Open AccessINTERPRETING LEAST SQUARES WITHOUT SAMPLING ASSUMPTIONS
Author(s) -
Beaton Albert E.
Publication year - 1981
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2333-8504.1981.tb01265.x
Subject(s) - statistics , goodness of fit , sampling (signal processing) , mathematics , generalized least squares , least squares function approximation , total least squares , standard error , regression analysis , least trimmed squares , statistical inference , confidence interval , regression , population , inference , econometrics , computer science , artificial intelligence , demography , filter (signal processing) , estimator , sociology , computer vision
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 is examined without sampling assumptions. It is shown that some of the output (e.g. standard errors, t, F, and p statistics) from standard 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.