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RAA602S - REGRESSION ANALYSIS AND ANOVA - 2ND OPP - JANUARY 2024 |
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n Am I B I A uni VE Rs I TY
OF SCIEnCE Ano TECHnOLOGY
FacultyofHealth,Natural
ResourceasndApplied
Sciences
Schoolof NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
PrivJte Bug13388
Windhoek
NAMIBIA
T: •264 61207 2913
E: ms.is@nust.na
\\N: 1Nww.nust.na
QUALIFICATION: BACHELOR OF SCIENCE IN APPLIED MATHEMATICS AND STATISTICS
QUALIFICATION CODE: 07BSAM
LEVEL: 6
COURSE:REGRESSION ANALYSIS AND ANOVA
COURSE CODE: RAA602S
DATE: JANUARY 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY/ SUPPLEMENTARY: EXAMINATION QUESTION PAPER
EXAMINER:
MODERATOR:
Mr Simon Pombili Kashihalwa
Prof Rakesh Kumar
INSTRUCTIONS:
1. Answer all questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the examiner.
4. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator
ATTACHEMENTS
1. F-Table
This paper consists of 4 pages including this front page
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QUESTION 1 (46]
1.1. For each of the following models state whether its parameters can be estimated
using standard linear regression techniques. If linear regression can be used, what
are the independent and dependent variables that should be used?
= a) Yi /Jo+ ePix,+e
[lJ
= --- b) Yi
1
Po+f31x,+c,
(3J
= c) Yi /Jo+ /J1x1 1 + /32xi2 where /32 is known to be 5.
[3J
1.2 A researcher is researching whether or not birds of prey exposed to pollutants lay eggs
with thinner shells. He collects a random sample of egg shells from each of 6 different
nests and tests for pollutant level, p and measures the thinning of the shell, t. the results
are shown in the table below
3
1
1
I
I
:I
~I
I
~I
~I
a) Explain why linear regression model may be appropriate to describe the relationship
between p and t.
[2J
b) Calculate the coefficient of correlation.
[SJ
c) Find the equation of the regression line.
[8J
d) The scientist reviews similar studies and finds that pollutant levels above 16 are
likely to result in the death of a chick soon after hatching. Estimate the minimum
thinning of the shell that is likely to results in the death of a chick.
[2]
1.3 Here is some SPSSoutput from the multiple linear regression with independent variables
slope, porosity, and cover.
Source DF
Model
Error
Total
Dependent variable: Soillost
Sum of squares Mean square
3
680.68178
F-
Value
10
696.58545
Pr>F
<.0001
Variable
Intercept
Slope
Porosity
Cover
Parameter Estimates
DF
Parameter Standard error t-value
1 -1.59534
-0.08841628
1 76.45678
44.29509
1 1.57585
2.154979077
1 -23.77054
-1. 78108244
Pr> it I
0.932
0.128
0.0681
0.1181
a) Complete the ANOVA table.
b) Compute coefficient of determination.
Regression Analysis and ANOVA (Course Code)
(SJ
[2]
2nd Opportunity- January 2024 2
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c) Compute the adjusted coefficient of determination.
(2]
d) Compute the missing standard errors and the t-values.
(4]
e) Using matrix form, state the fitted multiple linear regression model.
(S]
f) Use ANOVA to test the significance of the regression coefficients.
[4]
Question 2 (54)
2.1
Six different machines are being compared for use in manufacturing jackpots ram. The machines
are being compared with respect to durability and performance of the ram. A random sample of
4 rams from each machine is used to determine whether the mean durability and performance
varies from machine to machine.
Machine
1
2
3
4
5
6
17.5
16.4
14.3
14.6
17.5
11.9
16.9
19.2
13.5
16.7
19.2
15.1
15.8
17.7
11.8
20.8
16.5
14.3
18.6
15.4
10.5
18.9
20.5
16.8
Perform the analysis of variance at 0.05 level of significance and indicate whether or not the
mean durability and performance differ significantly for the six machines.
[18]
2.2
Assume that, in Windhoek between 2000 and 2008, the growth curve of internet subscribers is of
= the form Y aebxand that the following data were observed.:.
Year
# of internet subscribers
2000 2001 2002 2003 2004 2005 2006 2007
498 872 1527 2672 4677 8186 14325 25069
2008
43871
a) Find the regression coefficients a and b . Hint use the sequential method to code the
variable time, start with x =1 for 2000.
[21]
b) Predict the number of internet subscribers after four years.
[4]
Regression Analysis and ANOVA(Course Code)
2nd Opportunity- January 2024 3
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2.3
The ministry of safety and security carried out a study to identify factors associated with an
individual owning a gun or not, factors such as Sex, Age, Race,education were assessand the
model output presented below.
Variables in the equation
Variable
Male
Female*
B
-0.78
Age
0.02
White
Black*
1.618
Educat
-0.23
Constant -2.246
•Reference variable
S.E
0.124
0.004
0.197
0.02
0.363
Wald
39.624
32.65
67.534
1.37
38.224
OF sig
1
1
1
1
1
Odds Ratio
0.000
0.000
0.000
0.242
0.000
a) Construct the 9S% confidence interval for each parameter.
b) Estimate the odds for each parameter.
c) Write down the estimated model.
END
OR95%
Cl
[SJ
[SJ
(1)
Regression Analysis and ANOVA (Course Code)
2nd Opportunity- January 2024 4
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