Question 3. (To be done using 'R'). In this question, you are required to import BostonHousing data set from mlbench package in 'R', create a subset of only 3 variables: • per capita crime rate by town • average number of rooms per dwelling • weighted distances to five Boston employment centres, and then calculate certain basic multivariate statistics corresponding to these 3 columns from the data set, outlined below. Once you have successfully imported your data as a data frame: i) Calculate the sample mean vector j; ii) Calculate the sample covariance matrix S. Explain what the (2, 3) element of this matrix describes and interpret its value; ii) Calculate the diagonal matrix Ds and its inverse Ds iv) Calculate the sample correlation matrix R. Again, explain what the (3, 2) element of this matrix de- scribes and interpret its value; v) Write down the form of the (3 x 3) matrix of coefficients, denoted A, that considers the differences between each of the three variables; [Hint: Use the theory of linear combinations] vi) Calculate the sample mean vector i for the difference between each of the variables; vii) Calculate the sample covariance matrix S for the differences of the three variables; viii) Calculate the sample correlation matrix R, for the differences of the three variables. [For this question, you only need to submit the solution. You do not have to submit any code.]
Question 3. (To be done using 'R'). In this question, you are required to import BostonHousing data set from mlbench package in 'R', create a subset of only 3 variables: • per capita crime rate by town • average number of rooms per dwelling • weighted distances to five Boston employment centres, and then calculate certain basic multivariate statistics corresponding to these 3 columns from the data set, outlined below. Once you have successfully imported your data as a data frame: i) Calculate the sample mean vector j; ii) Calculate the sample covariance matrix S. Explain what the (2, 3) element of this matrix describes and interpret its value; ii) Calculate the diagonal matrix Ds and its inverse Ds iv) Calculate the sample correlation matrix R. Again, explain what the (3, 2) element of this matrix de- scribes and interpret its value; v) Write down the form of the (3 x 3) matrix of coefficients, denoted A, that considers the differences between each of the three variables; [Hint: Use the theory of linear combinations] vi) Calculate the sample mean vector i for the difference between each of the variables; vii) Calculate the sample covariance matrix S for the differences of the three variables; viii) Calculate the sample correlation matrix R, for the differences of the three variables. [For this question, you only need to submit the solution. You do not have to submit any code.]
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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I need last four parts (V ,VI,VII and VIII please don't send me first four parts other wise your solution will dislike . I have first four part need to be done last four parts In 3 hours
![Question 3. (To be done using 'R'). In this question, you are required to import BostonHousing data set
from mlbench package in 'R', create a subset of only 3 variables:
• per capita crime rate by town
• average number of rooms per dwelling
• weighted distances to five Boston employment centres,
and then calculate certain basic multivariate statistics corresponding to these 3 columns from the data set,
outlined below.
Once you have successfully imported your data as a data frame:
i) Calculate the sample mean vector j;
ii) Calculate the sample covariance matrix S. Explain what the (2, 3) element of this matrix describes and
interpret its value;
iii) Calculate the diagonal matrix Ds and its inverse Ds
iv) Calculate the sample correlation matrix R. Again, explain what the (3, 2) element of this matrix de-
scribes and interpret its value;
v) Write down the form of the (3 x 3) matrix of coefficients, denoted A, that considers the differences
between each of the three variables; [Hint: Use the theory of linear combinations]
vi) Calculate the sample mean vector i for the difference between each of the variables;
vii) Calculate the sample covariance matrix Sv for the differences of the three variables;
viii) Calculate the sample correlation matrix R, for the differences of the three variables.
[For this question, you only need to submit the solution. You do not have to submit any code.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53ca7829-60c0-4dfd-bc48-1a22de57999e%2F0e35416a-9130-4bde-a95a-b23dcd9e7c80%2F5iynveg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3. (To be done using 'R'). In this question, you are required to import BostonHousing data set
from mlbench package in 'R', create a subset of only 3 variables:
• per capita crime rate by town
• average number of rooms per dwelling
• weighted distances to five Boston employment centres,
and then calculate certain basic multivariate statistics corresponding to these 3 columns from the data set,
outlined below.
Once you have successfully imported your data as a data frame:
i) Calculate the sample mean vector j;
ii) Calculate the sample covariance matrix S. Explain what the (2, 3) element of this matrix describes and
interpret its value;
iii) Calculate the diagonal matrix Ds and its inverse Ds
iv) Calculate the sample correlation matrix R. Again, explain what the (3, 2) element of this matrix de-
scribes and interpret its value;
v) Write down the form of the (3 x 3) matrix of coefficients, denoted A, that considers the differences
between each of the three variables; [Hint: Use the theory of linear combinations]
vi) Calculate the sample mean vector i for the difference between each of the variables;
vii) Calculate the sample covariance matrix Sv for the differences of the three variables;
viii) Calculate the sample correlation matrix R, for the differences of the three variables.
[For this question, you only need to submit the solution. You do not have to submit any code.]
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