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RAA602S - REGRESSION ANALYSIS AND ANALYSIS OF VARIENCE - 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: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL: 7
COURSECODE: RAA602S
COURSE NAME: REGRESSIONANALYSISAND
ANALYSISOF VARIENCE
SESSION: NOVEMBER 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER
FIRSTOPPORTUNITY EXAMINATION QUESTION PAPER
Mr SP. KASHIHALWA
MODERATOR:
Prof R KUMAR
INSTRUCTIONS
1. 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
1. Non-programmable calculator without a cover.
2. Attached statistical tables(t-table and F-table)
THIS QUESTION PAPER CONSISTS OF 4 PAGES (Including this front page)
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Question 1 [13]
A police authority conducts an eight week experiment. In each week it records the number of
foot patrols, x in a small town and the number of reported crimes, yin that town. The data
are summarized as follows.
L L L x = 52
x 2 = 380
xy = 13 35
LY L = 225
y 2 = 7007 n = 8
1.1 Calculate the value of correlation coefficient for these data and interpret your answer [6]
1.2 Test the significance of the value in 1.1, use a = 0.05
[7]
Question 2 [19]
The following table shows the hours of sunshine during nine days in August and the number
of ice cream sold by a beach shop in Swakopmund.
Sunshine
4.3
6.9
0
10.4
5.2
1.8 is
I 9.2
I 2.1
I
Ice cream
224
208
123
419
230
184
I 362
I 351
J 196
I
2.1 Calculate the equation of the regression line and interpret it
[9]
2.2 Calculate the residuals for the days when the number of hours of sunshine was:
(i) 8.0
[2]
(ii) 6.9
[2]
2.3 On one of the days the shop closed early to allow the owner to attend a wedding. Suggest,
giving reason, which day was this
[2]
2.4 Use the regression equation to estimate the daily sales if there were 20 hours of sunshine.
Give two reasons why it would be inappropriate to do this.
[2]
2.5 If the equation in 2.1 is of the form Y = aebx_Will you use OLSto estimate the unknown
parameters and suggest any remedial action
[2]
2
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Question 3 [251
Variable
C
EDUC
EXP
FEMALE
MARRIED
R-squared
F-Statistics
Prob(F-statistic)
Adjusted R-squared
Dependent variable:Wage
Method: Least
square
Date: 15 /09/22 Time: 15h00
Sample: 1526
coefficients
Std. Error
t-statistics
-1.790662
0.751212
-2.383697
0.583323
0.051656
11.29246
0.055666
0.011055
5.03528
-2.067101
0.272208
-7.593839
0.660242
0.296851
2.22415
0.33158
Akaike info criterion
60.11832
Schwarz criterion
0
Hanna-Quinn Criterion
0.310547
DW stat.
Prob
0.0175
0.000
0.000
0.000
0.0266
5.088405
5.12895
5.10428
1.807244
3.1 Write the equation that was estimated from the above model output ( give your answer in 2
decimal places)
[6]
3.2 Interpret the coefficient of determination
[2]
3.3 Which information criterion was used to estimate the results above
[2]
3.4 Test the significance of EXPat 5% significant level
[7]
3.5 Interpret the coefficients of all exogenous variable
[8]
Question 4 [251
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
4.1 Find the regression coefficients a and b . Hint use the sequential method to code the
variable time, start with x =1 for 2000.
[21]
4.2 Predict the number of internet subscribers after four years
[4]
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Question 5 [18]
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]
4
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Numbers in each row of the table are values on a t•distributionwith
(df)degrees of freedom for selected right-tail(greater-thanl probabilities(p}.
df/p 0,40
0.25
0.10
0.05
0.025
1 0.324920 1.000000 3.0776B4 6.313752 12.70620
2 0.288675 0.816497 1.885618 2.919986 4.30265
3 0.276671 0.764892 1.637744 2.353363 3.18245
4 0.270722 0.740697 1.533206 2.131847 2.77645
5 0.267181 0.726687 1.475884 2.015048 2.57058
6 0,264835 0.717558 1.43975£ 1.943180 2.44691
7 0,263167 0.711142 1.414924 1.894579 2.36462
.
...
8 0,261921 0.706387 1.396815 1.859548 2.30600
9 0,260955 0.702722 1.383029 1.833113 2.26216
10 0,260185 0.699812 1.372184 1.812461 2.22814
11 0.259556 0.697445 1.363430 1.795885 2..20099
12 · 0.259033 0.695483 1.356217 1.782288 2.17881
13 ' 0,258.591 0.6938:29 1.350171 1,7709:!3 2J6037
14 0.258213 0.692417 1.3•15030 1.761310 2.14479
15 0.257885 0.691197 1,340606 1.753050 2.13145
16 0.257599 0.690132 1.336757 1.745884 2.11991
17 0.257347 0.689195 1.333379 1.739607 2.10982
18 0.257123 0.688364 1.330391 1.734-064 2.10092
19 , 0.256923 0.687621 1.3277213 1.729133 2.09302
20 0.256743 0.&86954 1.325341 1.724718 2.08596
21 0.256580 0.686352 1.323188 1.720743 2.07861
22 0,256:432 0.685805 1.321237 1.717144 2,07387
23 0.256297 0.685306 l.31946{1 1.713B72 2.06866
24 0.256173 0.684850 1.317836 1.710882 2.06390
25 0.256060 0.684430 1.316345 1.708141 2.05954
26 , 0.255955 0.684043 1.314972 1.705618 2.05553
2.7 0.255858 0.683685 1.313703 1.703288 2.05183
28 0,255768 0.683353 1.312527 1.701131 2.048•l1
29 0,255684 0.683044 1..311434 1.69S127 2,0•l523
30 . 0,255,605
z 0,253347
Cl --
0.682756 1,310415
I 0.674,490 1.281552
80%
1,697261
1.644854
90%
2.04227
1.95996
95%
0.01
31.B2052
6.96456
4.54070
3.74695
3.36493
3.14267
2.99795
2.89646
2.82144
2.763n
2.71808
2.6810D
2,65031
2,62449
2,60248
2.58349!
2.56693
2.55238
2.53-948
2.52798,
2.51765
2.50.832
2.49987
2.49216
2.4851l
2.47863
2.47266
2.46714
2,46202
2.45726
2.32635
98%
0.005
63.65674
9.92484
5,84091
4.60409
4.03214
3.70743
3.49948
3,35539
3.24984
3.16927
3.10581
3.05454
3.01228
2.97684
2.94671
2,92078
2,89823
2.87844
2,860'93
2.84534
2.83136
2,81876
2.80734
2.79694
2.78744
2.77871
2.77068
2.76326
2,75639
2,75000
2'.57583
S9%
0.0005
636.6192
31.5991
12.9240
8.6103
6.8688
5.9588
5.4079
5,0413
4.7809
4,5869
4.4370
43178
4.2208
4.11\\05
4,0728
4.0150
3.9651
3.9216
3.8834
3,8495
3,8193
3,7921
3.7676
3.7454
3.7251
3.7066
3.6896
3,6739
3.659~
3,6460
3.2905
99.9%
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Critical Values of the F-Distributioll: a= 0.05
Denom.
d.f.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
2G
26
27
28
29
:io
31
:i2
33
;34
35
:3G
37
38
39
40
41
42
4:3
44
45
4G
47
48
4!)
50
60
70
80
90
100
120
140
180
200
(X)
161.448
18.513
10.128
7.709
6.608
5.987
5.591
5.318
5.117
4.9G5
4.844
4.747
4.GG7
4.600
4.543
4.494
4.451
4.414
4.381
4.:l51
4.325
4.:301
4.279
4.2G0
4.242
4.225
4.210
4.19(i
4.183
4.171
4.160
4.14!)
4.139
4.1:lO
4.121
4.11:l
4.105
4.098
4.091
4.085
4.079
4.07:l
4.067
4.062
4.057
4.052
4.047
4.043
4.038
4.034
4.001
3.978
3.!JG0
3.!J47
:J.!)3(i
3.920
3.!J[)!)
3.894
:i.888
3.841
2
199.500
19.000
!l.552
6.944
5.786
5.14:3
4.737
4.459
4.256
4.10:.l
:.l.982
3.885
3.80G
3.7:.l9
3.682
3.634
3.5!l2
:.l.555
3.522
:.l.493
:l.467
:.l.44:.l
3.422
3.40:J
3.385
:.l.369
3.354
:.l.340
3.328
3.:316
3.305
3.295
3.285
:l.276
3.267
3.259
3.252
3.245
3.238
3.232
3.226
:l.220
3.214
3.209
3.204
:i.200
:.l.195
3.191
3.187
3.183
3.150
3.128
3.111
3.098
3.087
3.072
:.l.061
3.046
:1.041
2.996
3
215.i07
19.164
!J.277
6.591
5.409
4.757
4.347
4.066
3.8G:l
:l.708
:.l.587
3.490
3.411
3.344
3.287
3.239
3.197
:.l.160
3.127
:.l.0!l8
3.072
:.l.041)
3.028
3.00!l
2.991
2.975
2.960
2.!J47
2.934
2.922
2.91 l
2.!l0l
2.892
2.88:l
2.874
2.8(i(i
2.859
2.852
2.845
2.839
2.833
2.827
2.822
2.816
2.812
2.807
2.802
2.7!)8
2.7!l4
2.790
2.758
2.736
2.71!)
2.706
2.G!JU
2.680
2.GCi9
2.65G
2.Hci0
2.605
Numerat.or Degrees of Freedom
4
5
6
7
224.58'.l
19.247
9.117
6.388
5.192
230.162
19.296
!l.013
6.256
5.050
2:l:.l.986
19.330
8.!)41
6.163
4.950
2:i6.768
19.353
8.887
6.094
4.876
4.534
4.120
3.838
3.G33
3.478
4.387
3.!l72
3.687
:l.482
:.l.:.l26
4.284
3.8GG
3.58l
3_;174
3.217
,1.207
3.787
3.500
3.293
3. l:l5
:.l.357
3.259
3.179
:.l.112
3.056
3.204
3.106
:3.025
2.958
2.901
3.095
2.996
2.!ll5
2.848
2.790
3.012
2.913
2.832
2.764
2.707
3.007
2.!l65
2.928
2.895
2.866
2.852
2.810
2.77:.l
2.740
2.711
2.74l
2.69!)
2.6Gl
2.628
2.59!J
2.657
2.614
2.577
2.544
2.514
2.840
2.817
2.7!l6
2.776
2.759
2.685
2.661
2.6,10
2.621
2.603
2.573
2.549
2.528
2.508
2.400
2.488
2.4(i4
2.442
2.42:J
2.405
2.74:.l
2.728
2.714
2.701
2.G!l0
2.587
2.572
2.558
2.545
2.5:34
2.474
2.459
2.445
2.432
2.421
2.388
2.373
2.359
2.346
2.:134
2.679
2.G68
2.659
2.650
2.641
2.523
2.512
2.503
2.494
2.485
2.il09
2.:.l!J9
2.389
2.380
2.372
2.323
2.:31:i
2.303
2.2!)4
2.285
2.G34
2.626
2.GHl
2.612
2.606
2.477
2.470
2.4G3
2.456
2.449
2.364
2.356
2.:l49
2.342
2.336
2.277
2.270
2.2G2
2.255
2.249
2.600
2.594
2.589
2.584
2.57!)
2.443
2.4'.l8
2.432
2.427
2.422
2.330
2..124
2.:.ll8
2.313
2.308
2.243
2.237
2.232
2.226
2.221
2.574
2.570
2.5G5
2.561
2.557
2.417
2.413
2.40!)
2.404
2.400
2.304
2.299
2.295
2.2!J0
2.286
2.216
2.212
2.207
2.203
2.199
2.525
2.503
2.486
2.473
vw:i
2.368
2.346
2.329
2.316
2.305
2.254
2.231
2.214
2.201
2.l!Jl
2.167
2.143
2.126
2.ll3
2.103
2.447
2.43G
2.422
2.417
2.290
2.279
2.264
2.25!)
2.175
2.1Ci4
2.149
2.144
2.087
2.076
2.061
2.056
2.372
2.214
2.099
2.010
8
238.883
19.371
8.845
6.041
4.818
,1.147
3.72G
3.438
3.2:l0
:.l.072
2.948
2.849
2.767
2.69!)
2.641
2.591
2.548
2.510
2.477
2.447
2.420
2.3!)7
2.375
2.:.l55
2.337
2.:.l21
2.305
2.291
2.278
2.266
2.255
2.244
2.235
2.225
2.217
2.209
2.201
2.Hl4
2.187
2.180
2.174
2.1G8
2.163
2.157
2.152
2.147
2.143
2.138
2.134
2.130
2.097
2.074
2.056
2.0,J3
2.032
2.016
2.005
1.990
1.!185
1.938
9
240.543
19.385
8.812
5.999
4.772
4.099
:l.G77
3.388
3.179
:i.020
2.8!Hi
2.796
2.714
2.646
2.588
2.538
2.4!l4
2.456
2.423
2.3!l:.l
2.:l66
2.:.l42
2.320
2.300
2.282
2.2Ci5
2.250
2.23(i
2.223
2.211
2.199
2.189
2.179
2.170
2.161
2.153
2.145
2.1:18
2.131
2.124
2.118
2.112
2.lOCi
2.101
2.096
2.mn
2.086
2.082
2.077
2.073
2.040
2.017
l.9!J!J
l.!)86
l.!)75
l.!)59
l.!J47
1.932
l.!127
1.880
10
241.882
19.396
8.78G
5.964
4.735
4.060
3.G:l7
3.347
3.137
2.!)78
2.854
2.753
2.671
2.602
2.544
2.4!l4
2.450
2.412
2.378
2.:l48
2.321
2.297
2.275
2.255
2.236
2.220
2.204
2.l!J0
2.177
2.165
2.153
2.142
2.133
2.12:1
2.114
2.106
2.098
2.091
2.084
2.077
2.071
2.065
2.05!)
2.054
2.04!l
2.044
2.0:3!)
2.035
2.0:30
2.026
UJ93
1.969
l.!J5 l
1.938
1.927
l.!Jl0
l.8!J!l
1.88,1
1.878
1.831