HARAMAYA UNIVERSITY
COLLEGE OF CONTINUING AND DISTANCE EDUCATION
DEPARTMENT OF ECONOMICS
ASSIGNMENT FOR THE COURSE INTRODUCTION TO ECONOMETRICS
For Economics Department Students
STUDENT INFORMATION:
NAME: ______________________________________
DEPARTMENT: ______________________________
I.D. No: _____________________________________
CENTER: ____________________________________
1
Part I: Discussion Questions
Discuss the following question briefly
1. Define econometrics. (1 pts)
2. Explain the difference between correlation and causation. (1 pts)
3. How many types of economic data are there and explain them briefly. (1 pts)
4. Briefly explain the classical assumptions of the ordinary least square (OLS) method of
estimation and the problem of its violation. (2 pts)
PartII: Work out Questions
Workout the following question and show all the necessary steps
1. Show the mathematical derivation of the coefficients of a simple linear regression
function using the ordinary least square (OLS) method. (Show all the necessary steps).
(4 pts)
2. Suppose a researcher is using data for a sample of 200 employees to investigate the
relationship between hourly wage rates Yi (measured in birr per hour) and the firm’s
year of operation or tenure Xi (measured in years). Preliminary analysis of the sample
data produces the following sample information:
N = 200
Where,
=
-
for i = 1, 2, ..., N.
Use the above sample information to answer all the following questions. (Show
explicitly all formulas and calculations.)
a. Use the above information to compute OLS estimates of the intercept coefficient β 0
and the slope coefficient β1 (2 pts)
b. Interpret the slope coefficient estimate you calculated in part (a) -- i.e., explain in
words what the numeric value you calculated for
2
means. (1 pts)
c. Compute the value of R 2, the coefficient of determination, for the estimated OLS
sample regression equation. Briefly explain what the calculated value of R2 means.
(2 pts)
d. Using the sample value of the t-statistic, test the null hypothesis H0: β1 = 0 against
the alternative hypothesis H1: β1 ≠ 0 and draw inference. (Use
) = 0.03 and
level of significance = 0.05 ) (2 pts)
3. Estimate the spearman’s rank correlation coefficient and determine the nature of
hetroskedasticity for the hypothetical relationship between quantity demanded and
income for 20 observations. The sum of the square of the difference in rank between
the explanatory variable and error term is given by 1316. ( 2 pts)
4. Based on the following information answer questions number A through D
No
C(consumption)
Id (disposable income)
1
10600
12000
2
10800
12000
3
11100
13000
4
11400
13000
5
11700
14000
6
12100
14000
7
12300
15000
8
12600
15000
9
13200
16000
10
13000
16000
11
13300
17000
12
13600
17000
Test the existence of hetroskedasticity using the technique of Goldfeld Quandt by
dropping 1/3 of the observations from the middle.
3
A. Estimate the βs for both regressions. (3 pts)
B. Predict the value of the dependent variable(C) and calculate the residual value.
(3 pts)
C. Calculate the residual sum of square for both regressions. (2 pts)
D. Compare the F calculated of manipulation with the F tabulated value (at 5% level
of significant, 2 numerator degree of freedom and 2 denominator degree of
freedom the table value is 19) and what is your decision regarding to the
existence of hetroscedasticity. (2 pts)
5. Ayele one of the students of Economics in Haramaya University (Harar center) wants to
study the consumption pattern of Harar dwellers by formulation his simple regression
model as consumption (Y) is a function of family income(X1) and husband income(X2).
In addition he also found that there is a functional relationship between X1 and X2. The
predicted value of is given by
X̂ 1 = 2.34+ 0.095 X2 with R2=0.98
A. Define the concept of munticollinearity based on the above information (1 pts)
B. Is that possible to test the problem of multicollinearity based on the given
information (1 pts)
C. If your answer for the above question is yes test the existence of
multicollinearity with the appropriate tools. (1 pts)
4