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The Half-Half (HH) plot is a new graphical method to investigate qualitatively the shape of a regression curve. The empirical HH-plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatterplot. The plot displays jumps clearly and reveals further features of the regression curve. We prove a functional central limit theorem for the empirical HH-plot, with rate of convergence . In a simulation study, the good performance of the plot is demonstrated. The method is also applied to two case studies. The proofs and one more case study are deferred to a supplement, which is available online. [ABSTRACT FROM AUTHOR]

The analysis of screening experiments based on nonregular designs can lead to a model selection problem in which the number of variables is large, the number of trials is small, and there are constraints on model structure. Common subset selection methods do not perform well in this setting. We propose a new approach particularly well suited to screening. The method uses an intentionally nonconvergent stochastic search to generate a large set of well-fitting models, each with the same number of variables. Model selection is then viewed as a feature extraction problem from this set. An easy-to-use graphical method and an automatic approach are proposed to determine the best models. Computer code and additional supplementary materials are available online. [ABSTRACT FROM AUTHOR]

Proposes a graphical method for assessing parametric transformation of the response in a linear regression model. Examples of response formations using data from an experiment on the behavior of worsted yarns; Details of the proposed method; Application of the linearity condition to the marginal distribution of the predictors.

A graphical method for examining the assumptions of covariance analysis is presented. A plot of the response residuals (y - ŷ) versus the covariate residuals (χ - &χcirc;) provides a useful method for studying the relationship between the covariate and the response. It also aids in the detection of abnormal observations. [ABSTRACT FROM AUTHOR]

Critical to any regression analysis is the identification of observations that exert a strong influence on the fitted regression model. Traditional regression influence statistics such as Cook's distance and DFFITS, each based on deleting single observations, can fail in the presence of multiple influential observations if these influential observations “mask” one another, or if other effects such as “swamping” occur. Masking refers to the situation where an observation reveals itself as influential only after one or more other observations are deleted. Swamping occurs when points that are not actually outliers/influential are declared to be so because of the effects on the model of other unusual observations. One computationally expensive solution to these problems is the use of influence statistics that delete multiple rather than single observations. In this article, we build on previous work to produce a computationally feasible algorithm for detecting an unknown number of influential observations in the presence of masking. An important difference between our proposed algorithm and existing methods is that we focus on the data that remain after observations are deleted, rather than on the deleted observations themselves. Further, our approach uses a novel confirmatory step designed to provide a secondary assessment of identified observations. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Variable selection, the search for j relevant predictor variables from a group of p candidates, is a standard problem in regression analysis. The class of 1D regression models is a broad class that includes generalized linear models. We show that existing variable selection algorithms, originally meant for multiple linear regression and based on ordinary least squares and Mallows's Cp, can also be used for 1D models. Graphical aids for variable selection are also provided. [ABSTRACT FROM AUTHOR]