Abstract #301060

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JSM 2003 Abstract #301060
Activity Number: 181
Type: Contributed
Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Education
Abstract - #301060
Title: The True R-squared and the Truth About R-squared
Author(s): Nicolas Christou*+
Companies: University of California, Los Angeles
Address: 8130 Math Sciences Building, Los Angeles, CA, 90095-1554,
Keywords: true R-squared ; simulations ; regression
Abstract:

We discuss the true R-squared and compare it with the sample R-squared using simulations. With true R-squared we mean the population R-squared and it is defined as the ratio of the variance of the signal to the variance of the signal plus error. To compute it, we need to know the variance of the error term. This is possible in a simulation study. First, students must understand what constitutes a strong relationship between two variables. Starting with a deterministic model, we move to data with noise by adding some error. The added error will determine the true R-squared. Then, using least squares, we compute the traditional sample R-squared and see how much of the true R-squared we recover and how much the sample R-squared varies. This method assumes that students are familiar with correlation, random errors, probabilistic and deterministic models. It would probably be more suitable for students in a more advanced regression course rather than in an introductory course. Nevertheless, we believe the idea of the true R-squared, which is not mentioned in most (if not all) statistics textbooks, is important to understand relationships between variables.

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