Fill This Form To Receive Instant Help

Help in Homework
trustpilot ratings
google ratings


Homework answers / question archive / MACQUARIE UNIVERSITY STAT8121 Multivariate Analysis ASSIGNMENT 1 Due 23:55 21/08/2020 The pdf document is to be submitted via iLearn before the due date with your name and student number on the Örst page

MACQUARIE UNIVERSITY STAT8121 Multivariate Analysis ASSIGNMENT 1 Due 23:55 21/08/2020 The pdf document is to be submitted via iLearn before the due date with your name and student number on the Örst page

Statistics

MACQUARIE UNIVERSITY STAT8121 Multivariate Analysis ASSIGNMENT 1 Due 23:55 21/08/2020 The pdf document is to be submitted via iLearn before the due date with your name and student number on the Örst page. Question 1 Suppose that X1 s N(1; 2); X2 s N(4; 3) and Cov(X1; X2) = 1. Let X = X1 X2 ; A = 1 1 2 1 ; Y = Y1 Y2 and Y = AX: In a matrix form Önd (a) the mean of Y: (b) the variance-covariance matrix of Y: Show your working. Question 2 A researcher in the educational Öeld has collected the following test scores from a group of six students (n = 6). Student Language Aptitude x1 Analogical Reasoning x2 Geometric Reasoning x3 1 2 3 15 2 6 8 9 3 5 2 7 4 9 4 3 5 11 10 2 6 1 4 12 Let X = [x1 ; x2; x3]; x = [x1; x2; x3] T and 1 = [1; 1; 1; 1; 1; 1]T be the data matrix, sample mean column vector and all-ones column vector, respectively. (a) Find x: (b) Calculate 1x T : Show your working. (c) Calculate X 1x T . Show your working. (d) Calculate the SSCP (sum of squares and cross-products) matrix. Show your working. (e) Find S, the sample covariance matrix. (f) Is S a positive deÖnite matrix? Provide your reasoning. (g) Hence using S, Önd R, the sample correlation matrix. Question 3 Use the following R-code and obtain matrix C: rm(list=ls()) A <- matrix(rpois(64,5), 8, 8) A C= A %*% t(A) C (a) Provide a detailed description of matrix A including the dimension and commenting on how its elements were obtained. Hint: Use R-help: ?rpois( ) . (b) Obtain all eigen values and eigenvectors of matrix C. Provide the R-code and output. (c) Is C a positive deÖnite matrix? Explain your answer. (d) Let the matrix of the eigenvectors be U. Verify U TU = I using R. (e) Verify the SVD (singular value decomposition) for C using R.

Option 1

Low Cost Option
Download this past answer in few clicks

24.99 USD

PURCHASE SOLUTION

Already member?


Option 2

Custom new solution created by our subject matter experts

GET A QUOTE