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).
The assignment should be submitted to the assignment drop box named
“Economics 1”, which is located on level 5 of Chau Chak Wing building. The exact
location will be announced as soon as possible on UTS:Online. No late submissions
will be accepted. Please ensure that the coversheet is attached. The assignment
must be stapled with the coversheet. Write your name and student number at the
top of each page of the answer sheet.
In our experience, neater assignments receive higher marks, conditional on content.
As such, you are strongly encouraged (but not required) to type your assignments.
Mathematical symbols and formulas can remain hand-written.
Although you are allowed to verify your answers using statistical software, to help
yourself prepare for the examinations you are strongly encouraged to attempt the
assignment questions without the aid of statistical software. You can use a calculator
to answer the questions.
Please complete the declaration and list the student number and name of the
student contributing to this assignment.
Declaration
We hereby certify that this assignment is our own work, based on our personal study
and/or research and that we have acknowledged all material and sources used in the
preparation of this assignment. We also certify that the assignment has not
previously been submitted for assessment and that we have not copied in part or
whole or otherwise plagiarised the work of other students or authors.
Student Number

Family Name

First Name

Signature

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

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).
The assignment should be submitted to the assignment drop box named
“Economics 1”, which is located on level 5 of Chau Chak Wing building. The exact
location will be announced as soon as possible on UTS:Online. No late submissions
will be accepted. Please ensure that the coversheet is attached. The assignment
must be stapled with the coversheet. Write your name and student number at the
top of each page of the answer sheet.
In our experience, neater assignments receive higher marks, conditional on content.
As such, you are strongly encouraged (but not required) to type your assignments.
Mathematical symbols and formulas can remain hand-written.
Although you are allowed to verify your answers using statistical software, to help
yourself prepare for the examinations you are strongly encouraged to attempt the
assignment questions without the aid of statistical software. You can use a calculator
to answer the questions.
Please complete the declaration and list the student number and name of the
student contributing to this assignment.
Declaration
We hereby certify that this assignment is our own work, based on our personal study
and/or research and that we have acknowledged all material and sources used in the
preparation of this assignment. We also certify that the assignment has not
previously been submitted for assessment and that we have not copied in part or
whole or otherwise plagiarised the work of other students or authors.
Student Number

Family Name

First Name

Signature

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