Computer Assignments

Multivariate: Assignment 1 Matrix Algebra I Using the matrixXfound inFILE1write a matrix program to do the following: 1. PrintX2. Create a vector of variable totals 3. Create a vector of variable means 4. Compute the rawSSCPmatrix 5. Compute the deviation score matrix 6. Compute the deviationSSCPmatrix 7. Compute the covariance matrix 8. Compute the standard score matrix 9. Compute the correlation matrix Note: be sure to label your output and include comments and your program. Answers to Assignment 1 Multivariate: Assignment 2 Multiple Regression Using the matricesXandYfound inFILE2do the following: 1* Compute the vector of raw regression weights 2 Compute the standard error of the regression weights 3 Compute t-tests for each regression weight 4* Compute the vector of predicted scores 5* Compute the vector of residual scores 6* Compute the squared multiple correlation 7* Compute the F-ratio for the model 8 Compute the standard error of estimate 9 Compute the vector of standardized regression weights Note: be sure to label your output and include comments. Answers to Assignment 2 Multivariate: Assignment 3 Hotelling's T^{2}Using the matricesX1andX2found inFILE3do the following: 1. Compute the pooled within SSCP matrix 2. Compute the mean value vectors for each group 3. Compute the difference in the mean value vectors 4. Compute the Mahalanobis D^{2}statistic 5. Compute the Hotelling T^{2}statistic 6. Compute the F statistic 7. Give the degrees of freedom 8. State whether the multivariate analysis is significant Note: be sure to label your output and include comments. Answers to Assignment 3 ED210D: Assignment 4 One-way MANOVA Using the matricesX1,X2, andX3found inFILE4do the following: 1 Compute a mean value vector for each group 2 Compute the total SSCP matrix 3 Compute the pooled within SSCP matrix 4 Compute the between SSCP matrix 5 Compute the Wilk's L statistic 6 Compute the F statistic approximation 7 Give the degrees of freedom 8 Compute w^{2}_{m}(the multivariate strength of association) 9 State whether the multivariate analysis is significant and interpret the results Note: be sure to label your output and include comments. Answers to Assignment 4 Multivariate: Assignment 5 Matrix Algebra II Using the matrixXfound inFILE1do the following: 1. Compute the deviation SSCP matrix,S2. Compute the covariance matrix,C3. Compute the correlation matrix,R4. Compute the determinants ofS,CandR5. Compute the eigenvalues ofS,CandR6. Compute the eigenvectors ofS,CandRNote: be sure to label your output and include comments. Answers to Assignment 5 Multivariate: Assignment 6 Linear Discriminant Function Analysis Using the matricesX1,X2, andX3found inFILE4do the following (retain only the first two discriminant dimensions): 1. Compute a mean value vector for each group. 2. Compute the pooled within SSCP matrix,W. 3. Compute the between group SSCP matrix,B. 4. Compute the eigenvalues and eigenvectors forW. 5. Compute the canonical correlations. 6. Compute the standardized discriminant function weights. 7. Compute the Wilk's Lambda statistics. 8. Compute the chi-square statistic approximations. 9. Compute the degrees of freedom 10. State whether the multivariate analysis is significant. 11. Compute the discriminant structure matrix. Note: be sure to label your output and include comments. Multivariate: Assignment 7 Canonical Correlation Analysis Using the matrix^{-1}BXY(the first 3 columns ofXYare the Y variables while the last 5 columns are the X variables) found inFILE5do the following: 1. Compute the squared canonical correlation. 2. Compute the canonical correlation. 3. Compute the eignevalues ofAandB. 4. Compute the eigenvectors ofAandB. 5. Compute the F statistic approximations. 6. Compute the degrees of freedom. 7. Determine which canonical dimensions are significant. Note: be sure to label your output and include comments. Multivariate: Assignment 8 Factorial MANOVA Using the SAS IML procedure analyze the following data: B1 B2 Y1 Y2 Y1 Y2 __________________________________ A1 10 21 9 14 12 22 8 15 9 19 11 16 10 21 9 17 14 23 9 17 __________________________________ A2 11 23 11 15 14 27 12 18 13 24 10 16 15 26 9 17 14 24 9 18 __________________________________ A3 8 17 9 22 7 15 8 18 10 18 10 17 8 17 9 19 7 19 8 19 __________________________________ Note: be sure to label your output and include comments. Multivariate: Assignment 9 General Linear Model Using the SAS IML procedure analyze the data from Assignment 8 using the General Linear Model approach. For the purposes of this assignment, do not use the reparamenterization estimation procedue. Instead, use the standard method of orthogonal coding of the design matrix. Compute tests of significance as far as Wilks' Lambda. Note: be sure to label your output and include comments. Multivariate: Assignment 10 Principal Components & Factor Analysis Using the correlation matrixRfound inFILE6do the following: 1.* Compute the eigenvalues and eigenvectors ofR. 2.* Compute the component loading matrix. 3. Compute the squared multiple correlations for each variable. 4. Compute the reduced correlation matrixR1. 5. Compute the eigenvalues and eigenvectors forR1. 6. Compute the factor loading matrix. The variables in order are: total populatiom, median school years, total employment, misc. professional services, and median house value. Note: Only retain the first two eigenvalues and eigenvectors. Note: be sure to label your output and include comments. Answers to Assignment 10

Phil Ender, 12jul07, 4oct05