PPT-Least-Squares Regression:

Linear Regression Section 32 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 . Di64256erentiating 8706S 8706f Setting the partial derivatives to 0 produces estimating equations for the regression coe64259cients Because these equations are in general nonlinear they require solution by numerical optimization As in a linear model 1 Weighted Least Squares as a Solution to Heteroskedasticity 5 3 Local Linear Regression 10 4 Exercises 15 1 Weighted Least Squares Instead of minimizing the residual sum of squares RSS 1 x 1 we could minimize the weighted sum of squares WSS 946 Professor William Greene. Stern School of Business. IOMS Department. Department of Economics. Regression and Forecasting Models. Part . 1 . – . Simple Linear Model. Theory. Demand Theory: Q = f(Price). 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. Airport Noise and Home Values. J.P. Nelson (2004). “Meta-Analysis of Airport Noise and Hedonic Property Values: Problems and Prospects,” . Journal of Transport Economics and Policy. , Vol. 38, Part 1, pp. 1-28.. Professor William Greene. Stern School of Business. Department . of Economics. Econometrics I. Part . 5 – Regression. Algebra and Fit. The Sum of Squared Residuals. b. minimizes . e. 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.. Chapter 3 – Exploring Data. Day 3. Regression Line. A straight line that describes how a . _________ . variable, . __. ,. . changes as an . ___________ variable. , . ___. ,. . changes. used to . __________ . Some Review and Some New Ideas. Remember the concepts of variance and the standard deviation…. Variance is the square of the standard deviation. Standard deviation (s) - the square root of the sum of the squared deviations from the mean divided by the number of cases. . Created by Kathy Fritz. Forensic scientists must often estimate the age of an unidentified crime victim. Prior to 2010, this was usually done by analyzing teeth and bones, and the resulting estimates were not very reliable. A study described in the paper “Estimating Human Age from T-Cell DNA Rearrangements” (Current Biology [2010]) examined the. A statistical . process for estimating the relationships among variables. . REGRESSION ANALYSIS. Functional Relationship (Deterministic). An . exact relationship between the predictor . X.  and the response . : A British biometrician, Sir Francis Galton, defined regression as ‘stepping back towards the average’. He found that the offspring of abnormally tall or short parents tends to regress or step back to average.. Regression Trees. Characteristics of classification models. model. linear. parametric. global. stable. decision tree. no. no. no. no. logistic regression. yes. yes. yes. yes. discriminant. analysis.