Collinearity. Perfect Multicollinearity. If . X. does not have full rank, then at least one column can be written as a linear combination of the other columns.. 1. 3.6 Hidden Extrapolation in Multiple Regression. In prediction, exercise care about potentially extrapolating beyond the region containing the original observations.. Figure 3.10. An example of extrapolation in multiple regression.. NBA 2013/14 Player Heights and Weights. Data Description / Model. Heights (X) and Weights (Y) for 505 NBA Players in 2013/14 Season. . Other Variables included in the Dataset: Age, Position. Simple Linear Regression Model: Y = . Dummy variables as an independent variable. Dummy variable trap. Importance of the "reference group". Using dummy variables to test for equal means. Dummy variables for . Multiple categories. Ordinal variables. Example Data Set. Y. X. 5. 20. 6. 23. 7. 27. 8. 33. 8. 31. 9. 35. 10. 43. 5. 19. 6. 25. 7. 29. 8. 31. Estimate two models. Model with y-intercept. Y = a b * X. Regression Statistics. Multiple R. 0.984. A statistical . process for estimating the relationships among variables. . REGRESSION ANALYSIS. Functional Relationship (Deterministic). An . exact relationship between the predictor . X.  and the response . . Ranjan. . Parida. Asst.Prof. .. SPLS,CUTM. Example-2. Deviation method from mean. Regression equation for X on Y . X. -. . x̄. = b. xy. . (Y. -. ȳ ), . Where bxy is the regression co-efficient and . Obid. . A.Khakimov. OLS Estimation: Hetroscedasticity. If variance of residuals is constant then . Our equation collapses to original variance . Formula.. Consequences:. The regression coefficients are unbiased .