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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; üii) Calculate the diagonal matrix D, and its inverse D,-; 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.

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; üii) Calculate the diagonal matrix D, and its inverse D,-; 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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 D, and its inverse D,-; 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.
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; ii) Calculate the diagonal matrix D, and its inverse D,-; 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.
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