In the theory of linear models, the concept of degrees of freedom plays an important role.
This concept is often used for measurement of model complexity, for obtaining an unbiased …

It is commonly accepted that statistical modeling should follow the parsimony principle;
namely, that simple models should be given priority whenever possible. But little quantitative …

Inference for the general linear model makes several assumptions, including independence
of errors, normality, and homogeneity of variance. Departure from the latter two of these …

A method of estimating linear model dimension and variable selection is proposed. This new
criterion, which generalizes the Cp criterion, the Akaike information criterion (AIC), the Bayes …

We show that data augmentation provides a rather general formulation for the study of
biased prediction techniques using multiple linear regression. Variable selection is a limiting …

Statistical models usually involve some degree of approximation and therefore are nearly
always wrong. Because of this inexactness, an assessment of the influence of minor …

Inference from the fitting of linear models is basic to statistical practice, but the development
of strategies for analysis has been hindered by unnecessary complexities in the descriptions …

Working in the context of the linear model y= Xβ+ ε, we generalize the concept of variance
inflation as a measure of collinearity to a subset of parameters in β (denoted by β 1, with the …

When performing a regression or classification analysis, one needs to specify a statistical
model. This model should avoid the overfitting and underfitting of data, and achieve a low …

The coefficient of determination, aka R 2, is well-defined in linear regression models, and
measures the proportion of variation in the dependent variable explained by the predictors …