Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C.J. Anderson
Homework # 5
Answer Key
1. Problem 4.26 p 206, Johnson & Wichern (2007). Only do parts (a) and (b).
(a) Method involving the least work when using SAS/IML or other linear algebra
program. The square statistical di
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C.J. Anderson
Homework # 4
Answer Key
1. Problem 4.6, p 201, Johnson & Wichern (2007)
Part of explanation: Since X N3 (, ), to show independence all I need to do is
show that the covariance equals 0.
(a) 12 = 0; therefore, X1 a
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 Psych/594
C.J. Anderson
Homework # 8
Answer Key
1. Problem 6.8 in Johnson & Wichern, p 338. Do any computations using IML or your
favorite matrix computer program.
(a) Break up the observations into mean, treatment, and residual components
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
Edps/Soc 584 & Psych 594
Spring 2013
C.J.Anderson
Name:
Midterm Exam
Due Thursday March 14, 2013
At the Beginning of Lecture
There are 5 questions, most of which have multiple parts. The total number of points is
100. The point values for each question is
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C.J. Anderson
Homework # 4
Answer Key
1. Problem 4.6, p 201, Johnson & Wichern (2007)
Part of explanation: Since X N3 (, ), to show independence all I need to do is
show that the covariance equals 0.
(a) 12 = 0; therefore, X1 a
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C.J. Anderson
Homework # 3
Answer Key
1. Problem 2.27, page 106 in Johnson & Wichern.
Note: There is a typo in the text: part (e) is really (d) and part (f) is really (e).
Let
X1
X = X2 ,
X3
11 12 13
= 21 22 23
31 32 33
1
=
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 and Psych 594
Spring 2011
C. Anderson
Homework # 6
Answer Key
Use the High School and Beyond (hsb) data for this problem. This data set in on the
course website including a description of the variables and their coding.
Assuming that a sa
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 594 Psych 584
C.J. Anderson
Homework # 7
Answer Key
1. Problem 8.1 in Johnson & Wichern, p 470471.
The population principal components are
Y1 = 0.8944272X1 + 0.4472136X2
Y1 = 0.447214X1 + 0.8944272X2
The proportion of total population variance
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 Psych/594
C.J. Anderson
Homework # 8
Answer Key
1. Problem 6.8 in Johnson & Wichern, p 338. Do any computations using IML or your
favorite matrix computer program.
(a) Break up the observations into mean, treatment, and residual components
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C. Anderson
Homework # 9
1. Test the equality of the covariance matrices used in Problem 6.8, page 338 in Johnson
& Wichern (refer to homework #8).
Edited output from PROC DISCRIM with POOL=TEST option:
Covariance
Matrix Rank
G
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C.J. Anderson
Homework #10
Answer Key
In the homework assignments 8 and 9, you analyzed the sh data using MANOVA and
Prole analysis. For this homework you will analyze it using discriminant analysis.
1. It is reasonable to perf
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
Edps/Soc 584 & Psych 594
Spring 2013
C.J.Anderson
Name:
Midterm Exam
Due Thursday March 14, 2013
At the Beginning of Lecture
There are 5 questions, most of which have multiple parts. The total number of points is
100. The point values for each question is
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 594 & Psych 594
C.J. Anderson
Homework # 1
Answer Key
1. Problem 1.4, page 38 in Johnson & Wichern. Use your favorite method of plotting
univariate distributions instead of a dot diagram.
(a) Graphics: For the univariate distributions here are
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
Spring 2011
C.J. Anderson
Final Exam
Due 5 pm Monday May 6, 2013
There are 5 questions worth a total of 100 points. Your answers are due 5 pm May 6,
2013. You may turn in your answers to my mailbox in Education or my oce in Edu
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C. Anderson
Homework # 9
1. Test the equality of the covariance matrices used in Problem 6.8, page 338 in Johnson
& Wichern (refer to homework #8).
Edited output from PROC DISCRIM with POOL=TEST option:
Covariance
Matrix Rank
G
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
Spring 2011
C.J. Anderson
Final Exam
Due 5 pm Monday May 6, 2013
There are 5 questions worth a total of 100 points. Your answers are due 5 pm May 6,
2013. You may turn in your answers to my mailbox in Education or my oce in Edu
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 594 & Psych 594
C.J. Anderson
Homework # 1
Answer Key
1. Problem 1.4, page 38 in Johnson & Wichern. Use your favorite method of plotting
univariate distributions instead of a dot diagram.
(a) Graphics: For the univariate distributions here are
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C.J. Anderson
Homework # 3
Answer Key
1. Problem 2.27, page 106 in Johnson & Wichern.
Note: There is a typo in the text: part (e) is really (d) and part (f) is really (e).
Let
X1
X = X2 ,
X3
11 12 13
= 21 22 23
31 32 33
1
=
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 and Psych 594
Spring 2011
C. Anderson
Homework # 6
Answer Key
Use the High School and Beyond (hsb) data for this problem. This data set in on the
course website including a description of the variables and their coding.
Assuming that a sa
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 594 Psych 584
C.J. Anderson
Homework # 7
Answer Key
1. Problem 8.1 in Johnson & Wichern, p 470471.
The population principal components are
Y1 = 0.8944272X1 + 0.4472136X2
Y1 = 0.447214X1 + 0.8944272X2
The proportion of total population variance
Applied Multivariate Statistics in Educational and Psychological Research
PSYCH 594

Spring 2013
EdPsych/Soc 584 & Psych 594
C.J. Anderson
Homework #10
Answer Key
In the homework assignments 8 and 9, you analyzed the sh data using MANOVA and
Prole analysis. For this homework you will analyze it using discriminant analysis.
1. It is reasonable to perf