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Set the seed number to 1234098765 and the sample size to 100. Use the data-generating process for y_A.  Use the untransformed values of x1 and x2.  Assume that the error is homoskedastic. Estimate the model using least squares. Use the Breusch-Pagan Test. What is the Value of the test statistic?

Set the seed number to 1234098765 and the sample size to 100. Use the data-generating process for y_A.  Use the untransformed values of x1 and x2.  Assume that the error is homoskedastic. Estimate the model using least squares. Use the Breusch-Pagan Test. What is the Value of the test statistic?

MATLAB: An Introduction with Applications
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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Read the given information for Part A.

Set the seed number to 1234098765 and the sample size to 100. Use the data-generating process for y_A.  Use the untransformed values of x1 and x2.  Assume that the error is homoskedastic. Estimate the model using least squares. Use the Breusch-Pagan Test. What is the Value of the test statistic? (Note: Write the first three decimal places without rounding off. For instance, if what you got in R is 0.12309, you should write 0.123.)

########## ######## ######### library (MASS) #run install.packages ("MASS") if you haven't installed the package yet. #Invoking the MASS package enables `mvrnorm'. # library (lmtest) #This is needed to implement tests for heteroskedasticity. # set.seed ( 1 ) #usual seed number # N <- 1 #Size of the random sample. x1 <- rnorm(N, 0,20) #normal distribution x2 <- rnorm (N, 0,10) #normal distribution # x1 <- x2 <- # ########################### 2*x1 #normal distribution 2*x2 #normal distribution x1 <- 3*x1 #normal distribution x2 <- 3*x2 #normal distribution # #Generate new variables # x1sq <-x1^2 #square of x1 x2sq <-x2^2 #square of x2 int <-x1*x2 #interaction between x1 and x2 # # # epsilon1 <- rnorm (N, 0,1) #stochastic error term; variance of error is 1 epsilon1 <- sqrt(int) *epsilon1 epsilon1 <- -sqrt(int)*epsilon1 #Part A #The data-generating process is denoted by #(*). #The data-generating process highlights population-level relationships. This is your true model. No errors are present, and no #endogeneity issues arise. There are no measurement errors, as well. #Note that the interaction term between x1 and x2 is added. Usually, the #interaction term measures the joint effect of x1 and x2. # y_A < 1 +0.3*x1 +0.75*x2-0.9*x1sq -0.5*x2sq + 2.5*int + epsilon1 #(*) # #Note the respective coefficients of x1, x2, x1sq, x2sq, and int. # #Fit the model using OLS # model.A <- lm (y_A~x1+x2+x1sq +x2sq+int +1) # summary (model.A) # #Breush-Pagan Test #The result should not come as a surprise. Based on how the model was constructed, #no reason to believe that the variance will vary across observations. bptest(model.A) # #You should be able to interpret the statistics generated by the bptest. #BP is the test statistic, and df is the degrees of freedom. Based on the p-value, #we accept that errors are homoskedastic. Can you argue otherwise? # #Note that the fitted model is close to the DGP. Just check the model summary. # summary (model.A) #
Transcribed Image Text:########## ######## ######### library (MASS) #run install.packages ("MASS") if you haven't installed the package yet. #Invoking the MASS package enables `mvrnorm'. # library (lmtest) #This is needed to implement tests for heteroskedasticity. # set.seed ( 1 ) #usual seed number # N <- 1 #Size of the random sample. x1 <- rnorm(N, 0,20) #normal distribution x2 <- rnorm (N, 0,10) #normal distribution # x1 <- x2 <- # ########################### 2*x1 #normal distribution 2*x2 #normal distribution x1 <- 3*x1 #normal distribution x2 <- 3*x2 #normal distribution # #Generate new variables # x1sq <-x1^2 #square of x1 x2sq <-x2^2 #square of x2 int <-x1*x2 #interaction between x1 and x2 # # # epsilon1 <- rnorm (N, 0,1) #stochastic error term; variance of error is 1 epsilon1 <- sqrt(int) *epsilon1 epsilon1 <- -sqrt(int)*epsilon1 #Part A #The data-generating process is denoted by #(*). #The data-generating process highlights population-level relationships. This is your true model. No errors are present, and no #endogeneity issues arise. There are no measurement errors, as well. #Note that the interaction term between x1 and x2 is added. Usually, the #interaction term measures the joint effect of x1 and x2. # y_A < 1 +0.3*x1 +0.75*x2-0.9*x1sq -0.5*x2sq + 2.5*int + epsilon1 #(*) # #Note the respective coefficients of x1, x2, x1sq, x2sq, and int. # #Fit the model using OLS # model.A <- lm (y_A~x1+x2+x1sq +x2sq+int +1) # summary (model.A) # #Breush-Pagan Test #The result should not come as a surprise. Based on how the model was constructed, #no reason to believe that the variance will vary across observations. bptest(model.A) # #You should be able to interpret the statistics generated by the bptest. #BP is the test statistic, and df is the degrees of freedom. Based on the p-value, #we accept that errors are homoskedastic. Can you argue otherwise? # #Note that the fitted model is close to the DGP. Just check the model summary. # summary (model.A) #
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