Applied Multivariate Statistical AnalysisAspects of mulyivariate analysis; Matrix algebra and random vectors; Sampling geometry and random sampling; The multivariate normal distribution; Inferences about a mean vector; Comparisons of several multivariate means; Multivariate linear regression models; Analysis of covariance structure: principal components; Factor analysis and inference structured covarience matrices; Canonical correlation analysis; Classification and grouping techniques; Discrimination and classification; Clustering. |
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Page 233
... sum of squares is SS res = 12 + ( −2 ) 2 + 12 + ( − 1 ) 2 + 12 + 12 + ( −1 ) 2 + 02 = 10 The sums of squares satisfy the same decomposition , ( 6-30 ) , as the obser- vations . Consequently , SSobs SS mean + SStr + SSres = or 216 ...
... sum of squares is SS res = 12 + ( −2 ) 2 + 12 + ( − 1 ) 2 + 12 + 12 + ( −1 ) 2 + 02 = 10 The sums of squares satisfy the same decomposition , ( 6-30 ) , as the obser- vations . Consequently , SSobs SS mean + SStr + SSres = or 216 ...
Page 236
... sum of squares breakup in ( 6-31 ) . First we note that the cross - product can be written as - - - - ( Xej — X ) ... sum over j of the middle two expressions is the zero matrix because ne Σ ( xkj j = 1 8 ne X ) = 0. Next , summing the ...
... sum of squares breakup in ( 6-31 ) . First we note that the cross - product can be written as - - - - ( Xej — X ) ... sum over j of the middle two expressions is the zero matrix because ne Σ ( xkj j = 1 8 ne X ) = 0. Next , summing the ...
Page 279
... sum of squares is ê'ê = 1 [ 0 1 -2 1 0 ] -2 = 02 + 12 + ( − 2 ) 2 + 12 + 02 = 6 − □ Sum of Squares Decomposition 1 0 According to Result 7.1 , ŷ'ê = 0 so the total response sum of squares y'y = n Σy satisfies j = 1 y'y = = - ( ŷ + y ...
... sum of squares is ê'ê = 1 [ 0 1 -2 1 0 ] -2 = 02 + 12 + ( − 2 ) 2 + 12 + 02 = 6 − □ Sum of Squares Decomposition 1 0 According to Result 7.1 , ŷ'ê = 0 so the total response sum of squares y'y = n Σy satisfies j = 1 y'y = = - ( ŷ + y ...
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Matrix Algebra and Random Vectors | 35 |
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approximately axes calculate canonical correlations canonical variates chi-square chi-square distribution classification clusters confidence intervals confidence region correlation coefficient correlation matrix corresponding cross-products density determined discriminant eigenvalues eigenvectors ellipse ellipsoid Equation error Example Exercise F-distribution factor analysis factor loadings Figure function given H₁ large sample length likelihood ratio likelihood ratio test linear combinations MANOVA maximum likelihood estimates mean vector measurements multivariate normal n₁ n₂ normal distribution normal population observations obtained P₁ pairs parameters population mean Q-Q plots random sample random variables random vector regression model reject residual response Result rotated S₁ sample correlation sample covariance matrix sample mean sample variance scatterplot simultaneous confidence intervals Spooled squared distance statistical sum of squares Table treatment univariate V₁ values X₁ X₂ Y₁ Y₂ Z₁ zero μ₁ μ₂ μι Σ Σ