1. Suppose from a regression on 74 observations of a dependent variable on a constant and one independent variable, the SSR = 8.916
If the sample is divided into the first 30 observations and the last 24 observations and the same model is estimated on each subsample to get SSR1 = 1.215 and SSR2 = 3.4895
Carry out a test, to determine if there is heteroscedasticity in the model. What is the Null Hypothesis?
What are the test statistic and its distribution?
Test at the 1% level. What is the critical value? What is the decision?
2. How does Heteroscedasticity affect the least square estimator and forecasts?
3. Suppose the error variance of a model is describe by the equation σt2 = α0 + α1 Z1 + α2Z2 + εt
Describe how to use Feasible Generalized Least Squares to get efficient estimates of the coefficients of the model.
4. When two are more independent variables are correlated with one another the value of the R2 will be low . True or False
5. You estimate a model with 3 variables. You then add a fourth, the value of R2 increase by a small amount, the new estimated coefficient is statistically significant, the other coefficients change substantially and all their standard errors increase substantially. What is likely taking place?
6. Suppose you are given the following information:
Model 1 InYt = 4.99 +23.2D1 + 36.5D2 + .732 lnX1 – 2.798 D1lnX1 + 4.251 D2ln X1 – .371ln X2 +.405 D1lnX2 – .236 D2lnX2 adjusted R2= .921,SSR = .018645
Model 2 lnYt = 4.18 +.103D1 + .103D2 + .621 lnX1 – .201 lnX2adjusted R2= .852, SSR = .04195
Where n = 29 D1 = 1 for observations 12 to 20, (period 2) and 0 otherwise.D2 = 1 for observations 21 to 29, (period 3) and 0 otherwise
(a) What are the elasticities of Y with respect to X1 and X2 in period 1, 2, and 3
(b) How can one test the Null Hypothesis that there has been no structural change in the elasticities of Y with respect to X1 and X2 over the three time periods, observations 1 – 11, 12 – 20, and 21 – 29?
Write out the null and alternative hypotheses in term of the B’s. Calculate the test statistic, and its distribution.Carry out the test and the 1% level. What is the result?
7. Consider
Ŷt = 34 + 28 Xt n = 40 d = 3.2(3) (6)
With 1 independent variable and 40 observations at 5%, dL = 1.44 dU = 1.54. Is the error term first order autocorrelated at the 5% level?
What type (if any) autocorrelation is there?
8. Consider the model
Yt = B0 + B1X1 + B2X2 + ut with 30 observations.
Where it is possible that ut depends on, ut-1 and ut-2 and a random error term.
Describe how to carry out an LM test at the 5% level to determine if there is second-degree autocorrelation.
9. Describe the Cochrane-Orcutt Iterative procedure to correct for first order autocorrelation in the model Yt = B0 + B1X1 + B2X2 + ut
10. Consider a 3rd degree Autoregressive Conditional Heteroscedastic Model where σt2 = α0 + α1 u2 + α2u2 + α3u2 + εt
Explain how to carry out an ARCH test for this heteroscedasticity.
(i) What is the null hypothesis?
(ii) What is the auxiliary equations?
(iii) What is the test statistic, its distribution and degrees of freedom?
(iv) What is the decision rule?
CS 340 Milestone One Guidelines and Rubric Overview: For this assignment, you will implement the fundamental operations of create, read, update,
Retail Transaction Programming Project Project Requirements: Develop a program to emulate a purchase transaction at a retail store. This
7COM1028 Secure Systems Programming Referral Coursework: Secure
Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip
CS 340 Final Project Guidelines and Rubric Overview The final project will encompass developing a web service using a software stack and impleme
