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 84
... Exercise 2.8 . ( a ) Find A1 . ( b ) Compute the eigenvalues and eigenvectors of A ̄1 . ( c ) Write the spectral decomposition of A ' and compare with that of A from Exercise 2.8 . 2.10 . Consider the matrices 4.001 4.001 4.002001 A ...
... Exercise 2.8 . ( a ) Find A1 . ( b ) Compute the eigenvalues and eigenvectors of A ̄1 . ( c ) Write the spectral decomposition of A ' and compare with that of A from Exercise 2.8 . 2.10 . Consider the matrices 4.001 4.001 4.002001 A ...
Page 165
... Exercise 4.8 by I and postmultiply by [ AA ] - 4.10 . Show the following if 0 . ( a ) Check that Σ = I -1 Take ... Exercise 4.8 . = X2 . ( b ) Note from Exercise 4.9 we can write ( x -- X1 με I X2 με -Σ22'Σ21 [ - μ ) ' Σ ( Χ Σ1222'21 ) 0 ...
... Exercise 4.8 by I and postmultiply by [ AA ] - 4.10 . Show the following if 0 . ( a ) Check that Σ = I -1 Take ... Exercise 4.8 . = X2 . ( b ) Note from Exercise 4.9 we can write ( x -- X1 με I X2 με -Σ22'Σ21 [ - μ ) ' Σ ( Χ Σ1222'21 ) 0 ...
Page 431
... Exercise 9.1 . ( a ) Calculate communalities hi , i = 1 , 2 , 3 , and interpret these quantities . ( b ) Calculate Corr ( Z ,, F1 ) for i = 1 , 2 , 3. Which variable might carry the greatest weight in " naming " the common factor ? Why ...
... Exercise 9.1 . ( a ) Calculate communalities hi , i = 1 , 2 , 3 , and interpret these quantities . ( b ) Calculate Corr ( Z ,, F1 ) for i = 1 , 2 , 3. Which variable might carry the greatest weight in " naming " the common factor ? Why ...
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Matrix Algebra and Random Vectors | 35 |
Sample Geometry and Random Sampling | 88 |
35335 | 95 |
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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