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. 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. Linear Function. Y = a + bX. Fixed and Random Variables. A FIXED variable is one for which you have every possible value of interest in your sample.. Example: Subject sex, female or male.. A RANDOM variable is one where the sample values are randomly obtained from the population of values.. 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 = . Overview of Supervised Learning. Outline. Regression vs. Classification. Two . Basic Methods: Linear Least Square vs. Nearest Neighbors. C. lassification via Regression. C. urse of Dimensionality and . How to predict and how it can be used in the social and behavioral sciences. How to judge the accuracy of predictions. INTERCEPT and SLOPE functions. Multiple regression. This week. 2. Based on the correlation, you can predict the value of one variable from the value of another.. ;. 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. . 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.. Bias Variance Tradeoff. Guest Lecturer. Joseph E. Gonzalez. s. lides available here: . http://tinyurl.com/. reglecture. Simple Linear Regression. Y. X. Linear Model:. Response. Variable. Covariate. Slope. 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 . …. 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.