this problem, you will investigate the effects of autocorrelation on linear regression, using a simulated data set. Start by crea variance matrix reflecting autocorrelation: = 100 gmax = matrix(NA, nr=n, nc=n) # initialize the covariance matrix -gmax[1,1] = 1 r(i in 2:n){ Sigmax [i,i] = 1 for(j in 1:(i-1)){

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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In this problem, you will investigate the effects of autocorrelation on linear regression, using a simulated data set. Start by creating a
covariance matrix reflecting autocorrelation:
n = 100
Sigmax = matrix(NA, nr=n, nc=n) # initialize the covariance matrix
Sigmax[1,1] = 1
for(i in 2:n){
Sigmax [i,i] = 1
for(j in 1:(i-1)){
Sigmax [i, j]
Sigmax[j, i]
.9^abs (i-j)
Sigmax [i, j] # make the covariance matrix
# symmetric across the diagonal
} #end iter over j
} # end iter over i
Answer parts a-b by reading the code and/or looking at what the matrix Sigmax contains.
a. In this simulation, what is the value o?, the variance of the noise terms e?
Hint:
b. In this simulation, what is the value y, the correlation between noise terms that are separated by 1 time unit?
Transcribed Image Text:In this problem, you will investigate the effects of autocorrelation on linear regression, using a simulated data set. Start by creating a covariance matrix reflecting autocorrelation: n = 100 Sigmax = matrix(NA, nr=n, nc=n) # initialize the covariance matrix Sigmax[1,1] = 1 for(i in 2:n){ Sigmax [i,i] = 1 for(j in 1:(i-1)){ Sigmax [i, j] Sigmax[j, i] .9^abs (i-j) Sigmax [i, j] # make the covariance matrix # symmetric across the diagonal } #end iter over j } # end iter over i Answer parts a-b by reading the code and/or looking at what the matrix Sigmax contains. a. In this simulation, what is the value o?, the variance of the noise terms e? Hint: b. In this simulation, what is the value y, the correlation between noise terms that are separated by 1 time unit?
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