ERIC Number: ED224804
Record Type: RIE
Publication Date: 1981-Oct
Reference Count: 0
Interpreting Least Squares without Sampling Assumptions.
Beaton, Albert E.
Least squares fitting process as a method of data reduction is presented. The general strategy is to consider fitting (linear) models as partitioning data into a fit and residuals. The fit can be parsimoniously represented by a summary of the data. A fit is considered adequate if the residuals are small enough so that manipulating their signs and locations does not affect the summary more than a pre-specified amount. The effect of the residuals on the summary is shown to be (approximately) characterized by the output of standard regression programs. The general process of linear fitting models by least squares is covered in detail and discussed briefly in its relationship to standard hypothesis testing and to Fisher's randomization test. Fitting in weighted least squares and a comparison of fitting to standard methods are also discussed. 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. (PN)
Descriptors: Goodness of Fit, Least Squares Statistics, Mathematical Models, Measurement Techniques, Regression (Statistics), Research Methodology, Sampling, Statistical Analysis
Educational Testing Service, Research Publications R116, Princeton, NJ 08541.
Publication Type: Reports - Research
Education Level: N/A
Authoring Institution: Educational Testing Service, Princeton, NJ.
Identifiers: Data Interpretation; Inference (Statistical); Linear Models; Randomization