23571: INTRODUCTORY ECONOMETRICS
SPRING SEMESTER, 2015
ASSIGNMENT PART A (INDIVIDUAL ASSESSMENT)
COVER SHEET
Due Thursday September 10 2015, 17:00
This assignment is worth 10% of your final grade.
Limit your answer to 5 pages (single-sided).
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“Economics 1”, which is located on level 5 of Chau Chak Wing building. The exact
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23571 Introductory Econometrics
Spring 2015
Assignment A
You must attach the coversheet to your answers. Read the instructions on the
coversheet. Try to keep your answers short and clear. Questions (h) and (i)
require knowledge from “Two-variable regression: hypothesis testing”. This
assignment has a total of 10 marks.
In an earlier tutorial, you were introduced to a data set that came from a job training
experiment conducted for low-income men in the United States in 1976. In this
question, you are given extra information for 5 individuals in the data set. The data is
given as follows:
Observation
1
2
3
4
5
re78
9.93
3.59
24.90
7.50
0.28
educ
11
9
12
11
8
age
37
22
30
27
33
You will operate on the above data of 5 observations throughout this assignment. The
variables are defined as follows:
re78 = earnings in 1978, measured in thousand dollars
educ = years of education
age = individual’s age in years
(a)(1pt) Reconstruct the following frequency table on your answer sheet and fill in the
missing information.
Age<30
Age>=30
Educ<10
Educ>=10
(b)(1pt) Reconstruct the following table on your answer sheet. Compute an estimate
of the following conditional means.
Answer
E(re78|educ=12)
E(re78|educ<10)
E(re78|educ<10 and age<30)
E(re78|educ>=8 and age<40)
(c)(1pt) Compute the sample variance of age, as well as the sample covariance
between re78 and age.
(d)(1pt) Use the OLS formula in lecture 2 to compute the sample regression line of
the regression of re78 on age. (Note: round your answers to 3 significance figures)
(e)(1pt) Suppose you regress re78 on age using observation 1 only. What result will
you get? Briefly explain why this result occurs.
(f)(2pt) Suppose the population model is
re78 = 1 + 0.2*age + u.
On your answer sheet, reconstruct the following table and fill in the missing
information.
Observation re78 (Y)
age (X)
E(Y|X)
u
1
2
3
4
5
37
22
30
27
33
8.4
1.53
9.93
3.59
24.90
7.50
0.28
Predicted
Y( )
Residual
(
(g)(1pt) In part (f), observation 3 has a very large positive random error (u). Does it
imply that the population model is incorrect? Briefly explain.
(h)(1pt) This question continues part (d). The rest of the estimation result is:
78
se:
(28.75)
t-stat: (0.097)
p-val: (0.929)
*
(0.951)
(0.228)
(0.834)
Briefly interpret the coefficients (values given in part (d)) and the p-values in this
regression.
(i)(1pt) We are interested in testing the following hypothesis:
H0: ?age = 0.2; H1: ?age ? 0.2
With the aid of a statistical table, find the critical value associated with a significance