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RAA602S - REGRESSION ANALSIS AND ANALYSIS OF VARIANCE - 2ND OPP - JANUARY 2025 |
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n Am I BI A uni VER s ITY
0 F SCIEnCE Ano TECHn OLOGY
-P
FacultoyfHealthN, atural
ResourcaensdApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
Statisticsand ActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: +264612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: BACHELOR of SCIENCE IN APPLIED MATHEMATICS AND STATISTICS
QUALIFICATION CODE: 07BSAM
COURSE: REGRESSION ANALYSIS AND ANALYSIS OF
VARIANCE
LEVEL: 6
COURSE CODE: RAA602S
DATE: JANUARY 2025
DURATION: 3 HOURS
SESSION: 1
MARKS: 90
SECOND OPPORTUNITY: EXAMINATION QUESTION PAPER
EXAMINER:
MODERATOR:
MR. ANDREW ROUX
DR. J. MWANYEKANGE
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
A TTACHEMENTS
1. Statistical Formulae Sheet
2. F - & t - Distribution Table
This paper consists of 4 pages including this front page
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QUESTION 1
[25]
1.1 From first principles, carefully (show all steps to) derive the Machine
Formula for computing the sample correlation coefficient, r from the raw
scores
(10)
1.2 Use a data set below to compute the sample correlation coefficient, r
(5)
Student
A
B
C
D
E
F
G
H
I
J
Subject X
9
8
7
6
6
5
5
4
3
2
Subject Y
3
2
5
5
4
7
6
6
6
7
1.3) Test the coefficient of correlation ( at a= 0.05) obtained in Question 1.2 (10)
QUESTION 2 [151
Use the following sample statistics to test a claim that differences exist between the
population means.
Sample 1
Sample 1
Sample 2
Sample 3
Sample Size
Sample Mean
n-
X
Sample Std
Dev.
Sx
49
45
29
8.36
7.91
9.02
2.98
3.15
3.62
Level of Sign. a = 0.05
REGRESSIONANALYSISAND ANALYSISOF VARIANCE(RAA602S)
2NoOpportunity January 2025
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QUESTION 3 [301
A recent survey conducted in the north western parts of Namibia, considered the
impacts of variables such as water consumption (liters), average daily temperature (
° C ) and wind speed (km/h) upon the heights (meters) of a random sample of
thirteen (13) Mopani trees.
Data as shown below, was collected over a period of one week. ( 1 - 7 June 2010)
Multiple Regression Model : y = bo+ b, x, b x + 2 2 b + 2 X3 + &
= = = Where, y Height (m) ; x, ave. water cons. (I) ; Xi average daily temperature
(C) ; x3 = wind speed (km/h) & & = Error of estimate
Tree
A
B
C
D
E
F
G
H
I
J
K
L
M
Height(M)
7.3
7.6
8.5
8.4
7.2
7.3
8.4
7.3
6.5
8.5
7.4
7.2
7.1
Water
Consumption (I)
15.2
17.3
16.6
16.1
15.2
15.3
16.6
15.7
13.6
14.2
15.1
14.5
14.7
Temo(°C)
19.8
20.1
20.2
20.2
19.8
20.5
20.4
20.4
17.2
21.8
20.7
20.9
19
Wind Speed
(km/h)
9.1
8.1
6.9
7.2
9.1
9.1
7
9
4.7
5.9
8.8
6
6.3
SUMMARY
OUTPUT
ReqressJOnStat/'St/'CS
Multiple R
a
R Square
0.72867958
Adjusted R
Square
0.63823944
Standard Error
0.387825876
Observations
b
ANOVA
Reqression
Residual
Total
df
ss
MS
F
3
C
1.211850194
f
9
1.353680188
d
12
e
REGRESSIONANALYSISAND ANALYSISOF VARIANCE(RAA602S)
2NDOpportunity January 2025
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Intercept
Water(!)
Temp ( °C)
Wind Speed
(km/h)
Coefficients
g
0.353675684
0.373454365
-0.216606917
Standard Error
2.423717 412
h
0.110691029
t Stat
-1.53889168
2.960164673
i
j
-2.54302051
P-va/ue
0.158213725
0.015955249
0.008206742
0.031554017
Consult the Microsoft Excel print-out to answer the following questions :
3.1) Find the following missing values, ( a - j )
3.2) Assess the fit of this model by considering the:
3.2.1) The Standard Error of Estimate (SEE)
3,2.2) The ANOVA table. ( use a= 0.01 )
( 2 X 10 = 20)
(3)
(7)
QUESTION 4 [ 201
The following table gives the number of refrigerators sold by 4 salesmen in three
months May, June, July.
Months
A
May
50
June
46
July
39
Salesmen
B
C
40
48
48
50
44
40
D
39
45
39
4.1) Is there a significant difference in the sales of refrigerator made by the four
salesmen?
(10)
4.2) Is there a significant difference in the sales of refrigerator made during
different months?
(10)
XXXXXXXXXXXXXXXEXNXDXXXXXXXXXXXXXXXXXXXXXX
REGRESSIONANALYSISAND ANALYSISOF VARIANCE(RAA602S)
2NDOpportunity January 2025
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F-table 0.05
Table of F-statistics P=0.05
1111~'~1'1'141'1'1'1'1'FFFFFFFFFFFFFFFFFFFFFFFFFFF I>1~~ 0 1000 1
~110.1319.ss
las4~ 19.2819.1219.01la.94 la.89la.as la.a1 la.79 la.76la.74 la.73 la.71 la.70la.69 la.6a la.67 la.67 la.66 la.6s la.64la.63 la.62 la.62 la.60la.s9 la.s9 la.sa la.s7 la.s7 la.s6 la.ss 1a.s4la.s3 la.s3
1
1~17.71
fs.63~ 16.9416.s916.3916.2l66.16l6.0916.o416.ools.96 ls.94 ls.91 1s.a9ls.a7 ls.a61s.a4 ls.a3 1s.a2ls.a1 ls.so ls.79 ls.77 ls.76 ls.?s ls.7s ls.73 ls.72 ls.71 ls.70 ls.69 ls.68 ls.67 ls.66 ls.65 ls.64 ls.63
1516.61 ls.79 ls.41 ls.19 ls.as 14.9514.aa14.8214.7714.7414.7104.6814.6614.6414.6214.6014.5914.5814.5714.5614.54l4.s314.s214.SO14.so14.4814.4614.4514.4414.4134.4214.4214.414.3914.3714.37143515
1~ls.99
i111s.s9
ls.1414.7614.5314.3914.2814.2114.1514.1014.0614.0314.0013.9813.9613.9413.9213.9113.9013.8813.8713.8613.84l3.a313.a213.a113.7913.771133.7.7641133.7.7s313.7213.7113.6913.6813.67
132317 14.7414.35j4.1213.9713.8713.7913.7313.6813.6143.6013.5713.ssj3.5313.5113.4913.4813.4713.4613.4413.4313.4113.4013.39j3.38j3.3613.3413.3313.3213.3103.2913.2913.2713.2s13.24l3.23
1r-s-1s.32 14.4614.0713.8143.6913.5813.so13.4413.3913.3513.3113.2813.2613.2413,2213.2013.1913.1713.1163.ls 13.1313.1213.loj3.09j3.oa 13.o613.o413.o313.0213.0112.9912.9912.9712.9s12.9412.93 f2.93r-s-
iutl9 119[s.u 14.26j3.8613.6313.4813.37j3.2913.2313.1813.1413.1103.0713,0513.0313.01j2.9912.9712.9612.9512.9412.9212.90j2.8912.8712.8612.84j2.83j2.81j2.8012.7912.7812.7712.76j2.7312.7212.71
,i1014.96
il1114.84
111214.75
14.1013.7113.4813.3313.2j23.1413.o713.0212.9812.9412.91l2.a9 12.86j2.8s 12.8312.a1j2.8012.7912.77lvs 12.7412.7212.7112.70l2.6aj2.66j2.6s 12.6412.6212.6112.60l2.s9 12.s612.ss12.54 P-54i10
~111 j3.9813.s913.3613.2013.0913.01l2.9s 12.90l2.8s 12.8212.7912.7612.7412.72lvo 12.6912.6712.66l2.6s 12.6312.61j2.s912.sa 12.s712.ssl2.s3 l2.s2 l2.s1 12.4912.4812.4712.4612.4312.4212,41
13.8913.4913.2613.113.oo12.9112.8s12.8012.7s12.7212.6912.6612.6412.6212.60l2.s8 l2.s7 l2.s6 l2.s4 l2.s2 l2.s1 12.49l2.4a12.4712.4412.4312.4112.4012.3812.3712.36l2.3s 12.3212.3112.30 !230112
111314.67
r1'114.6o
~14.54
1.~14.49
13.8113.4113.1813.0312.9212.a312.7712.7112.6712.6312.6012.s812.ss12.s3l2.s1 12.so12.4812.4712.4612.4412.4212.4112.3912.3812.3612.3412.3312.3112.3012.2812.2712.2612.2312.2212.21 jut113
fz.i3114 13.7413.3413.112.9612.8s12.76lvo 12.6s12.6012.s712.s312.s112.4a12.4612.4412.4312.4112.4012.3912.3712.3s12.3312.3212.3112.2812.2712.2s12.2412.2212.2112.2012.1912.1612.1412.14
13.6813.2913.0162.9012.7912.7112.64l2.s9 l2.s4 l2.s1 12.4812.4512.4212.4012.3812.3712.3512.3412.3312.3112.29j2.2712.26l2.2s 12.2212.2012.1912.1812.16l2.1s 12.1412.1212.1012.oa12.07 [2.o7~
13.6313.2413.012.8s12.7412.66l2.s9 l2.s4 12.4912.4612.4212.4012.3712.3512.3312.3212.3012.2912.28l2.2s 12.2412.2212.2112.1912.17l2.1s 12.1412.1212.1112.0912.0812.0712.0412.0212.02[2-ot~
11714.45
1il1814.41
11914.38
13.5913.2012.9612.8112.7012.6112.ss12.49l2.4s 12.4112.3812.3512.3312.3112.2912.2712.2612.2412.2132.2112.1912.1712.1612.11s 2.1212.1012.0912.0812.0612.os12.0312.0211.9911.97j1.97 ~117
[L92113 13.ss13.1612,9312.7712.66l2.s8 12.s112.4612.4112.3712.3412.3112.2912.2712.2s12.2312.2212.2012.1912.1712.1s12.1312.1212.1112.oa12.0612.os12.0412.0212.0011.9191.9811.9511.9311.92
13.5213.1312.9012.7412.63l2.s4 l2.4a 12.4212.3812.3412.3112.2812.2612.2312.2112.20l2.1a 12.1712.1612.1312.1112.1012.0812.0712.os12.0312.0112.0011.9811.9711.9611.9411.9111.8911.88 [LBs~
~14.35
f2214.30
rus-122 13.4913.1012.8712.7112.6l20.s1 l2.4s 12.3912.3s12.3112.2a12.2s12.2312.2012.11a2.1712.1s12.1412.1212.1012.0812.0712.1o2s.0412.0111.9911.9811.9711.9511.9311.9211l1.9.a18 l1.a6 l1.8s
13.4413.os12.8212.6612.ss12.4612.4012.3412.3012.2612.2312.2012.17121.21.s1312.1112.1012.0812.0712.1o2s.0312.0112.0011.9811.9611.9411.9211.9111.8911.8811.861111..a8s211.8011.79
[03124 112414.26 13.4013.0112.7812.62l2.s1 12.4212.3612.3012.2s12.2212.1812.1s12.1312.1112.0912.0712.os12.0412.0312.0011.9811.9711.9511.9411.9111.89l1.a8 11.8611.84l1.a3 l1.a211.8011.7711.7511.74
112514.23 13.3712.9812.74l2.s912.4712.3912.3212.2712.2212l.21.81s 12.1212.0912.0712.o1s2.0312.0212.0011.9911.9711.9511.9311.9111.9011.871l11..aas411.8211.Bo11.7911.7811.7611.7311.7111.7[01.69125
;f'2s [ii6f'2s 14.20 13.3412.9slv1 12.s612.4512.3612.2912.2412.19l2.1s 12.12j2.0912.0612.04j2.0212.0011.9911.9711.9611.9311.9111.9011.8811.8711.8411.8211.8011.7911.77l1.7s 11.7411.7311.6911.6711.66
f3clj4.1713.32 j2.9212.69l2.s3 12.4212.3312.2712.2112.1612.1312.0912.0612.0412.01j1.9911.9811.9611.9511.93j1.9111.8911.87l1.8s 11.8411.8111.7911.7711.7611.7411.72j1.7111.7011.6611.6411.63 [ii2[3c>
~135 f3"sl4.12 13.2712.a712.6412.49j2.3712.2912.2212.1612.11j2.0812.0412.0111.9911.96jl.9411.9211.91l1.a91l1.88s l1.a3j1.8211.8011.7911.7611.7411.7211.7011.6811.l616.6s 11.5311.60l1.s7 l1.s7
lf4o ~!40 14.08 13.2312.8412.6112.4s12.34l2.2s 12.1812.1212.0812.0412.0011.97j1.9s 11.9211.9011.8911.87l1.8s 11.8411.8111.7911.7711.7611.74ji.72 j1.6911.6711.6611.6411.6121.61l1.s911.ss l1.s3 l1.s2
1145 ~145 j4.06 13.2012.81j2.s8 12.42j2.3112.2212.1s12.1012.os12.0111.9711.9411.9211.8911.8711.86ji.8411.8211.8111.7811.7611.7411.7311.7111.6811.6611.5411.6311.60l1.s9 l1.s711.ss l1.s1 11.4911.48
rso14.03 13.181v9 12.s612.4012.2912.2012.1312.0712.0311.9911.9s11.9211.8911.8711.8s11.8311.8111.8011.7811.7611.7411.7211.7011.6911.6611.6311.6111.60l1.s8 l1.s6 l1.s4 11.s211.4811.45jl.4s ~[so
V-~ 1
;!6014.oo 13.1512.7512.s312.37l2.2s j2.1712.10j2.04j1.99l1.9s 11.92l1.a9 11.8611.8411.8211.aoj1.7811.76j1.7s 11.7211.7011.6811.66l1.6s 11.62j1.s9 l1.s7 j1.s6 l1.s3 j1.s2 11.so11.4811.4411.4111.40
f7o [usf?o 13.98 13.1312.7412.soj2.3s 12.2312.1412.0712.0211.9711.9311.89j1.8611.84j1.8111.7911.77l1.7s 11.7411.7211.7011.67l1.6s jl.64 j1.62j1.s9 l1.s7 11.ssl1.s3 11.so11.4911.4711.4511.4011.37ju6
1
113Jrso- '.j7io j3.96 j3.ll 12.7212.4912.3312.2112.1312.0612.00j1.9s 11.9111.88jl.84 11.82jl.79 ji.77 11.7511.7311.7211.7011.68l1.6s 11.6311.6211.60l1.s7 l1.s4 l1.s2 l1.s1 11.4811.46l1.4s 11.43lu8 lus jl.34
if"Tooj3.94 j3.09lvo 12.4512.31j2.1912.10jz.03 11.97j1.93j1.89l1.8s j1.8211.7911.77j1.7s 11.7311.7111.6911.6811.6511.5311.61l1.s9 l1.s7 l1.s4 l1.s211.4911.4811.4511.4311.4111.3911.3411.31luo [us~
'fToo13.89 13.0412.6s12.4212.2612.1412.0611.9811.9311.8811.8411.80j1.7711.7411.7211.6911.6711.6611.6411.6211.60l1.s711.ss l1.s3 l1.s2 11.48jl.46 11.43j1.4111.3911.36lus lu211.26 11.22[l.21[1.igf"Too
ifsoo\\3.86 13.0112.6212.3912.2312.1212.0311.9611.90l1.8s 11.8111.7711.7411.7111.6911.6611.6411.6211.61l1.s9 l1.s6 l1.s4 l1.s2 11.so11.48l1.4s 11.4211.40lu8 11.35lu2 luo 11.2811.2111.1611.14 [t.i2fsci"(l
fu1[1.0il 111000 13.85 13.oo12.6112.3812.2212.1112.02l1.9s l1.a911.8411.8011.7611.7311.7011.68l1.6s 11.6311.6111.60l1.s8 11.ssl1.s3 l1.s1 11.4911.4711.4311.41lu8 11.3611.33lu1 11.2911.2611.19l1.13
j 1000
'I> I> 1000 11.04 13.oo12.6112.3712.2112.1012.01jl.94 11.8811.8311.79l1.7s 11.7211.6911.6711.6411.6211.61l1.s9 l1.s7 l1.s4 l1.s2 11.so11.4811.46j1.4211.40lu7 lus luz luo 11.28l1.2s 11.1711.1111.08 [i:o3 1000
:11 ~1~'1'1'141'1'1'1'1'FFFFFFFFFFFFFFFFFFFFFFFFFFol
I1000 1000
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t Table
cum. prob
one-tail
two-tails
df
1
2
3
4
5
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
60
80
100
1000
z
t .50
0.50
1.00
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.900
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0%
t .75
0.25
0.50
t .BO
0.20
0.40
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703 ..
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688•
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.681
0.679
0.678
0.677
0.675
0.674
50%
1.376
1.061
0.978
0.941
0.920
0.906
o'.896
0.889
0.883
0.879
0.876
0.873
0.870
0.868
0.866
0.865
0.863
0.862
0.861
0.860
0.859
0.858
0.858
0.857
0.856
0.856
0.855
0.855
0.854
0.854
0.851
0.848
0.846
0.845
0.842
0.842
60%
t .85
0.15
0.30
t .90
0.10
0.20
t .95
0.05
0.10
t .975
0.025
0.05
t .99
0.01
0.02
t .995
0.005
0.01
t .999
0.001
0.002
t .9995
o.ooosj
0.001
1.963
1.386
1.250
1.190
1.156
1.134
1.J 19
1.108
1.100
1.093
1.088
1.083
1.079
1.076
1.074
1.071
1.069
1.067
1.066
1.064
1.063
1.061
1.060
1.059
1.058
1.058
1.057
1.056
1."055
1.055
1.050
1.045
1.043
1.042
1.037
1.036
70%
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1:333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
. 1.310
1.303
1.296
1.292
1.290
1.282
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1:~60•·
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.684
1.671
1.664
1.660
1.646
12.71
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.021
2.000
1.990
1.984
1.962
1.282 1.645 1.960
80% 90% 95%
Confidence Level
31.82
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
· 2.583
2.567
2.552
2.539.
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.390
2.374
2.364
2.330
2.326
98%
63.66
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779'
2.771
2.763
2.756
2.750
2.704
2.660
2.639
2.626
2.581
2.576
99%
318.31
22.327
10.215
7.173
5.893
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.505
3.485
3.467
3.450
3.435,
3.421
3.408
3.396
3.385
3.307
3.232
3.195
3.174
3.098
3.090
99.8%
636.62
31.599
12.924
8.610
6.869
4.437
4.318
4.221
4.140
4.073
4.015/
3.965
3.922
3.883
3.850
3.819
3.792
3.768
3.745
3.725
3.707
3.690
3.674,
3.659
3.646
3.551
3.460
3.416
3.390
3.300
3.291
99.9%
t-table.xls 7/14/2007