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 . 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. 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) . Adaptive Filters. Definition. With the arrival of new data samples estimates are updated recursively.. Introduce a weighting factor to the sum-of-error-squares definition. Weighting factor. Forgetting factor. 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.. Data. Model with only main . effects (JMP output): . Center. . Level Least Sq Mean . Mean. . 1 4.00 4.00 . 2 6.00 6.00 . Pg 337..345: 3b, 6b (form and strength). Page 350..359: 10b, 12a, 16c, 16e. Homework Turn In…. A straight line that describes how a response variable y changes as an explanatory variable x changes. . Do Now:. Do heavier cars really use more gasoline? In the following data set, . x. is the weight of some randomly selected cars (in hundreds of pounds), and . y. is the gas mileage (in mpg) for that car. This data set comes from . Paige Thielen, ME535 Spring 2018. Abstract. Various methods of accelerometer calibration can be used to increase the precision of acceleration measurements. The methods tested are two 12-parameter linear least squares optimizations, one using four calibration orientations, one using eight orientations, and two 15-parameter least squares optimizations using eight and 19 calibration orientations. Based on the data gathered, while it is not necessary to change the calibration method currently in use, good results could be obtained from applying a 12-parameter, 8-orientation least squares calibration without significant increase in time required for calibration.. 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. 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 . 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.