QUESTION 1

a) Differentiate between mathematical model and econometric model.

b) Discuss four (4) assumptions of the classical linear regression model.

c) Using Ordinary Least Squares procedure, derive the estimated coefficients for the following regression equation.]

d) Write down the equations for the following functional forms:

i) log-log

ii) log-linear

iii) linear-log

QUESTION 2

Using quarterly data for 10 years, the regression results are given in the following table where CAR = number of new car sales per thousand population, PRICE = new car price index, INC = per-capita real disposable income (in RM), IR = interest rate and UN = unemployment rate.

Values in parentheses are standard errors.

a) Based on Model A, answer the following questions.

i) How would you retrieve R2 from the adjusted R2 given above?

ii) Write down the estimated equation.

iii) For each slope coefficient, test whether or not it is zero at 5% level of significance. 

iv) Suppose income is measured in thousands Ringgit (INC*), write down the new regression equation.

v) Test the overall significance of the estimated regression at 5%.

b) Which of the three models is the best? Explain what criteria you used. 

QUESTION 3

a) Explain the meaning of heteroscedasticity.

b) State three (3) consequences of ignoring heteroscedasticity.

c) Consider the model of a number of firms:

i) Write down the auxiliary equation for the variance of et, so that White's test for heteroscedasticity can be carried out.

ii) From (i), state the null and alternative hypotheses that there is no heteroscedasticity.

iii) What is the test statistic and numerical value of the degree of freedom?

iv) Determine the critical value for a 5% test and describe the decision rule.

v) If heteroscedasticity is detected, describe two (2) remedial measures that can be applied.

vi) Suggest two (2) tests which can be used to detect heteroscedasticity.

QUESTION 4

a) What is dummy variable?

b) The following model indicates the average annual salary of unskilled labour that may differ among three countries (Malaysia, Indonesia and Bangladesh).

i) Determine the mean annual salary for Malaysia, Indonesia and Bangladesh.

ii) What is the difference between ANOVA and ANCOVA models?

c) The Business-Economics Society from Universiti Teknologi MARA conducted a research on starting salary of Business Administration Graduates. The research objective is to assess whether taking econometrics will affect starting salary. Using an econometrics approach, the following model was estimated.

where SSALARY = starting salary, CGPA = cumulative grade point average on a 4.0 scale, EMETRCS = 1 if student took econometrics, and EMETRCS = 0 otherwise.

i) Interpret the estimated equation.

ii) How would you modify the equation to see if women had lower starting salaries than men? (Hint: a dummy variable GENDER is defined as 1 if female; 0 otherwise)

iii) How would you modify the equation (3.1) to see if the value of econometrics was the same for men and women?

iv) What would happen if regression equation (3.2) is estimated? Justify your answer.

v) For those who took econometrics with CGPA 3.5, compute the starting salary(ssalary).

vi) Construct a 95% confidence interval estimate of the starting salary.

QUESTION 5

a) i) Define multicollinearity. 

ii) Let It be the exports at time t, GDPt be the gross domestic product and CPIt be the consumer price index. The estimation results are as follows:

Note: Values in parentheses are f-statistics.

Based on the information above, do you suspect that there is multicollinearity in Model 3? Explain.

iii) Refer to Model 3 and the information given in the above table, compute the variance inflation factor (VIF) and what is your conclusion?

iv) Discuss two (2) remedial measures to overcome multicollinearity.

b) Why is serial correlation considered as a serious problem?

c) How to detect autocorrelation using Durbin-Watson test?