Question 1. Consider a p-dimensional response variable j, containing p variables, with n observation vectors j1, ..., n. The sample mean vecior of these observation vectors is denoted by j = (1/n)E, . a) Given that the sample covariance matrix, S, is defined by E ( – 5) (5. – 5)", i) Show that S = n - 1 ii) Using the above result, show that S can alternatively be defined as s=" (1-) . S = n- 1 where Y is the data matrix, I is the identity matrix and J is a matrix of 1's. [Hint: Consider re-writing the mean vector i in terms of the data matrix (see lecture notes).) b) Consider the following (3x3) data matrix, containing three observations of three variables yı, yz and y3: 5 2 2 1 3 5 6 4 1 Y = Calculate i) The sample covariance matrix S (hy hand): ii) The sample correlation matrix R (by hand) using the equation R= D,-SD,-1, and comment on each of the three elemenis in the first column of this matrix. [Hint: Recall how to find the inverse of a diagonal matrix.]
Question 1. Consider a p-dimensional response variable j, containing p variables, with n observation vectors j1, ..., n. The sample mean vecior of these observation vectors is denoted by j = (1/n)E, . a) Given that the sample covariance matrix, S, is defined by E ( – 5) (5. – 5)", i) Show that S = n - 1 ii) Using the above result, show that S can alternatively be defined as s=" (1-) . S = n- 1 where Y is the data matrix, I is the identity matrix and J is a matrix of 1's. [Hint: Consider re-writing the mean vector i in terms of the data matrix (see lecture notes).) b) Consider the following (3x3) data matrix, containing three observations of three variables yı, yz and y3: 5 2 2 1 3 5 6 4 1 Y = Calculate i) The sample covariance matrix S (hy hand): ii) The sample correlation matrix R (by hand) using the equation R= D,-SD,-1, and comment on each of the three elemenis in the first column of this matrix. [Hint: Recall how to find the inverse of a diagonal matrix.]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I need part B to be solve correctly in one hour please provide correct solution and get thumb up
![Question 1. Consider a p-dimensional response variable j, containing p variables, with n observation
vectors j1, ..., īn. The sample mean vecior of these observation vectors is denoted by j = (1/n) E, Ii.
a) Given that the sample covariance matrix, S, is defined by
n
1
S =
n – 12 (i – 5) (5: – 5)",
i=1
i) Show that
S =
n - 1
j – nýj
ii) Using the above result, show that S can alternatively be defined as
1
S =
п - 1
I
where Y is the data matrix, I is the identity matrix and J is a matrix of 1's.
[Hint: Consider re-writing the mean vector in terms of the data matrix (see lecture notes). )
b) Consider the following (3×3) data matrix, containing three observations of three variables y1, y2 and y3:
-()
5 2 2
1 3 5
6 4
Y =
1
Calculate
i) The sample covariance matrix S (hy hand);
ii) The sample correlation matrix R (by hand) using the equation
R= D,-'SD,-1,
and comment on each of the three elemenis in the first column of this matrix.
[Hint: Recall how to find the inverse of a diagonal matrix.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8268f00-1e22-49fe-9b99-9cbbb3c8020a%2Fb1062024-ed0e-4021-8ee9-7381590cb159%2Fh5v2jtk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 1. Consider a p-dimensional response variable j, containing p variables, with n observation
vectors j1, ..., īn. The sample mean vecior of these observation vectors is denoted by j = (1/n) E, Ii.
a) Given that the sample covariance matrix, S, is defined by
n
1
S =
n – 12 (i – 5) (5: – 5)",
i=1
i) Show that
S =
n - 1
j – nýj
ii) Using the above result, show that S can alternatively be defined as
1
S =
п - 1
I
where Y is the data matrix, I is the identity matrix and J is a matrix of 1's.
[Hint: Consider re-writing the mean vector in terms of the data matrix (see lecture notes). )
b) Consider the following (3×3) data matrix, containing three observations of three variables y1, y2 and y3:
-()
5 2 2
1 3 5
6 4
Y =
1
Calculate
i) The sample covariance matrix S (hy hand);
ii) The sample correlation matrix R (by hand) using the equation
R= D,-'SD,-1,
and comment on each of the three elemenis in the first column of this matrix.
[Hint: Recall how to find the inverse of a diagonal matrix.]
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