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AEM702S - APPLIED ECONOMETRIC MODELLING - 1ST OPP - NOV 2022 |
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nAmlBIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURAL RESOURCESAND APPLIEDSCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelorof Sciencein Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL: 7
COURSE CODE: AEM702S
COURSE NAME: Applied Econometric Modelling
SESSION: November: 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER
FIRSTOPPORTUNITY EXAMINATION QUESTION PAPER
Prof. RakeshKumar
MODERATOR:
Prof. Peter Njuho
INSTRUCTIONS
l. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLEMATERIALS
l. Non-programmable calculator without a cover.
2. Statistical tables will be provided.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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Question 1. [Total Marks: 20]
(a) Discussthe method of indirect least squares.
{10 marks)
(b) In a two variable linear regression model, show that the variance of least square
/3-
cr2
estimator 2 is
.
L.. xi
{10 marks)
Question 2. [Total Marks: 20]
(a) Prove that the residuals Ui in the regression model~ = {30 + {31 Xi + iti are uncorrelated
with the predicted ~?
(10 marks)
(b) Discussthe method of generalized least squares in handling the problem of
heteroscedasticity.
(10 marks)
Question 3. [Total Marks: 20]
A real estate company (DLF) is interested to determine the relationship between the selling
price of a flat and its size. A sample of 10 flats is selected at random, the detail is given below.
Flat
Selling
Price
(1000s
NAO):Y
Size of
flat
(square
feet): X
245
1400
312
1600
279
1700
308
1875
199
1100
219
1550
405
2350
324
2450
319
1425
255
1700
(a) Find the regression equation of flat selling price on the size of flat. Predict the price for a
flat with 2000 square feet area.
(12 marks)
(b)What is the estimated change in the average value of flat selling price because of one unit
change in size of the flat?
(3 marks)
(c) Determine how much variation in flat prices is explained by variation in the size of the flat.
(5 marks)
Question 4. [Total Marks: 20]
(a) Discussthe Koyck's approach to distributed lag models.
{10 marks)
(b Discussthe estimation of parameters of a regression model in presence of perfect
multicollinearity.
{10 marks)
Question 5. [Total Marks: 20]
Given the following information on dependent variable Y and two independent variables X2
and X3:
Number of observations, n=15.
= Y- 1942.33, X- 2 = 2126.33, X- 3 = 8.0, IC~- Y- ) 2= 830121.33,
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I(X2i - X- 2) 2 = 1103111.33, L(X3i - -X3) 2 =280
l xx=
15
[31182905
31895
68922.513
272144
120
272144
1240
l Xy
=
29135
[62294075983241
37.2324 -0.0225
l (xX)- 1 = [-0.0225 0.00001
1.3367
-0.0008
1.3367 -0.0008 0.0540
y'y = 57,420
p Residual Sum of Squares (RSS),Lu/ = y'y- Xy =1976.8557
Explained Sum of Squares (ESS)=828144.4778
Total Sum of Squares (TSS)= 830121.333
Answer the following questions:
(a) Find p.
(b) Fit the regression model of Yon X2and X3.
(c) Find R2 •
(d) Develop ANOVA table and test the hypothesis H0 : {32 = /33 = 0.
(6 marks)
(4 marks)
(4marks)
(6 marks)
--------------------------------------END OF QUESTIONPAPER..................................................................
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