Applied Multivariate Statistical AnalysisThis market leading text provides experimental scientists in a wide variety of disciplines with a readable introduction to the statistical analysis of multivariate observations. Its overarching goal is to provide readers with the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. The Fourth Edition has been revised to take greater advantage of graphical displays of multivariate data and of statistical software programs that facilitate the analysis of complex data. *NEW - Graphical displays of multivariate data moved from Chapter 12 to chapter 1 and many new illustrations and graphics have been added to provide a more visual approach to the subject. *NEW - discussions of important topics including: - Detecting Outliers and Data Cleaning in Chapter 4.- Multivariate Quality Control in Chapter 5. - Monitoring Quality with Principal Components in Chapter 8.- Correspondence Analysis, Biplots, and Procrustes Analysis in Chapter 12. *NEW - Expanded coverage of the following topics: Generalized variance, Assessing normality and transformations to normality, Repeated measures designs, Model checking and other aspects of regre |
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Page 34
... axes are indicated . They are parallel to the x , and 2 axes . For the choice of a11 , a12 , and a22 in footnote 2 , the x and x2 axes are at an angle with respect to the X1 and x2 axes . The generalization of the distance formulas of ...
... axes are indicated . They are parallel to the x , and 2 axes . For the choice of a11 , a12 , and a22 in footnote 2 , the x and x2 axes are at an angle with respect to the X1 and x2 axes . The generalization of the distance formulas of ...
Page 464
... axes that are parallel to the original axes x1 , x2 , ... , xp . It will be con- venient to set μ = 0 in the argument that follows . ' = From our discussion in Section 2.3 with A = ΣΤΙ we can write Yı = = ex , y2 = ex , ... , Yp where ...
... axes that are parallel to the original axes x1 , x2 , ... , xp . It will be con- venient to set μ = 0 in the argument that follows . ' = From our discussion in Section 2.3 with A = ΣΤΙ we can write Yı = = ex , y2 = ex , ... , Yp where ...
Page 479
... axes of the hyperellipsoid , and their absolute values are the lengths of the projections of x - x in the directions of the axes ê . Consequently , the sample principal components can be viewed as the result of translating the origin of ...
... axes of the hyperellipsoid , and their absolute values are the lengths of the projections of x - x in the directions of the axes ê . Consequently , the sample principal components can be viewed as the result of translating the origin of ...
Contents
MATRIX ALGEBRA AND RANDOM VECTORS | 49 |
Concepts | 86 |
SAMPLE GEOMETRY AND RANDOM SAMPLING | 116 |
Copyright | |
13 other sections not shown
Common terms and phrases
A₁ approximation axes calculate canonical correlations canonical variates chi-square classification cluster columns confidence intervals Consider Construct coordinates correlation coefficient correlation matrix corresponding cross products density determined diagonal dimensions discriminant eigenvalues eigenvectors ellipse ellipsoid equation error Example Exercise factor analysis factor loadings factor model Figure function given H₁ interpretation linear combinations MANOVA maximum likelihood estimates mean vector measurements methods multivariate normal n₁ n₂ normal distribution observations obtained orthogonal P₁ pairs predictor prior probabilities Q-Q plot R₁ random variables random vector regression model residual response Result rotated sample canonical sample correlation sample covariance matrix sample mean sample principal components sample variance scatter plot simultaneous confidence intervals standardized statistical statistical distance sum of squares Table tion U₁ univariate V₁ values X₁ X₂ Y₁ Y₂ Z₁ zero μ₁ μ₂ μι