Weighted LeastSquares Regression
A technique for correcting the
problem of heteroskedasticity by loglikelihood estimation of a weight that
adjusts the errors of prediction
Weighted Least-Squares Regression: Charles M. Friel Ph.D., Criminal Justice Center,
5.2 Linear Smoothing
In this section, some of the most common smoothing methods are introduced and
discussed.
5.2.1 Kernel Smoothers
The simplest of smoothing methods is a kernel smoother. A point
domain of the mean function
is fixed in the
, and a smooth
LeverageandInfluence
In Linear Regression (Simple or Multiple), any prediction yi* can be represented as
a linear combination of the observations yj :
yi* = j hij yj
The coefficient of observation yi, that is hii , is called the leverage of that
observati
Department of Geography
UNIVERSITY OF FLORIDA, SPRING 2012
GEO 4167c section #6647 / GEO 6161 section # 8377
Intermediate Quantitative Methods
Instructor: Timothy J. Fik, Associate Professor
Prerequisite: GEO 3162 / GEO 6160 or equivalent
Time/Location: T
Geographically
weighted regression
Danlin Yu
Yehua Dennis Wei
Dept. of Geog., UWM
with modifications by T. Fik (Univ. of FL)
Outline of the presentation
1.
2.
3.
4.
5.
Spatial non-stationarity: an example
GWR some definitions
6 good reasons using GWR
Cali
Introduction to Spatial Modeling
Statistical options tend to be limited in most GIS
applications.
This is likely to be redressed in the future.
We will look at spatial statistics in general terms, and
conclude with a review of the software available.
B
Regression Analysis Tutorial
183
LECTURE / DISCUSSION Weighted Least Squares
Econometrics Laboratory C University of California at Berkeley C 22-26 March 1999
Regression Analysis Tutorial
184
Introduction
In a regression problem with time series data (whe
OLS Under Heteroskedasticity Testing for Heteroskedasticity
Heteroskedasticity and Weighted Least Squares
Walter Sosa-Escudero
Econ 507. Econometric Analysis. Spring 2009
April 14, 2009
Walter Sosa-Escudero
Heteroskedasticity and Weighted Least Squares
OL
Extending Linear Regression: Weighted Least Squares, Heteroskedasticity, Local Polynomial Regression
36-350, Data Mining 23 October 2009
Contents
1 Weighted Least Squares 2 Heteroskedasticity 2.1 Weighted Least Squares as a Solution to Heteroskedasticity
Recall our recent Reading Assignments. Read and review: (a) the technical appendix in your textbook on Matrix approach to LS regression. Basic Econometrics by D. Gujarati, 2007, 4th edition. and/or (b) the posted Matrix Algebra review and the Matrix Appro
II. Testing for Multicollinearity
When two or more independent variables in a regression model are highly correlated with one another (or collinear), they will contribute "redundant" explanatory information. Hence, not all of those independent variables
More on the Reliability, Precision, and Performance of the regression model and its estimated parameters. As the least-squares coefficient/parameter estimates ( j's) and the SRF's ability to explain variation in the dependent variable (Y) can vary from sa
AN INTRODUCTION TO TREND SURFACE ANALYSIS
D.Unwin
ISSN 0305-6142 ISBN 0 902246 51 8 1978 David J. Unwin
CONCEPTS AND TECHNIQUES IN MODERN GEOGRAPHY No. 5
CATMOG
(Concepts and Techniques in Modern Geography) CATMOG has been created to fill a teaching need
Board of the Foundation of the Scandinavian Journal of Statistics 2004. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA Vol 31: 515534, 2004
Functional Coefficient Regression Mode
Polynomial regression
Daniel Borcard, Dpartement de sciences biologiques, Universit de Montral Reference: Legendre and Legendre (1998) p. 526
A variant form of multiple regression can be used to fit a nonlinear model of an explanatory variable x (or sever
Lab#1, Spring 2012 (25 points) GEO 4167/GEO 6161 Intermediate Quantitative Methods (Fik) Name: _ Score: _ Instructions: Complete this lab to the best of your abilities. Attach your work sheets, relevant computer output, results, and write-up to this cover
GEOGRAPHICALLY WEIGHTED REGRESSION
WHITE PAPER
MARTIN CHARLTON A STEWART FOTHERINGHAM
National Centre for Geocomputation National University of Ireland Maynooth Maynooth, Co Kildare, IRELAND
March 3 2009
The authors gratefully acknowledge support from a S
Geographically Weighted Regression
A Tutorial on using GWR in ArcGIS 9.3
Martin Charlton A Stewart Fotheringham
National Centre for Geocomputation National University of Ireland Maynooth Maynooth, County Kildare, Ireland http:/ncg.nuim.ie
The authors grat
Review of Matrix Algebra
Matrices
A matrix is a rectangular or square array of values arranged in rows and columns. An m n matrix A, has m rows and n columns, and has a general form of
a11 a = 21 . am1 a12 a22 . am 2 . a1n . a2 n . . . amn mn
mn
1
Exa