Multivariate statistics : a practical approach

Preface.- 1 The data.- Discussion.- 2 Univariate plots and descriptive statistics.- Discussion.- Further study.- 3 Scatterplot, correlation and covariance.- Discussion.- Further study.- 4 Face plots.- Discussion.- Further study.- 5 Multiple linear regression.- 5.1 Introductory remarks.- 5.2 The model of multiple linear regression.- 5.3 Least squares estimation.- 5.4 Residual analysis.- 5.5 Model building, analysis of variance.- 5.6 The overall test of significance.- 5.7 Coefficient of determination and multiple correlation.- 5.8 Tests of partial hypotheses.- 5.9 Standard errors of the regression coefficients.- 5.10 Selection of a subset of regressors.- Discussion.- Further study.- 6 Linear combinations.- 6.1 Introduction.- 6.2 A special linear combination.- 6.3 Linear combinations of two variables.- 6.4 Linear combinations of several variables.- 6.5 Mean and standard deviation of linear combinations.- Discussion.- Further study.- 7 Linear discriminant analysis for two groups.- 7.1 Introduction.- 7.2 Multivariate standard distance.- 7.3 Relationship between discriminant analysis and multiple linear regression.- 7.4 Testing hypotheses about the discriminant function.- 7.5 Screening a discriminant function.- 7.6 Further uses of the coefficient of determination.- 7.7 Classification of observations.- Discussion.- Further study.- Examples.- 8 Identification analysis.- 8.1 Introduction.- 8.2 Identification analysis as a special case of discriminant analysis.- 8.3 More about standard distance.- 8.4 Identification of a bank note.- 8.5 Analysis of outliers.- Discussion.- Further study.- Examples.- 9 Specification analysis.- 9.1 Standard distance between a sample and a hypothetical mean vector.- 9.2 Specification analysis of the bank notes.- 9.3 Confidence regions for a mean vector.- 9.4 A more general model.- 9.5 Specification faces.- Further study.- Examples.- 10 Principal component analysis.- 10.1 Introduction.- 10.2 Principal components of two variables.- 10.3 Properties of principal components in the multidimensional case.- 10.4 Principal component analysis of the genuine bank notes.- 10.5 The singular case.- 10.6 Principal components, standard distance, and the multivariate normal distribution.- 10.7 Standard errors of the principal component coefficients and related problems.- 10.8 Principal component analysis of several groups.- Discussion.- Further study.- Examples.- 11 Comparing the covariance structures of two groups.- 11.1 Introduction.- 11.2 The bivariate case.- 11.3 The multivariate case.- 11.4 Comparison of the covariance matrices of the genuine and forged bank notes.- 11.5 Partial statistics for the analysis of Ymaxand Ymix.- 11.6 Stepwise analysis of Ymax and Ymix.- 11.7 Relationships to standard distance and principal component analysis.- 11.8 Critical values of the distribution of Fmaxand Fmix.- Discussion.- Further study.- Examples.- 12 Exercises.- 12.1 Exercises based on the bank note data.- 12.2 Additional exercises.- 13 Mathematical appendix.- 13.1 Introduction and preliminaries.- 13.2 Data matrix, mean vector, covariance and correlation.- 13.3 Multiple linear regression.- 13.4 Linear combinations.- 13.5 Multivariate standard distance and the linear discriminant function.- 13.6 Principal component analysis.- 13.7 Comparison of two covariance matrices.- References. Content: Front Matter....Pages i-ix The data....Pages 1-10 Univariate plots and descriptive statistics....Pages 11-18 Scatterplot, correlation and covariance....Pages 19-37 Face plots....Pages 38-53 Multiple linear regression....Pages 54-74 Linear combinations....Pages 75-87 Linear discriminant analysis for two groups....Pages 88-135 Identification analysis....Pages 136-155 Specification analysis....Pages 156-180 Principal component analysis....Pages 181-233 Comparing the covariance structures of two groups....Pages 234-262 Exercises....Pages 263-275 Mathematical appendix....Pages 276-287 Back Matter....Pages 288-296