JSM 2004 - Toronto

Abstract #301865

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Activity Number: 443
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Education
Abstract - #301865
Title: Statistical Properties of the Slope Mean
Author(s): Lewis VanBrackle*+
Companies: Kennesaw State University
Address: Mailbox 1204, Kennesaw, GA, 30144,
Keywords: regression ; estimation
Abstract:

In a recently submitted paper, Ji and Kicey examined the invariance properties of means in general and the "slope mean" in particular. In the context of regression through the origin, the slope mean is defined as the tangent of the mean of the angles between the x- axis and the lines from the origin through the data points. Examining the statistical properties of the slope mean is an excellent exercise for undergraduate mathematics and statistics majors. In the process of evaluating the statistical properties of the slope mean and comparing them to the properties of other slope estimators, such as the average of the slopes of the lines from the origin through the data points and the usual ordinary least squares estimator, students can apply techniques they have learned in a variety of mathematics and statistics courses. This presentation will show how the Fundamental Theorem of Calculus, the Central Limit Theorem, the Gauss-Markov Theorem, Taylor's series approximations, calculation of probabilities by numerical integration and simulation can all be applied in deriving the statistical properties of the slope mean.

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