A new type of graphical representation which is called “Linked lines rotation graphics” for looking at multivariate data is discussed. The plot of this graph is to use the linked lines chart corresponding to p-variate data and the locus which is plotted by rotating the end point of the linked lines chart. Further, the cross linked lines rotation graphics as extension is discussed. Some examples of the real linked lines rotation graphics are given as illustration.

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Influence functions are derived for the parameters in the factor analysis (FA) regression and some measures are proposed to evaluate the influence on the estimated regression weights β_F and on the squared correlation coefficient r²(β_F). As an application, a numerical study is conducted to illustrate the present procedure and to show fundamental properties of influence in FA regression from the sensitivity perspective.

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We consider a model y_i=g(x_i)+ε_i where x_i is an independent variable and ε_i's are iid random error with mean 0 and variance σ². If the regression function g(x) is smooth enough, then we may have an approximation g(x)=g(x₀)+g'(x₀)(x-x₀) for |x-x₀|≤h where h is small enough. Thus, at a given point x in the range of the independent variable, a locally weighted linear regression estimate g(x)=αx+β_xx sounds very reasonable. However, performance of the estimate depends on h that determines the amount of smoothing. In this article, a bootstrap method is applied for the choice of the smoothing parameter and also for some distributional problems. Simulation study is carried out for various regression functions.

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We compare the performance of several multiple pairwise comparisons methods with right censored data using computer simulation. Together with classical one-step Bonferroni-type and Scheffé-type multiple comparisons procedures, several kinds of stepwise procedures are studied. As a result, the reranking Peritz-type closed-step-down procedure is found to be the most powerful among these procedures. Shaffer's method is preferable to the other Bonferroni-type procedures. Several kinds of rank tests are used for the construction of multiple comparisons tests. Corresponding to the underlying survival distribution family, the best lifetime test statistic varies. This result is interpreted in connection with the Pitman asymptotic relative efficiencies of the overall test statistics. The maximum Type I familywise error rates would exceed the nominal level if we use step-down multiple comparisons procedures based on the logrank test.

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Various measures have been proposed for detecting the influential observations in linear regression model but most of them require a large amount of computing time in practical problems. This article concerns an efficient computational method for computing the influential measure, C_Dm (X′(D_m)X(D_m), pS²(D_m)), proposed by Cook and Weisberg (1982).

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A simple method of generating physical random digits is described. In this method, an electronic decade counter is incremented by the clock pulses. As the overflow is ignored, the counter keeps counting from 0 to 9. Whenever a micro-computer is interrupted by a rare random signal caused by a radiant ray detection, a digit in the counter is latched and loaded in the memory. These digits are used as the random numbers of one figure or several figures. This method is the most simple one of the traditional methods. A mathematical estimation for the occurrence probabilities of each digit suggests that the maximum deviation from the equiprobabilities 1/10, is less than (6×10^-9).

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Motivated by influence curve for the parameter vector, Cook's distance has several interesting features and thus plays an important role in linear regression diagnostics. Although Cook's distance is usually compared with various percentiles of an F-distribution, it sometimes puzzles statistics users since F-distribution is not the correct sampling distribution of Cook's distance.
In this paper, we study the large-sample property of Cook's distance under the assumption of multivariate normality of predictor variables. Also we construct a table of critical values of Cook's distance as a diagnostics tool in linear regression.

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Most data analysis systems seem to be convenient for statisticians, but novices in statistics cannot master them easily since it is hard to select appropriate procedures for an observation. The application with the technique of knowledge processing to data analysis is an attractive idea, but there is little research on selecting procedures because of some difficulties in the construction of its knowledge. We shall discuss its difficulties and how to construct the knowledge of data analysis, and offer an implementation of the system with knowledge supports.

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