Related Experiment Video
Updated: Mar 16, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
Published on: October 27, 2016
A Geometric Analysis of When Fixed Weighting Schemes Will Outperform Ordinary Least Squares
1Department of Psychological Sciences, University of Missouri, 219 McAlester Hall, Columbia, MO, USA. stoberc@missouri.edu.
Abstract:
Many researchers have demonstrated that fixed, exogenously chosen weights can be useful alternatives to Ordinary Least Squares (OLS) estimation within the linear model (e.g., Dawes, Am. Psychol. 34:571-582, 1979; Einhorn & Hogarth, Org. Behav. Human Perform. 13:171-192, 1975; Wainer, Psychol. Bull. 83:213-217, 1976). Generalizing the approach of Davis-Stober, Dana, and Budescu (Psychometrika 75:521-541, 2010b), I present an analytic method to determine when a choice of fixed weights will incur less mean squared error than OLS as a function of sample size, error variance, and model predictability. Geometrically, I solve for the region of population β that favors a choice of fixed weights over OLS. I derive closed-form upper and lower bounds on the volume of this region, giving tight bounds on the proportion of population β favoring a choice of fixed weights. I illustrate this methodology with several examples and provide a MATLAB(©) (The MathWorks, Matlab software, version 2009b, 2010) programming implementation of the major results.
Related Concept Videos
Weighted Mean
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
Residuals and Least-Squares Property
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Calibration Curves: Linear Least Squares
For data that follow a straight line, the standard method for fitting is the linear...
Geometric Mean
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
Quadratic Models
Linearization and Approximation

