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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 24 Dec 2010 15:31:52 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t1293204584gh0lmosjcr8ruz8.htm/, Retrieved Tue, 30 Apr 2024 05:24:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115121, Retrieved Tue, 30 Apr 2024 05:24:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Multiple Regressi...] [2010-12-17 13:46:43] [1251ac2db27b84d4a3ba43449388906b]
-   PD  [Multiple Regression] [Multiple Regressi...] [2010-12-17 15:41:32] [1251ac2db27b84d4a3ba43449388906b]
-   P     [Multiple Regression] [MR Paper (monthly...] [2010-12-17 16:35:58] [1251ac2db27b84d4a3ba43449388906b]
-   PD      [Multiple Regression] [MR Paper (month)] [2010-12-17 16:45:18] [1251ac2db27b84d4a3ba43449388906b]
-   P         [Multiple Regression] [MR Paper (trend)b] [2010-12-18 12:41:58] [1251ac2db27b84d4a3ba43449388906b]
- RMPD          [Classical Decomposition] [CD] [2010-12-18 14:47:46] [1251ac2db27b84d4a3ba43449388906b]
- RM              [Exponential Smoothing] [Exponential Smoot...] [2010-12-18 18:46:08] [1251ac2db27b84d4a3ba43449388906b]
-   P                 [Exponential Smoothing] [] [2010-12-24 15:31:52] [4f70e6cd0867f10d298e58e8e27859b5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14.458
13.594
17.814
20.235
21.811
21.439
21.393
19.831
20.468
21.080
21.600
17.390
17.848
19.592
21.092
20.899
25.890
24.965
22.225
20.977
22.897
22.785
22.769
19.637
20.203
20.450
23.083
21.738
26.766
25.280
22.574
22.729
21.378
22.902
24.989
21.116
15.169
15.846
20.927
18.273
22.538
15.596
14.034
11.366
14.861
15.149
13.577
13.026
13.190
13.196
15.826
14.733
16.307
15.703
14.589
12.043
15.057
14.053
12.698
10.888
10.045
11.549
13.767
12.434
13.116
14.211
12.266
12.602
15.714
13.742
12.745
10.491
10.057
10.900
11.771
11.992
11.933
14.504
11.727
11.477
13.578
11.555
11.846
11.397
10.066
10.269
14.279
13.870
13.695
14.420
11.424
9.704
12.464
14.301
13.464
9.893
11.572
12.380
16.692
16.052
16.459
14.761
13.654
13.480
18.068
16.560
14.530
10.650
11.651
13.735
13.360
17.818
20.613
16.231
13.862
12.004
17.734
15.034
12.609
12.320
10.833
11.350
13.648
14.890
16.325
18.045
15.616
11.926
16.855
15.083
12.520
12.355

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115121&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115121&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.480421268200843
beta0.0199237820561068
gamma0.495517190826123

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.480421268200843 \tabularnewline
beta & 0.0199237820561068 \tabularnewline
gamma & 0.495517190826123 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115121&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.480421268200843[/C][/ROW]
[ROW][C]beta[/C][C]0.0199237820561068[/C][/ROW]
[ROW][C]gamma[/C][C]0.495517190826123[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115121&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.480421268200843
beta0.0199237820561068
gamma0.495517190826123






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1317.84816.25683199786321.59116800213676
1419.59218.89626501046450.695734989535488
1521.09220.80163073508220.290369264917782
1620.89920.79873783656680.100262163433207
1725.8925.9419731335047-0.0519731335046565
1824.96525.0729905458009-0.107990545800888
1922.22523.9751040036675-1.75010400366747
2020.97721.3866845709481-0.409684570948105
2122.89721.64197638636651.25502361363350
2222.78522.9062922648777-0.121292264877731
2322.76923.3828607372404-0.613860737240394
2419.63718.76766308192470.869336918075337
2520.20320.08630034033170.116699659668310
2620.4521.7894375673915-1.33943756739151
2723.08322.59582581324050.487174186759457
2821.73822.6235491927387-0.88554919273869
2926.76627.2295612400831-0.463561240083109
3025.2826.1200570971972-0.840057097197231
3122.57424.2123205430961-1.63832054309614
3222.72921.9884080566350.740591943365004
3321.37823.2016226397241-1.82362263972410
3422.90222.57978598991420.322214010085844
3524.98923.09409385387961.89490614612038
3621.11620.04152527708371.07447472291629
3715.16921.2424042607255-6.0734042607255
3815.84619.5149993446043-3.66899934460429
3920.92719.56841106831261.3585889316874
4018.27319.5656146982232-1.29261469822315
4122.53823.9850682666054-1.44706826660541
4215.59622.197079140875-6.601079140875
4314.03417.1519060148900-3.11790601488996
4411.36614.6512841657522-3.28528416575221
4514.86113.05330384095121.80769615904876
4615.14914.54636056268390.602639437316109
4713.57715.4208436360836-1.84384363608365
4813.02610.14563236514962.88036763485039
4913.1910.17585271700713.01414728299293
5013.19613.3223700100955-0.126370010095545
5115.82616.2950800490145-0.469080049014472
5214.73314.63709911844000.0959008815600324
5316.30719.6025959512777-3.29559595127774
5415.70315.50062491454500.202375085455026
5514.58914.58691842646980.00208157353019445
5612.04313.5381397873835-1.49513978738354
5715.05714.12458554210420.932414457895812
5814.05314.8916690997237-0.83866909972367
5912.69814.4348338803330-1.73683388033304
6010.88810.41934198541090.468658014589092
6110.0459.294297519143110.750702480856885
6211.54910.49211318116621.05688681883380
6313.76713.9036402629653-0.136640262965344
6412.43412.5126021152704-0.0786021152703604
6513.11616.4811897961192-3.36518979611921
6614.21113.20580778773651.00519221226353
6712.26612.5933436186570-0.327343618657027
6812.60210.96479351778391.63720648221611
6915.71413.67503215309022.03896784690981
7013.74214.5222842222188-0.780284222218846
7112.74513.8673557549460-1.12235575494603
7210.49110.7258793510906-0.234879351090576
7310.0579.339702429776080.717297570223916
7410.910.60422683129980.295773168700189
7511.77113.3394546704025-1.56845467040255
7611.99211.25842154436540.733578455634605
7711.93314.7617431838948-2.82874318389483
7814.50412.86512633893041.63887366106957
7911.72712.2159321633832-0.488932163383241
8011.47711.01590912485460.461090875145414
8113.57813.25366100049370.324338999506342
8211.55512.5240182546296-0.969018254629624
8311.84611.66123614895090.184763851049114
8411.3979.359617157222922.03738284277708
8510.0669.315380140752780.750619859247223
8610.26910.4928556446657-0.223855644665703
8714.27912.49897262239001.78002737761003
8813.8712.65184874459501.21815125540495
8913.69515.5079970441796-1.81299704417958
9014.4215.2965058733267-0.876505873326696
9111.42412.9138739684875-1.48987396848749
929.70411.4908188866763-1.78681888667628
9312.46412.6051509499796-0.141150949979597
9414.30111.30616535310702.99483464689295
9513.46412.66997312098870.794026879011284
969.89311.1690821105613-1.27608211056126
9711.5729.201029380214732.37097061978527
9812.3810.92091045495421.4590895450458
9916.69214.28242229060822.40957770939178
10016.05214.63006506643311.42193493356693
10116.45916.8426439494949-0.383643949494942
10214.76117.6115636959491-2.85056369594911
10313.65414.1563493489163-0.502349348916315
10413.4813.17443778676090.305562213239071
10518.06815.78088327438032.28711672561972
10616.5616.54231854331530.0176814566846772
10714.5315.9671594359957-1.43715943599574
10810.6512.8979731468994-2.24797314689945
10911.65111.42925618089930.221743819100698
11013.73511.88853991127341.84646008872657
11113.3615.6912834972136-2.33128349721361
11217.81813.47207623888574.34592376111428
11320.61316.61756393478573.99543606521426
11416.23118.8900960167736-2.65909601677363
11513.86216.1682140241811-2.3062140241811
11612.00414.5472018155865-2.54320181558646
11717.73416.28745330120971.44654669879025
11815.03416.0449672498692-1.01096724986921
11912.60914.5754094216707-1.96640942167075
12012.3211.01249166183111.30750833816887
12110.83311.8910735500971-1.05807355009709
12211.3512.1448715172094-0.794871517209405
12313.64813.56884418517030.0791558148296971
12414.8914.21563420959860.674365790401389
12516.32515.46070318672670.864296813273342
12618.04514.4394340423533.605565957647
12715.61614.80178789419690.814212105803133
12811.92614.6324538911486-2.70645389114858
12916.85517.3334884643763-0.478488464376301
13015.08315.5270479253007-0.444047925300689
13112.5214.0828736784164-1.56287367841638
13212.35511.55960094624720.795399053752753

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 17.848 & 16.2568319978632 & 1.59116800213676 \tabularnewline
14 & 19.592 & 18.8962650104645 & 0.695734989535488 \tabularnewline
15 & 21.092 & 20.8016307350822 & 0.290369264917782 \tabularnewline
16 & 20.899 & 20.7987378365668 & 0.100262163433207 \tabularnewline
17 & 25.89 & 25.9419731335047 & -0.0519731335046565 \tabularnewline
18 & 24.965 & 25.0729905458009 & -0.107990545800888 \tabularnewline
19 & 22.225 & 23.9751040036675 & -1.75010400366747 \tabularnewline
20 & 20.977 & 21.3866845709481 & -0.409684570948105 \tabularnewline
21 & 22.897 & 21.6419763863665 & 1.25502361363350 \tabularnewline
22 & 22.785 & 22.9062922648777 & -0.121292264877731 \tabularnewline
23 & 22.769 & 23.3828607372404 & -0.613860737240394 \tabularnewline
24 & 19.637 & 18.7676630819247 & 0.869336918075337 \tabularnewline
25 & 20.203 & 20.0863003403317 & 0.116699659668310 \tabularnewline
26 & 20.45 & 21.7894375673915 & -1.33943756739151 \tabularnewline
27 & 23.083 & 22.5958258132405 & 0.487174186759457 \tabularnewline
28 & 21.738 & 22.6235491927387 & -0.88554919273869 \tabularnewline
29 & 26.766 & 27.2295612400831 & -0.463561240083109 \tabularnewline
30 & 25.28 & 26.1200570971972 & -0.840057097197231 \tabularnewline
31 & 22.574 & 24.2123205430961 & -1.63832054309614 \tabularnewline
32 & 22.729 & 21.988408056635 & 0.740591943365004 \tabularnewline
33 & 21.378 & 23.2016226397241 & -1.82362263972410 \tabularnewline
34 & 22.902 & 22.5797859899142 & 0.322214010085844 \tabularnewline
35 & 24.989 & 23.0940938538796 & 1.89490614612038 \tabularnewline
36 & 21.116 & 20.0415252770837 & 1.07447472291629 \tabularnewline
37 & 15.169 & 21.2424042607255 & -6.0734042607255 \tabularnewline
38 & 15.846 & 19.5149993446043 & -3.66899934460429 \tabularnewline
39 & 20.927 & 19.5684110683126 & 1.3585889316874 \tabularnewline
40 & 18.273 & 19.5656146982232 & -1.29261469822315 \tabularnewline
41 & 22.538 & 23.9850682666054 & -1.44706826660541 \tabularnewline
42 & 15.596 & 22.197079140875 & -6.601079140875 \tabularnewline
43 & 14.034 & 17.1519060148900 & -3.11790601488996 \tabularnewline
44 & 11.366 & 14.6512841657522 & -3.28528416575221 \tabularnewline
45 & 14.861 & 13.0533038409512 & 1.80769615904876 \tabularnewline
46 & 15.149 & 14.5463605626839 & 0.602639437316109 \tabularnewline
47 & 13.577 & 15.4208436360836 & -1.84384363608365 \tabularnewline
48 & 13.026 & 10.1456323651496 & 2.88036763485039 \tabularnewline
49 & 13.19 & 10.1758527170071 & 3.01414728299293 \tabularnewline
50 & 13.196 & 13.3223700100955 & -0.126370010095545 \tabularnewline
51 & 15.826 & 16.2950800490145 & -0.469080049014472 \tabularnewline
52 & 14.733 & 14.6370991184400 & 0.0959008815600324 \tabularnewline
53 & 16.307 & 19.6025959512777 & -3.29559595127774 \tabularnewline
54 & 15.703 & 15.5006249145450 & 0.202375085455026 \tabularnewline
55 & 14.589 & 14.5869184264698 & 0.00208157353019445 \tabularnewline
56 & 12.043 & 13.5381397873835 & -1.49513978738354 \tabularnewline
57 & 15.057 & 14.1245855421042 & 0.932414457895812 \tabularnewline
58 & 14.053 & 14.8916690997237 & -0.83866909972367 \tabularnewline
59 & 12.698 & 14.4348338803330 & -1.73683388033304 \tabularnewline
60 & 10.888 & 10.4193419854109 & 0.468658014589092 \tabularnewline
61 & 10.045 & 9.29429751914311 & 0.750702480856885 \tabularnewline
62 & 11.549 & 10.4921131811662 & 1.05688681883380 \tabularnewline
63 & 13.767 & 13.9036402629653 & -0.136640262965344 \tabularnewline
64 & 12.434 & 12.5126021152704 & -0.0786021152703604 \tabularnewline
65 & 13.116 & 16.4811897961192 & -3.36518979611921 \tabularnewline
66 & 14.211 & 13.2058077877365 & 1.00519221226353 \tabularnewline
67 & 12.266 & 12.5933436186570 & -0.327343618657027 \tabularnewline
68 & 12.602 & 10.9647935177839 & 1.63720648221611 \tabularnewline
69 & 15.714 & 13.6750321530902 & 2.03896784690981 \tabularnewline
70 & 13.742 & 14.5222842222188 & -0.780284222218846 \tabularnewline
71 & 12.745 & 13.8673557549460 & -1.12235575494603 \tabularnewline
72 & 10.491 & 10.7258793510906 & -0.234879351090576 \tabularnewline
73 & 10.057 & 9.33970242977608 & 0.717297570223916 \tabularnewline
74 & 10.9 & 10.6042268312998 & 0.295773168700189 \tabularnewline
75 & 11.771 & 13.3394546704025 & -1.56845467040255 \tabularnewline
76 & 11.992 & 11.2584215443654 & 0.733578455634605 \tabularnewline
77 & 11.933 & 14.7617431838948 & -2.82874318389483 \tabularnewline
78 & 14.504 & 12.8651263389304 & 1.63887366106957 \tabularnewline
79 & 11.727 & 12.2159321633832 & -0.488932163383241 \tabularnewline
80 & 11.477 & 11.0159091248546 & 0.461090875145414 \tabularnewline
81 & 13.578 & 13.2536610004937 & 0.324338999506342 \tabularnewline
82 & 11.555 & 12.5240182546296 & -0.969018254629624 \tabularnewline
83 & 11.846 & 11.6612361489509 & 0.184763851049114 \tabularnewline
84 & 11.397 & 9.35961715722292 & 2.03738284277708 \tabularnewline
85 & 10.066 & 9.31538014075278 & 0.750619859247223 \tabularnewline
86 & 10.269 & 10.4928556446657 & -0.223855644665703 \tabularnewline
87 & 14.279 & 12.4989726223900 & 1.78002737761003 \tabularnewline
88 & 13.87 & 12.6518487445950 & 1.21815125540495 \tabularnewline
89 & 13.695 & 15.5079970441796 & -1.81299704417958 \tabularnewline
90 & 14.42 & 15.2965058733267 & -0.876505873326696 \tabularnewline
91 & 11.424 & 12.9138739684875 & -1.48987396848749 \tabularnewline
92 & 9.704 & 11.4908188866763 & -1.78681888667628 \tabularnewline
93 & 12.464 & 12.6051509499796 & -0.141150949979597 \tabularnewline
94 & 14.301 & 11.3061653531070 & 2.99483464689295 \tabularnewline
95 & 13.464 & 12.6699731209887 & 0.794026879011284 \tabularnewline
96 & 9.893 & 11.1690821105613 & -1.27608211056126 \tabularnewline
97 & 11.572 & 9.20102938021473 & 2.37097061978527 \tabularnewline
98 & 12.38 & 10.9209104549542 & 1.4590895450458 \tabularnewline
99 & 16.692 & 14.2824222906082 & 2.40957770939178 \tabularnewline
100 & 16.052 & 14.6300650664331 & 1.42193493356693 \tabularnewline
101 & 16.459 & 16.8426439494949 & -0.383643949494942 \tabularnewline
102 & 14.761 & 17.6115636959491 & -2.85056369594911 \tabularnewline
103 & 13.654 & 14.1563493489163 & -0.502349348916315 \tabularnewline
104 & 13.48 & 13.1744377867609 & 0.305562213239071 \tabularnewline
105 & 18.068 & 15.7808832743803 & 2.28711672561972 \tabularnewline
106 & 16.56 & 16.5423185433153 & 0.0176814566846772 \tabularnewline
107 & 14.53 & 15.9671594359957 & -1.43715943599574 \tabularnewline
108 & 10.65 & 12.8979731468994 & -2.24797314689945 \tabularnewline
109 & 11.651 & 11.4292561808993 & 0.221743819100698 \tabularnewline
110 & 13.735 & 11.8885399112734 & 1.84646008872657 \tabularnewline
111 & 13.36 & 15.6912834972136 & -2.33128349721361 \tabularnewline
112 & 17.818 & 13.4720762388857 & 4.34592376111428 \tabularnewline
113 & 20.613 & 16.6175639347857 & 3.99543606521426 \tabularnewline
114 & 16.231 & 18.8900960167736 & -2.65909601677363 \tabularnewline
115 & 13.862 & 16.1682140241811 & -2.3062140241811 \tabularnewline
116 & 12.004 & 14.5472018155865 & -2.54320181558646 \tabularnewline
117 & 17.734 & 16.2874533012097 & 1.44654669879025 \tabularnewline
118 & 15.034 & 16.0449672498692 & -1.01096724986921 \tabularnewline
119 & 12.609 & 14.5754094216707 & -1.96640942167075 \tabularnewline
120 & 12.32 & 11.0124916618311 & 1.30750833816887 \tabularnewline
121 & 10.833 & 11.8910735500971 & -1.05807355009709 \tabularnewline
122 & 11.35 & 12.1448715172094 & -0.794871517209405 \tabularnewline
123 & 13.648 & 13.5688441851703 & 0.0791558148296971 \tabularnewline
124 & 14.89 & 14.2156342095986 & 0.674365790401389 \tabularnewline
125 & 16.325 & 15.4607031867267 & 0.864296813273342 \tabularnewline
126 & 18.045 & 14.439434042353 & 3.605565957647 \tabularnewline
127 & 15.616 & 14.8017878941969 & 0.814212105803133 \tabularnewline
128 & 11.926 & 14.6324538911486 & -2.70645389114858 \tabularnewline
129 & 16.855 & 17.3334884643763 & -0.478488464376301 \tabularnewline
130 & 15.083 & 15.5270479253007 & -0.444047925300689 \tabularnewline
131 & 12.52 & 14.0828736784164 & -1.56287367841638 \tabularnewline
132 & 12.355 & 11.5596009462472 & 0.795399053752753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115121&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]17.848[/C][C]16.2568319978632[/C][C]1.59116800213676[/C][/ROW]
[ROW][C]14[/C][C]19.592[/C][C]18.8962650104645[/C][C]0.695734989535488[/C][/ROW]
[ROW][C]15[/C][C]21.092[/C][C]20.8016307350822[/C][C]0.290369264917782[/C][/ROW]
[ROW][C]16[/C][C]20.899[/C][C]20.7987378365668[/C][C]0.100262163433207[/C][/ROW]
[ROW][C]17[/C][C]25.89[/C][C]25.9419731335047[/C][C]-0.0519731335046565[/C][/ROW]
[ROW][C]18[/C][C]24.965[/C][C]25.0729905458009[/C][C]-0.107990545800888[/C][/ROW]
[ROW][C]19[/C][C]22.225[/C][C]23.9751040036675[/C][C]-1.75010400366747[/C][/ROW]
[ROW][C]20[/C][C]20.977[/C][C]21.3866845709481[/C][C]-0.409684570948105[/C][/ROW]
[ROW][C]21[/C][C]22.897[/C][C]21.6419763863665[/C][C]1.25502361363350[/C][/ROW]
[ROW][C]22[/C][C]22.785[/C][C]22.9062922648777[/C][C]-0.121292264877731[/C][/ROW]
[ROW][C]23[/C][C]22.769[/C][C]23.3828607372404[/C][C]-0.613860737240394[/C][/ROW]
[ROW][C]24[/C][C]19.637[/C][C]18.7676630819247[/C][C]0.869336918075337[/C][/ROW]
[ROW][C]25[/C][C]20.203[/C][C]20.0863003403317[/C][C]0.116699659668310[/C][/ROW]
[ROW][C]26[/C][C]20.45[/C][C]21.7894375673915[/C][C]-1.33943756739151[/C][/ROW]
[ROW][C]27[/C][C]23.083[/C][C]22.5958258132405[/C][C]0.487174186759457[/C][/ROW]
[ROW][C]28[/C][C]21.738[/C][C]22.6235491927387[/C][C]-0.88554919273869[/C][/ROW]
[ROW][C]29[/C][C]26.766[/C][C]27.2295612400831[/C][C]-0.463561240083109[/C][/ROW]
[ROW][C]30[/C][C]25.28[/C][C]26.1200570971972[/C][C]-0.840057097197231[/C][/ROW]
[ROW][C]31[/C][C]22.574[/C][C]24.2123205430961[/C][C]-1.63832054309614[/C][/ROW]
[ROW][C]32[/C][C]22.729[/C][C]21.988408056635[/C][C]0.740591943365004[/C][/ROW]
[ROW][C]33[/C][C]21.378[/C][C]23.2016226397241[/C][C]-1.82362263972410[/C][/ROW]
[ROW][C]34[/C][C]22.902[/C][C]22.5797859899142[/C][C]0.322214010085844[/C][/ROW]
[ROW][C]35[/C][C]24.989[/C][C]23.0940938538796[/C][C]1.89490614612038[/C][/ROW]
[ROW][C]36[/C][C]21.116[/C][C]20.0415252770837[/C][C]1.07447472291629[/C][/ROW]
[ROW][C]37[/C][C]15.169[/C][C]21.2424042607255[/C][C]-6.0734042607255[/C][/ROW]
[ROW][C]38[/C][C]15.846[/C][C]19.5149993446043[/C][C]-3.66899934460429[/C][/ROW]
[ROW][C]39[/C][C]20.927[/C][C]19.5684110683126[/C][C]1.3585889316874[/C][/ROW]
[ROW][C]40[/C][C]18.273[/C][C]19.5656146982232[/C][C]-1.29261469822315[/C][/ROW]
[ROW][C]41[/C][C]22.538[/C][C]23.9850682666054[/C][C]-1.44706826660541[/C][/ROW]
[ROW][C]42[/C][C]15.596[/C][C]22.197079140875[/C][C]-6.601079140875[/C][/ROW]
[ROW][C]43[/C][C]14.034[/C][C]17.1519060148900[/C][C]-3.11790601488996[/C][/ROW]
[ROW][C]44[/C][C]11.366[/C][C]14.6512841657522[/C][C]-3.28528416575221[/C][/ROW]
[ROW][C]45[/C][C]14.861[/C][C]13.0533038409512[/C][C]1.80769615904876[/C][/ROW]
[ROW][C]46[/C][C]15.149[/C][C]14.5463605626839[/C][C]0.602639437316109[/C][/ROW]
[ROW][C]47[/C][C]13.577[/C][C]15.4208436360836[/C][C]-1.84384363608365[/C][/ROW]
[ROW][C]48[/C][C]13.026[/C][C]10.1456323651496[/C][C]2.88036763485039[/C][/ROW]
[ROW][C]49[/C][C]13.19[/C][C]10.1758527170071[/C][C]3.01414728299293[/C][/ROW]
[ROW][C]50[/C][C]13.196[/C][C]13.3223700100955[/C][C]-0.126370010095545[/C][/ROW]
[ROW][C]51[/C][C]15.826[/C][C]16.2950800490145[/C][C]-0.469080049014472[/C][/ROW]
[ROW][C]52[/C][C]14.733[/C][C]14.6370991184400[/C][C]0.0959008815600324[/C][/ROW]
[ROW][C]53[/C][C]16.307[/C][C]19.6025959512777[/C][C]-3.29559595127774[/C][/ROW]
[ROW][C]54[/C][C]15.703[/C][C]15.5006249145450[/C][C]0.202375085455026[/C][/ROW]
[ROW][C]55[/C][C]14.589[/C][C]14.5869184264698[/C][C]0.00208157353019445[/C][/ROW]
[ROW][C]56[/C][C]12.043[/C][C]13.5381397873835[/C][C]-1.49513978738354[/C][/ROW]
[ROW][C]57[/C][C]15.057[/C][C]14.1245855421042[/C][C]0.932414457895812[/C][/ROW]
[ROW][C]58[/C][C]14.053[/C][C]14.8916690997237[/C][C]-0.83866909972367[/C][/ROW]
[ROW][C]59[/C][C]12.698[/C][C]14.4348338803330[/C][C]-1.73683388033304[/C][/ROW]
[ROW][C]60[/C][C]10.888[/C][C]10.4193419854109[/C][C]0.468658014589092[/C][/ROW]
[ROW][C]61[/C][C]10.045[/C][C]9.29429751914311[/C][C]0.750702480856885[/C][/ROW]
[ROW][C]62[/C][C]11.549[/C][C]10.4921131811662[/C][C]1.05688681883380[/C][/ROW]
[ROW][C]63[/C][C]13.767[/C][C]13.9036402629653[/C][C]-0.136640262965344[/C][/ROW]
[ROW][C]64[/C][C]12.434[/C][C]12.5126021152704[/C][C]-0.0786021152703604[/C][/ROW]
[ROW][C]65[/C][C]13.116[/C][C]16.4811897961192[/C][C]-3.36518979611921[/C][/ROW]
[ROW][C]66[/C][C]14.211[/C][C]13.2058077877365[/C][C]1.00519221226353[/C][/ROW]
[ROW][C]67[/C][C]12.266[/C][C]12.5933436186570[/C][C]-0.327343618657027[/C][/ROW]
[ROW][C]68[/C][C]12.602[/C][C]10.9647935177839[/C][C]1.63720648221611[/C][/ROW]
[ROW][C]69[/C][C]15.714[/C][C]13.6750321530902[/C][C]2.03896784690981[/C][/ROW]
[ROW][C]70[/C][C]13.742[/C][C]14.5222842222188[/C][C]-0.780284222218846[/C][/ROW]
[ROW][C]71[/C][C]12.745[/C][C]13.8673557549460[/C][C]-1.12235575494603[/C][/ROW]
[ROW][C]72[/C][C]10.491[/C][C]10.7258793510906[/C][C]-0.234879351090576[/C][/ROW]
[ROW][C]73[/C][C]10.057[/C][C]9.33970242977608[/C][C]0.717297570223916[/C][/ROW]
[ROW][C]74[/C][C]10.9[/C][C]10.6042268312998[/C][C]0.295773168700189[/C][/ROW]
[ROW][C]75[/C][C]11.771[/C][C]13.3394546704025[/C][C]-1.56845467040255[/C][/ROW]
[ROW][C]76[/C][C]11.992[/C][C]11.2584215443654[/C][C]0.733578455634605[/C][/ROW]
[ROW][C]77[/C][C]11.933[/C][C]14.7617431838948[/C][C]-2.82874318389483[/C][/ROW]
[ROW][C]78[/C][C]14.504[/C][C]12.8651263389304[/C][C]1.63887366106957[/C][/ROW]
[ROW][C]79[/C][C]11.727[/C][C]12.2159321633832[/C][C]-0.488932163383241[/C][/ROW]
[ROW][C]80[/C][C]11.477[/C][C]11.0159091248546[/C][C]0.461090875145414[/C][/ROW]
[ROW][C]81[/C][C]13.578[/C][C]13.2536610004937[/C][C]0.324338999506342[/C][/ROW]
[ROW][C]82[/C][C]11.555[/C][C]12.5240182546296[/C][C]-0.969018254629624[/C][/ROW]
[ROW][C]83[/C][C]11.846[/C][C]11.6612361489509[/C][C]0.184763851049114[/C][/ROW]
[ROW][C]84[/C][C]11.397[/C][C]9.35961715722292[/C][C]2.03738284277708[/C][/ROW]
[ROW][C]85[/C][C]10.066[/C][C]9.31538014075278[/C][C]0.750619859247223[/C][/ROW]
[ROW][C]86[/C][C]10.269[/C][C]10.4928556446657[/C][C]-0.223855644665703[/C][/ROW]
[ROW][C]87[/C][C]14.279[/C][C]12.4989726223900[/C][C]1.78002737761003[/C][/ROW]
[ROW][C]88[/C][C]13.87[/C][C]12.6518487445950[/C][C]1.21815125540495[/C][/ROW]
[ROW][C]89[/C][C]13.695[/C][C]15.5079970441796[/C][C]-1.81299704417958[/C][/ROW]
[ROW][C]90[/C][C]14.42[/C][C]15.2965058733267[/C][C]-0.876505873326696[/C][/ROW]
[ROW][C]91[/C][C]11.424[/C][C]12.9138739684875[/C][C]-1.48987396848749[/C][/ROW]
[ROW][C]92[/C][C]9.704[/C][C]11.4908188866763[/C][C]-1.78681888667628[/C][/ROW]
[ROW][C]93[/C][C]12.464[/C][C]12.6051509499796[/C][C]-0.141150949979597[/C][/ROW]
[ROW][C]94[/C][C]14.301[/C][C]11.3061653531070[/C][C]2.99483464689295[/C][/ROW]
[ROW][C]95[/C][C]13.464[/C][C]12.6699731209887[/C][C]0.794026879011284[/C][/ROW]
[ROW][C]96[/C][C]9.893[/C][C]11.1690821105613[/C][C]-1.27608211056126[/C][/ROW]
[ROW][C]97[/C][C]11.572[/C][C]9.20102938021473[/C][C]2.37097061978527[/C][/ROW]
[ROW][C]98[/C][C]12.38[/C][C]10.9209104549542[/C][C]1.4590895450458[/C][/ROW]
[ROW][C]99[/C][C]16.692[/C][C]14.2824222906082[/C][C]2.40957770939178[/C][/ROW]
[ROW][C]100[/C][C]16.052[/C][C]14.6300650664331[/C][C]1.42193493356693[/C][/ROW]
[ROW][C]101[/C][C]16.459[/C][C]16.8426439494949[/C][C]-0.383643949494942[/C][/ROW]
[ROW][C]102[/C][C]14.761[/C][C]17.6115636959491[/C][C]-2.85056369594911[/C][/ROW]
[ROW][C]103[/C][C]13.654[/C][C]14.1563493489163[/C][C]-0.502349348916315[/C][/ROW]
[ROW][C]104[/C][C]13.48[/C][C]13.1744377867609[/C][C]0.305562213239071[/C][/ROW]
[ROW][C]105[/C][C]18.068[/C][C]15.7808832743803[/C][C]2.28711672561972[/C][/ROW]
[ROW][C]106[/C][C]16.56[/C][C]16.5423185433153[/C][C]0.0176814566846772[/C][/ROW]
[ROW][C]107[/C][C]14.53[/C][C]15.9671594359957[/C][C]-1.43715943599574[/C][/ROW]
[ROW][C]108[/C][C]10.65[/C][C]12.8979731468994[/C][C]-2.24797314689945[/C][/ROW]
[ROW][C]109[/C][C]11.651[/C][C]11.4292561808993[/C][C]0.221743819100698[/C][/ROW]
[ROW][C]110[/C][C]13.735[/C][C]11.8885399112734[/C][C]1.84646008872657[/C][/ROW]
[ROW][C]111[/C][C]13.36[/C][C]15.6912834972136[/C][C]-2.33128349721361[/C][/ROW]
[ROW][C]112[/C][C]17.818[/C][C]13.4720762388857[/C][C]4.34592376111428[/C][/ROW]
[ROW][C]113[/C][C]20.613[/C][C]16.6175639347857[/C][C]3.99543606521426[/C][/ROW]
[ROW][C]114[/C][C]16.231[/C][C]18.8900960167736[/C][C]-2.65909601677363[/C][/ROW]
[ROW][C]115[/C][C]13.862[/C][C]16.1682140241811[/C][C]-2.3062140241811[/C][/ROW]
[ROW][C]116[/C][C]12.004[/C][C]14.5472018155865[/C][C]-2.54320181558646[/C][/ROW]
[ROW][C]117[/C][C]17.734[/C][C]16.2874533012097[/C][C]1.44654669879025[/C][/ROW]
[ROW][C]118[/C][C]15.034[/C][C]16.0449672498692[/C][C]-1.01096724986921[/C][/ROW]
[ROW][C]119[/C][C]12.609[/C][C]14.5754094216707[/C][C]-1.96640942167075[/C][/ROW]
[ROW][C]120[/C][C]12.32[/C][C]11.0124916618311[/C][C]1.30750833816887[/C][/ROW]
[ROW][C]121[/C][C]10.833[/C][C]11.8910735500971[/C][C]-1.05807355009709[/C][/ROW]
[ROW][C]122[/C][C]11.35[/C][C]12.1448715172094[/C][C]-0.794871517209405[/C][/ROW]
[ROW][C]123[/C][C]13.648[/C][C]13.5688441851703[/C][C]0.0791558148296971[/C][/ROW]
[ROW][C]124[/C][C]14.89[/C][C]14.2156342095986[/C][C]0.674365790401389[/C][/ROW]
[ROW][C]125[/C][C]16.325[/C][C]15.4607031867267[/C][C]0.864296813273342[/C][/ROW]
[ROW][C]126[/C][C]18.045[/C][C]14.439434042353[/C][C]3.605565957647[/C][/ROW]
[ROW][C]127[/C][C]15.616[/C][C]14.8017878941969[/C][C]0.814212105803133[/C][/ROW]
[ROW][C]128[/C][C]11.926[/C][C]14.6324538911486[/C][C]-2.70645389114858[/C][/ROW]
[ROW][C]129[/C][C]16.855[/C][C]17.3334884643763[/C][C]-0.478488464376301[/C][/ROW]
[ROW][C]130[/C][C]15.083[/C][C]15.5270479253007[/C][C]-0.444047925300689[/C][/ROW]
[ROW][C]131[/C][C]12.52[/C][C]14.0828736784164[/C][C]-1.56287367841638[/C][/ROW]
[ROW][C]132[/C][C]12.355[/C][C]11.5596009462472[/C][C]0.795399053752753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115121&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115121&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1317.84816.25683199786321.59116800213676
1419.59218.89626501046450.695734989535488
1521.09220.80163073508220.290369264917782
1620.89920.79873783656680.100262163433207
1725.8925.9419731335047-0.0519731335046565
1824.96525.0729905458009-0.107990545800888
1922.22523.9751040036675-1.75010400366747
2020.97721.3866845709481-0.409684570948105
2122.89721.64197638636651.25502361363350
2222.78522.9062922648777-0.121292264877731
2322.76923.3828607372404-0.613860737240394
2419.63718.76766308192470.869336918075337
2520.20320.08630034033170.116699659668310
2620.4521.7894375673915-1.33943756739151
2723.08322.59582581324050.487174186759457
2821.73822.6235491927387-0.88554919273869
2926.76627.2295612400831-0.463561240083109
3025.2826.1200570971972-0.840057097197231
3122.57424.2123205430961-1.63832054309614
3222.72921.9884080566350.740591943365004
3321.37823.2016226397241-1.82362263972410
3422.90222.57978598991420.322214010085844
3524.98923.09409385387961.89490614612038
3621.11620.04152527708371.07447472291629
3715.16921.2424042607255-6.0734042607255
3815.84619.5149993446043-3.66899934460429
3920.92719.56841106831261.3585889316874
4018.27319.5656146982232-1.29261469822315
4122.53823.9850682666054-1.44706826660541
4215.59622.197079140875-6.601079140875
4314.03417.1519060148900-3.11790601488996
4411.36614.6512841657522-3.28528416575221
4514.86113.05330384095121.80769615904876
4615.14914.54636056268390.602639437316109
4713.57715.4208436360836-1.84384363608365
4813.02610.14563236514962.88036763485039
4913.1910.17585271700713.01414728299293
5013.19613.3223700100955-0.126370010095545
5115.82616.2950800490145-0.469080049014472
5214.73314.63709911844000.0959008815600324
5316.30719.6025959512777-3.29559595127774
5415.70315.50062491454500.202375085455026
5514.58914.58691842646980.00208157353019445
5612.04313.5381397873835-1.49513978738354
5715.05714.12458554210420.932414457895812
5814.05314.8916690997237-0.83866909972367
5912.69814.4348338803330-1.73683388033304
6010.88810.41934198541090.468658014589092
6110.0459.294297519143110.750702480856885
6211.54910.49211318116621.05688681883380
6313.76713.9036402629653-0.136640262965344
6412.43412.5126021152704-0.0786021152703604
6513.11616.4811897961192-3.36518979611921
6614.21113.20580778773651.00519221226353
6712.26612.5933436186570-0.327343618657027
6812.60210.96479351778391.63720648221611
6915.71413.67503215309022.03896784690981
7013.74214.5222842222188-0.780284222218846
7112.74513.8673557549460-1.12235575494603
7210.49110.7258793510906-0.234879351090576
7310.0579.339702429776080.717297570223916
7410.910.60422683129980.295773168700189
7511.77113.3394546704025-1.56845467040255
7611.99211.25842154436540.733578455634605
7711.93314.7617431838948-2.82874318389483
7814.50412.86512633893041.63887366106957
7911.72712.2159321633832-0.488932163383241
8011.47711.01590912485460.461090875145414
8113.57813.25366100049370.324338999506342
8211.55512.5240182546296-0.969018254629624
8311.84611.66123614895090.184763851049114
8411.3979.359617157222922.03738284277708
8510.0669.315380140752780.750619859247223
8610.26910.4928556446657-0.223855644665703
8714.27912.49897262239001.78002737761003
8813.8712.65184874459501.21815125540495
8913.69515.5079970441796-1.81299704417958
9014.4215.2965058733267-0.876505873326696
9111.42412.9138739684875-1.48987396848749
929.70411.4908188866763-1.78681888667628
9312.46412.6051509499796-0.141150949979597
9414.30111.30616535310702.99483464689295
9513.46412.66997312098870.794026879011284
969.89311.1690821105613-1.27608211056126
9711.5729.201029380214732.37097061978527
9812.3810.92091045495421.4590895450458
9916.69214.28242229060822.40957770939178
10016.05214.63006506643311.42193493356693
10116.45916.8426439494949-0.383643949494942
10214.76117.6115636959491-2.85056369594911
10313.65414.1563493489163-0.502349348916315
10413.4813.17443778676090.305562213239071
10518.06815.78088327438032.28711672561972
10616.5616.54231854331530.0176814566846772
10714.5315.9671594359957-1.43715943599574
10810.6512.8979731468994-2.24797314689945
10911.65111.42925618089930.221743819100698
11013.73511.88853991127341.84646008872657
11113.3615.6912834972136-2.33128349721361
11217.81813.47207623888574.34592376111428
11320.61316.61756393478573.99543606521426
11416.23118.8900960167736-2.65909601677363
11513.86216.1682140241811-2.3062140241811
11612.00414.5472018155865-2.54320181558646
11717.73416.28745330120971.44654669879025
11815.03416.0449672498692-1.01096724986921
11912.60914.5754094216707-1.96640942167075
12012.3211.01249166183111.30750833816887
12110.83311.8910735500971-1.05807355009709
12211.3512.1448715172094-0.794871517209405
12313.64813.56884418517030.0791558148296971
12414.8914.21563420959860.674365790401389
12516.32515.46070318672670.864296813273342
12618.04514.4394340423533.605565957647
12715.61614.80178789419690.814212105803133
12811.92614.6324538911486-2.70645389114858
12916.85517.3334884643763-0.478488464376301
13015.08315.5270479253007-0.444047925300689
13112.5214.0828736784164-1.56287367841638
13212.35511.55960094624720.795399053752753






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13311.58108403351868.0443595637017615.1178085033355
13412.41906732310928.4805896036975516.3575450425208
13514.465649016945410.149021686119818.7822763477709
13615.242604713062610.565457472802619.9197519533226
13716.221089732646911.197027316761521.2451521485323
13815.490584850829410.130355928569020.8508137730898
13913.36779699132487.6800424995299219.0555514831196
14011.85878470588675.8505415043108217.8670279074626
14116.417493237891510.094546791734122.7404396840489
14214.83819933953438.2053387677377621.4710599113309
14313.31195594482426.373163455354320.2507484342941
14412.15429572898674.9128905246805519.3957009332929

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 11.5810840335186 & 8.04435956370176 & 15.1178085033355 \tabularnewline
134 & 12.4190673231092 & 8.48058960369755 & 16.3575450425208 \tabularnewline
135 & 14.4656490169454 & 10.1490216861198 & 18.7822763477709 \tabularnewline
136 & 15.2426047130626 & 10.5654574728026 & 19.9197519533226 \tabularnewline
137 & 16.2210897326469 & 11.1970273167615 & 21.2451521485323 \tabularnewline
138 & 15.4905848508294 & 10.1303559285690 & 20.8508137730898 \tabularnewline
139 & 13.3677969913248 & 7.68004249952992 & 19.0555514831196 \tabularnewline
140 & 11.8587847058867 & 5.85054150431082 & 17.8670279074626 \tabularnewline
141 & 16.4174932378915 & 10.0945467917341 & 22.7404396840489 \tabularnewline
142 & 14.8381993395343 & 8.20533876773776 & 21.4710599113309 \tabularnewline
143 & 13.3119559448242 & 6.3731634553543 & 20.2507484342941 \tabularnewline
144 & 12.1542957289867 & 4.91289052468055 & 19.3957009332929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115121&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]133[/C][C]11.5810840335186[/C][C]8.04435956370176[/C][C]15.1178085033355[/C][/ROW]
[ROW][C]134[/C][C]12.4190673231092[/C][C]8.48058960369755[/C][C]16.3575450425208[/C][/ROW]
[ROW][C]135[/C][C]14.4656490169454[/C][C]10.1490216861198[/C][C]18.7822763477709[/C][/ROW]
[ROW][C]136[/C][C]15.2426047130626[/C][C]10.5654574728026[/C][C]19.9197519533226[/C][/ROW]
[ROW][C]137[/C][C]16.2210897326469[/C][C]11.1970273167615[/C][C]21.2451521485323[/C][/ROW]
[ROW][C]138[/C][C]15.4905848508294[/C][C]10.1303559285690[/C][C]20.8508137730898[/C][/ROW]
[ROW][C]139[/C][C]13.3677969913248[/C][C]7.68004249952992[/C][C]19.0555514831196[/C][/ROW]
[ROW][C]140[/C][C]11.8587847058867[/C][C]5.85054150431082[/C][C]17.8670279074626[/C][/ROW]
[ROW][C]141[/C][C]16.4174932378915[/C][C]10.0945467917341[/C][C]22.7404396840489[/C][/ROW]
[ROW][C]142[/C][C]14.8381993395343[/C][C]8.20533876773776[/C][C]21.4710599113309[/C][/ROW]
[ROW][C]143[/C][C]13.3119559448242[/C][C]6.3731634553543[/C][C]20.2507484342941[/C][/ROW]
[ROW][C]144[/C][C]12.1542957289867[/C][C]4.91289052468055[/C][C]19.3957009332929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115121&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115121&T=3

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13311.58108403351868.0443595637017615.1178085033355
13412.41906732310928.4805896036975516.3575450425208
13514.465649016945410.149021686119818.7822763477709
13615.242604713062610.565457472802619.9197519533226
13716.221089732646911.197027316761521.2451521485323
13815.490584850829410.130355928569020.8508137730898
13913.36779699132487.6800424995299219.0555514831196
14011.85878470588675.8505415043108217.8670279074626
14116.417493237891510.094546791734122.7404396840489
14214.83819933953438.2053387677377621.4710599113309
14313.31195594482426.373163455354320.2507484342941
14412.15429572898674.9128905246805519.3957009332929


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')