Exam (elaborations) Nursing course. ETF2100_5910_Assignment1_2020_S2_SOLUTION.pdf.pdf

ETF2100/5910 Introductory Econometrics
Assignment 1, Semester 2, 2020



IMPORTANT NOTES:

• Type your answers using Microsoft Word or write your answers clearly. You must submit a
PDF file to Moodle. Other file formats are not accepted.

• Notation used in the assignment needs to be typed or written correctly and properly. Marks
are also awarded for presentation.

• When doing calculation, keep at least 4 decimal in each step for precision. For final answer, 3
decimal point is sufficient, unless specified otherwise in the question.

• In this assignment, when you need to use t critical value, you can either find it using Eviews
or use the statistical table.

• This assignment is worth 20% of this unit’s total mark.

• ETF2100 students must answer Question 1B and Question 2.

• ETF5910 students must answer all question (i.e., Question 1A, Question 1B, and Question 2.)

• Total marks for ETF2100 and ETF5910 students are 60 and 70, respectively.

• Marks will be deducted for late submission on the following basis: 10% for each day late, up
to a maximum of 3 days. Assignments more than 3 days late will not be marked.




Question 1A: FOR ETF5910 ONLY (10 Marks)
*Please begin this question on a new page
For any sample of data (xi , yi ) with N observations:

(a) Show that (5 Marks)

N N N N
X X 1 X X
(xi − x̄)(yi − ȳ) = x i yi − xi yi (1)
i=1 i=1
N i=1 i=1

N
X N
X
Answer — (xi − x̄) (yi − ȳ) = (xi yi − xi ȳ − yi x̄ + x̄ȳ)
i=1 i=1
N
X XN N
X
= xi yi − ȳ xi − x̄ yi + N x̄ȳ
i=1 i=1 i=1


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, N N N N N N N
X 1 X X 1 X X 1 X 1 X
= xi y i − yi xi − xi yi + N xi yi
i=1
N i=1 i=1 N i=1 i=1 N i=1 N i=1
N N N
X 1 X X
= xi y i − xi yi
i=1
N i=1 i=1

(b) Show that (5 Marks)

N N N
!2
X X 1 X
(xi − x̄)2 = x2i − xi (2)
i=1 i=1
N i=1

N
X N
X
(xi − x̄)2 = x2i − 2xi x̄ + x̄2


Answer —
i=1 i=1
N
X XN
= x2i − 2x̄ xi + N x̄2
i=1 i=1
N N
!2 N
!2
X 2 X 1 X
= x2i − xi + xi
i=1
N i=1
N i=1
N N
!2
X 1 X
= x2i − xi
i=1
N i=1




Question 1B: For Both ETF2100 and ETF5910 (34 Marks)
*Please begin this question on a new page
In 2000, data were collected for 200 CEO Salaries (measured in millions of dollars) and their
company’s return on equity, RoE (measured in percent) over the previous three years. Consider the
following linear regression model.

Si = β1 + β2 Ri + ei (3)
where Si is the CEO’s salary, Ri is his/her company ROE, and ei is an error term, each for a CEO i.
You have no prior beliefs regarding the precise value of β2 . You obtain the following sample statistics:

200
X 200
X 200
X
Ri = 3110.9, Si = 500.3, Ri2 = 63786.9,
i=1 i=1 i=1
200
X 200
X
Ri Si = 10524.8, (Si − S̄i )2 = 419.2
i=1 i=1


(a) Using the information above and the fact that for any sample of data (xi , yi ) with N observations
the following relations hold:




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