PPT-REGRESSION ANALYSIS AND ORDINARY LEAST SQUARES (OLS)

A statistical process for estimating the relationships among variables REGRESSION ANALYSIS Functional Relationship Deterministic An exact relationship between the predictor  X  and the response . 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 Ordinary Least Squares – a regression estimation technique that calculates the Beta-hats -- estimated parameters or coefficients of the model – so as to minimize the sum of the squared residuals.. Professor William Greene. Stern School of Business. IOMS Department . Department of Economics. Statistics and Data Analysis. Part . 6 – Regression Model-1. Conditional Mean . U.S. Gasoline Price. 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). 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. 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. 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 . __________ . prcomp. {stats. }. . Performs a principal components analysis on the given . data . matrix and . . . returns . the results as an object of class . prcomp. .. Usage. prcomp. (x. , . …). 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. . INTRODUCTİON. . HISTORY. 1822-1911. : . Sir . Galton . "REGRESSION" WAS COINED. 1805. : . LENARDE. METHOD OF LEAST SQUARES. 1809. : . GAUSS. METHOD OF LEAST SQUARES. . HISTORY. 1857-1936. : . Karl Pearson. 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 .