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Interpreting Least Squares Without Sampling Assumptions

Author(s):
Beaton, Albert E.
Publication Year:
1981
Report Number:
RR-81-38
Source:
ETS Research Report
Document Type:
Report
Page Count:
75
Subject/Key Words:
Goodness of Fit, Sampling, Statistical Analysis

Abstract

Least squares fitting is perhaps the most commonly used tool of statisticians. Under sampling assumptions, statistical inference makes possible the estimation of population parameters and their confidence intervals and also the testing of hypotheses. In this paper the properties of least squares fitting are examined without sampling assumptions. It is shown that some of the output (e.g., standard errors, t, F, and p statistics) from standar regression programs can be interpreted as (approximate) measures of goodness-of-fit of a model to the observed data. The interpretation is also applicable in weighted least squares situations such as robust regression. (75pp.)

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