PDF-Extending Linear Regression Weighted Least Squares Heteroskedasticity Local Polynomial

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). Least Squares. Method. of . Least. . Squares. :. Deterministic. . approach. . The. . inputs. u(1), u(2), ..., u(N) . are. . applied. . to. . the. . system. The. . outputs. y(1), y(2), ..., y(N) . 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. 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 = . Definition. Consequences of heteroscedasticity. Testing for . Heteroskedasticity. Breusch-Pagan. White test (2 forms). Fixing the problem. Robust standard errors. Weighted Least Squares. Fixing heteroskedasticity in LPM model.. Model . the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed . data.. Formally, the model for multiple linear regression, given . In linear regression, the assumed function is linear in the coefficients, for example, . .. Regression is nonlinear, when the function is a nonlinear in the coefficients (not x), e.g., . T. he most common use of nonlinear regression is for finding physical constants given measurements.. 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) . using a linear equation.. What. is . what. ? . Regression: One variable is considered dependent on the other(s). Correlation: No variables are considered dependent on the other(s). Multiple regression: More than one independent variable. Instructor: Prof. Wei Zhu. 11/21/2013. AMS 572 Group Project. Motivation & Introduction – Lizhou Nie. A Probabilistic Model for Simple Linear Regression – Long Wang. Fitting the Simple Linear Regression Model – . 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 .