PPT-Prediction variance in Linear Regression

Assumptions on noise in linear regression allow us to estimate the prediction variance due to the noise at any point Prediction variance is usually large when you are far from a data point We distinguish between interpolation when we are in the convex hull of the data points and extrapolation where we are outside. 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 Professor William Greene. Stern School of Business. Department . of Economics. Econometrics I. Part . 6 – Finite Sample Properties of Least Squares. Terms of Art. Estimates and estimators. Properties of an estimator - the sampling distribution. Professor William Greene. Stern School of Business. Department . of Economics. Econometrics I. Part . 10 . - . Prediction. Forecasting. Objective: Forecast. Distinction: Ex post vs. Ex ante forecasting. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. 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.. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. ;. some. do’s . and. . don’ts. Hans Burgerhof. Medical. . S. tatistics. and . Decision. Making. Department. of . Epidemiology. UMCG. . Help! Statistics! Lunchtime Lectures. When?. Where?. What?. Partial Regression Coefficients. b. i. is an . Unstandardized Partial Slope. Predict Y from X. 2. Predict X. 1. from X. 2. Predict from. That is, predict the part of Y that is not related to X. Given a domain, we can reduce the prediction error by good choice of the sampling points.. The choice of sampling locations is called “design of experiments” or DOE.. In this lecture we will consider DOEs for linear regression using linear and quadratic polynomials and where errors are due to noise in the data.. 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. . 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. explore how to model an outcome variable in terms of input variable(s) using linear regression, principal component analysis and Gaussian processes. At the end of this class you should be able to . …. 1. 2. Office Hours. :. More office hours, schedule will be posted soon.. . On-line office hours are for everyone, please take advantage of them.. . Projects:. Project guidelines and project descriptions will be posted Thursday 9/25.. 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.