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## Mathematica Applicanda

1975 | 3 | 5 |
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### Multivariate analysis of covariance and some applications of it

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In many physical problems we make use of experimental data in which each measured unit is characterized by a definite system of properties. A large number of such properties are necessary to interpret the results of an experiment. However, complete information can be used only if all properties observed during the experiment are considered simultaneously. For this reason the application of multivariate analysis of variance or covariance is justified when processing data with many properties. In this work we discuss the theory and practical applications of univariate and multivariate analysis of covariance. This work is a continuation of a paper by B. Ceranka and the author [Mat. Stos. (3) 4 (1975), 65–75; MR0451560], and generalizes multivariate analysis of covariance for block designs to an arbitrary experimental arrangement. A general linear model of multivariate analysis of covariance, a special case of which yields analysis of variance and regression analysis, is given in Chapter 1. Chapter 2 is devoted to analysis of covariance in one and many variables and to the testing of hypotheses concerning the main and auxiliary variables. In this chapter we introduce estimators for the matrices of regression coefficients of the main variables relative to the auxiliary variables and for the matrix of parameters. Formulas are given for the sums of squares and for the matrices of the sums of squares which are needed in hypothesis testing in the analysis of covariance. Practical applications of multivariate analysis of covariance are illustrated with an example of the growth of plants. (MR0483212)
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1975
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2016-04-27
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