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RAA602S - REGRESSION ANALYSIS AND ANALYSIS OF VARIENCE - 2ND OPP - JAN 2023 |
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nAmlBIA unlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF HEALTH, NATURAL RESOURCES AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL: 7
COURSE CODE: RAA602S
COURSE NAME: REGRESSIONANALYSISAND
ANALYSIS OF VARIENCE
SESSION: JANUARY 2023
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SUPPLEMENTARY/ SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
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.
PERMISSIBLE MATERIALS
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 [23]
James obtains cash from ATM. He suspects that the rate at which he spends cash is affected
by the amount of the cash he withdrew at his previous visit to an ATM. To investigate this he
deliberately varies the amount he withdraws. He records, for each visit to an ATM, the
amount, N$ withdrawn and the number of hours, until his next visit to an ATM.
Withdrawal
X
y
1 2 3 4 5 6 7 8 9 10
40 10 100 110 120 150 20 90 80 130
56 62 195 330 94 270 48 196 214 286
1.1 Calculate the equation of the regression line for these data
[6]
1.2 James made one withdrawal immediately before going on a weekend visit to
Swakopmund. Identify the most likely withdrawal, giving a reason
[3]
1.3 Following another withdrawal, James was confined to bed for several days with COVID-
19. Identify the most likely withdrawal, giving a reason
[3]
1.4 Interpret, in context, the gradient of the regression line.
[2]
1.5 Comment on the evidence, if any, that James's rate of spending cash is affected by the
amount he withdraws
[3]
1.6 Calculate the coefficient of correlation and interpret your answer
[6]
Question 2 [26]
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 is of the form Y aebx .
Sunshine
4.3
6.9
0
10.4
5.2
1.8
8
9.2
2.1 I
Ice cream 224
208
123
419
230
184
362
351
196 I
2.1 Calculate the equation of the regression line and interpret it
[13]
= 2.2 Test at a 0.05 if there is a significant relationship between Sunshine and the number
of ice cream
[13]
2
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Question 3 [33]
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
............
...........
0.751212
0.051656
-2.383697
11.29246
............
...........
...........
0.011055
0.272208
0.296851
5.03528
-7.593839
2.22415
0.33158
Akaike info criterion
60.11832
Schwarz criterion
0
Hanna-Quinn Criterion
0.310547
OW stat
3.1 Estimate/fill in the missing values of each coefficients
3.2 Write down the estimated equations from the above model (2 decimal places)
3.3 Interpret the coefficient of determination
3.4 Comment on the value of the OW statistics
3.5 State the hypothesis for the F-test and it is decision rule
3.6 interpret the results of the F-test in one sentence
3.7 Interpret the coefficients of all exogenous variable
Prob
0.0175
0.000
0.000
0.000
0.0266
5.088405
5.12895
5.10428
1.807244
(10]
[6]
[2]
[2]
[3]
[2]
(8)
3
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Question 4 [18]
Consider the following model Y = /30 + /31x1 + /32 x 2 + /33X3+ /34x4 + E
4.1 List three methods you will use to do variable selection
[6]
4.2 Use the above model and clearly indicates all the steps for Forward Stepwise Selection [12]
4
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Numbers in each row ofthe table are values on a t-distributionwith
(dt) degrees of freedom for selected right-tail (greater-thanl probabilities ·(p}.
dflp 0.40
0.25
0.10
0.05
0.025
0.01
0.005
1 0,324920 1.000000 3.077684 6.313752 12.701i20 31.82052 63.65674
2 0.288675 0.816497 1.885618 2.919986 4.30265 :6.96456 9,92484
3 0.276671 0.764892 t637744 2.353363 3.1824-5 4.54-070 5.84{}91
4 0.270722 0.740697 1.533206 2.131847 2.77645 3.74695 4.60409
5 0.267181 0.726687 1,475884 2.015048 2.57058 3.36493 4.03214
6 0.264835 0.717558 1.43975£ 1.943180 2.44691 3.14267 3.70743
7 0,263167 0.711142 1.414924 1.89~579 2.36462 2.99795
--
-- -
8 0,261921 0.7063'87 1.396815 1,859548 2.30600 2,89:646
I 9 0.260.955 0.702722 1.383029 1.833113 2.26216 2.82144
10 0.260185 0.699812 1.372184 1.812461 2.22814 2.76377
-
n o.2sgs56 0.697445 1.363430 1.795.885 2.20099 2.71808
3.499•i8
3.35539
3,24984
3.16927
3.10581
12 0.259033 0.695483 1.356217 1.782288 2.17881 2.68100 3.05454
13 0,258591 0.6938:29 L350171 1.770933 2.16037 2.65031 3.01228
14 , 0.258213 0.692417 1_3q5030 1.761310 2.14479 2.62449 VJ7684
15 0.257885 0.691197 l ,3•10606 1.753050 2.13145 2.60248 2,94671
16 0.257599 0.690132 1.336757 1.745884 2.11991 2.58349 2.92D78
17 0.257347 0.&89195 1.333379 1.739607 2.10982 2.56693 2,89823
18 0.257123 0.688364 1.330391 1.730064 2.10092 2.55238 2.87844
19 0.256923 0.687621 1.32772.8 1.7:W133 2.093(}2 253948 2.86093
20 0,256743 0.6-86954 1.325341 1.724718 2.08596 2.52798, 2.84534
21 0.256580 0.686352 1.323188 1.720743 2.07961 2,51765 2.83136
22 0.256432 0.685805 1.321237 1.717144 2.07387 2.5DS32 2,81876
23 0.256297 0.6-85306 1.31946{1 1.713872 2.06866 2,49987 2.80734
24 0.256173 0.684S50 1.317835 1.710'882 2.06380 2.49216 2.79694
25 0.256060 0.684430 1.316345 1.70$141 2.0595-4 2.48511 2.78744
26 0.2'l5955 0.684043 1.314972 1.705618 2.05553 2.47863, 2.77871
27 0.255,858 0.683685 1.313703 1.703288 2.05183 2.47266 2:.77068
28 •I 0.255768 0.683353 l ,312527 1.701131 2.04841 .2.4671~ 2.76326
29 0,255684 0.6B30,l4 1.3114.34 1.699'127 2.04523 2.46202 2.75639
30 0:255605 0.682756 L310415 1.697261 2.04227 2.45726 2.75000
z 0,253347 0.674490 1.281552 1.644854 1.95996 2.32635, 2.57583
Cl --
--
80%
90%
95%
98%
919'%
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
4.1405
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
3,6139
3.659<i
3.6460
3.2905
99,9%
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Critical Values of the F-Distribution: a= 0.05
Denom.
d.f.
2
3
4
5
6
7
8
9
lU
11
12
13
14
15
16
17
18
19
20
21
22
23
24
2G
26
27
28
29
.10
31
:!2
33
:14
3G
3(i
37
38
39
40
41
42
43
44
45
46
47
48
49
50
60
70
80
!JO
100
120
140
180
200
CX)
1
lCil.448
18.513
Hl.128
7.709
6.608
5.987
5.5!Jl
5.318
5.117
4.965
4.844
4.747
4.fiG7
4.600
4.543
4.494
4.451
4.414
4.381
4.:.151
4.:125
4.:.101
4.279
4.260
4.242
4.225
4.210
4.196
4.183
4.171
4.160
4.14!)
4.139
4.1:lO
4.121
4.ll:.l
4.lOG
4.0!)8
4.0!Jl
4.085
4.079
4.073
4.067
4.062
4.057
4.052
4.047
4.043
4.o:.is
4.034
4.001
3.978
:.1.!J60
3.947
3.9:.!6
3.920
:.1.900
3.894
:1.888
3.841
2
HHJ.500
19.000
!J.552
6.944
5.786
5.143
4.737
4.459
4.256
4.103
3.!J82
3.88G
:I.ROG
3.73!)
3.682
3.634
:J.5!12
3.555
3.522
3.4!l3
3.4G7
3.443
3.422
3.40:.1
3.385
3.36!)
3.354
3.340
3.328
:urn
3.305
3.2!)5
3.28G
:1.27(i
3.267
3.259
3.252
3.245
3.238
3.232
3.226
:!.220
3.214
3.209
3.204
:1.200
3.195
3.191
3.187
3.183
3.lGO
3.128
3.111
3.098
3.087
3.072
3.061
3.046
:1.041
2.996
3
215.707
19.164
9.277
6.G91
5.409
4.757
4.347
4.066
:1.8G3
3.708
3.587
3.490
:l.411
3.344
3.287
3.239
3. l!l7
3.160
3.127
3.098
3.072
3.049
3.028
3.00!)
2.991
2.!J75
2.960
2.!)47
2.934
2.922
2.911
2.!)01
2.892
2.88:l
2.874
2.86(i
2.8G9
2.852
2.84G
2.839
2.833
2.827
2.822
2.816
2.812
2.807
2.802
2.798
2.7!J4
2.790
2.7G8
2.736
2.71D
2.706
2.Ci!J(j
2.680
2.G60
2.655
2.(i50
2.605
Numerat.or Degrees of Freedom
4
5
6
7
224.58:l
19.247
9.117
6.388
5.192
230.1Ci2
19.296
!J.013
6.256
5.0-'iO
233.986
19.330
8.!)41
6.163
4.%0
23Ci.768
19.353
8.887
6.094
4.876
4.534
4.120
3.838
3.G:J:l
3.478
4.387
3.!)72
3.687
3.482
3.326
4.284
3.8Ci(i
3.581
:1.:174
3.217
4.207
3.787
3.GOO
3.2!)3
3.135
3.357
3.2G!J
3.179
3.112
3.056
3.204
3.106
:l.025
2.%8
2.901
3.0!J5
2.996
2.!ll5
2.848
2.790
3.012
2.913
2.832
2.764
2.707
3.007
2.9(i5
2.928
2.895
2.8G6
2.852
2.810
2.773
2.740
2.711
2.741
2.6!19
2.661
2.628
2.5!l9
2.GG7
2.Gl4
2.577
2.544
2.514
2.840
2.817
2.796
2.776
2.7G9
2.685
2.661
2.640
2.G21
2.603
2.573
2.549
2.528
2.508
2.490
2.488
2.464
2.442
2.423
2.405
2.743
2.728
2.714
2.701
2.(i90
2.587
2.572
2.558
2.545
2.-'i'.!4
2.474
2.45!)
2.445
2.432
2.421
2.:l88
2.373
2.35!)
2.34G
2.:1:14
2.67!)
2.(i(i8
2.6G!J
2.(i50
2.641
2.523
2.512
2.503
2.494
2.48G
2.409
2.3!l!J
2.389
2.:180
2.372
2.:.123
2.31:l
2.303
2.294
2.285
2.634
2.626
2.619
2.612
2.606
2.477
2.470
2.46:J
2.456
2.449
2.3Ci4
2.3G6
2.349
2.342
2.336
2.277
2.270
2.262
2.2G5
2.249
2.600
2.594
2.589
2.584
2.579
2.443
2.4:l8
2.432
2.427
2.422
2.330
2.324
2.318
2.313
2.308
2.243
2.237
2.232
2.226
2.221
2.574
2.570
2.565
2.561
2.557
2.417
2.413
2.409
2.404
2.400
2.:io4
2.299
2.295
2.290
2.286
2.216
2.212
2.207
2.20:.i
2.199
2.52G
2.503
2.48(i
2.473
2.4Ci:l
2.3Ci8
2.346
2.32!)
2.316
2.305
2.254
2.231
2.214
2.201
2.l!Jl
2.167
2.143
2.12Ci
2.113
2.10:.1
2.447
2.4:.l(i
2.422
2.417
2.290
2.27!)
2.26<1
2.25!)
2.li5
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
4.147
3.72G
3.'138
:1.2:10
3.072
2.!J48
2.849
2.7G7
2.6!)!)
2.(itll
2.G91
2.548
2.510
2.477
2.447
2.420
2.397
2.375
2.355
2.337
2.321
2.305
2.2!)1
2.278
2.2Gfi
2.255
2.244
2.235
2.225
2.217
2.20!)
2.201
2.l!l4
2.187
2.180
2.174
2.168
2.163
2.157
2.152
2.147
2.143
2.138
2.134
2.130
2.0!)7
2.074
2.056
2.043
2.0:.12
2.016
2.005
1.990
l.!)85
1.938
9
240.543
19.385
8.812
G.999
4.772
4.099
:l.G77
3.388
3.17!)
:.1.020
2.8!J(i
2.796
2.714
2.646
2.588
2.G38
2.494
2.456
2.423
2.303
2.:l66
2.342
2.320
2.300
2.282
2.265
2.250
2.236
2.223
2.211
2.199
2.18!)
2.li9
2.170
2.161
2.153
2.145
2.1:18
2.131
2.124
2.118
2.112
2.106
2.101
2.0!)6
2.0!)1
2.086
2.082
2.077
2.073
2.040
2.017
!.!)!)!)
1.986
l.!)75
l.959
l.!)47
1.932
l.!J27
1.880
10
241.882
19.396
8.786
5.964
4.715
,J.060
3.G:!7
3 ..1,17
3.137
2.!)78
2.854
2.7G3
2.671
2.602
2.544
2.494
2.450
2.412
2.378
2.:548
2.321
2.297
2.275
2.255
2.236
2.220
2.204
2.l!JO
2.177
2.1G5
2.153
2.142
2.1:n
2.123
2.114
2.lOCi
2.098
2.091
2.084
2.077
2.071
2.065
2.051)
2.05,1
2.049
2.044
2.0:l9
2.035
2.0:.10
2.026
1.9!):.l
1.969
l.!)51
1.938
l.!J27
1.910
l.8!J!J
1.884
1.878
1.831