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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 12 Dec 2017 18:28:19 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/12/t1513100074zm78bm6196mtdri.htm/, Retrieved Fri, 01 Nov 2024 00:09:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309169, Retrieved Fri, 01 Nov 2024 00:09:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponentional tri...] [2017-12-12 17:28:19] [cbdc27eb3c0ce1e50616f96e5af4492f] [Current]
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Dataseries X:
97.7
88.9
96.5
89.5
85.4
84.3
83.7
86.2
90.7
95.7
95.6
97
97.2
86.6
88.4
81.4
86.9
84.9
83.7
86.8
88.3
92.5
94.7
94.5
98.7
88.6
95.2
91.3
91.7
89.3
88.7
91.2
88.6
94.6
96
94.3
102
93.4
96.7
93.7
91.6
89.6
92.9
94.1
92
97.5
92.7
100.7
105.9
95.3
99.8
91.3
90.8
87.1
91.4
86.1
87.1
92.6
96.6
105.3
102.4
98.2
98.6
92.6
87.9
84.1
86.7
84.4
86
90.4
92.9
105.8
106
99.1
99.9
88.1
87.8
87.1
85.9
86.5
84.1
92.1
93.3
98.9
103
98.4
100.7
92.3
89
88.9
85.5
90.1
87
97.1
101.5
103
106.1
96.1
94.2
89.1
85.2
86.5
88
88.4
87.9
95.7
94.8
105.2
108.7
96.1
98.3
88.6
90.8
88.1
91.9
98.5
98.6
100.3
98.7
110.7
115.4
105.4
108
94.5
96.5
91
94.1
96.4
93.1
97.5
102.5
105.7
109.1
97.2
100.3
91.3
94.3
89.5
89.3
93.4
91.9
92.9
93.7
100.1
105.5
110.5
89.5
90.4
89.9
84.6
86.2
83.4
82.9
81.8
87.6
94.6
99.6
96.7
99.8
83.8
82.4
86.8
91
85.3
83.6
94
100.3
107.1
100.7
95.5
92.9
79.2
82
79.3
81.5
76
73.1
80.4
82.1
90.5
98.1
89.5
86.5
77
74.7
73.4
72.5
69.3
75.2
83.5
90.5
92.2
110.5
101.8
107.4
95.5
84.5
81.1
86.2
91.5
84.7
92.2
99.2
104.5
113
100.4
101
84.8
86.5
91.7
94.8
95




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309169&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309169&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.489424633285978
beta0.0033405842979422
gamma0.580456908917259

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.489424633285978 \tabularnewline
beta & 0.0033405842979422 \tabularnewline
gamma & 0.580456908917259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309169&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]0.489424633285978[/C][/ROW]
[ROW][C]beta[/C][C]0.0033405842979422[/C][/ROW]
[ROW][C]gamma[/C][C]0.580456908917259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309169&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.489424633285978
beta0.0033405842979422
gamma0.580456908917259







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397.298.5406902105951-1.34069021059513
1486.687.0283710321231-0.428371032123081
1588.488.5362752897322-0.136275289732211
1681.481.5279709764879-0.127970976487887
1786.986.9768580107083-0.0768580107083352
1884.984.9172526075208-0.0172526075207884
1983.781.73166005581831.96833994418172
2086.885.1221931133311.67780688666898
2188.390.7055617471191-2.40556174711909
2292.595.0023707788639-2.50237077886389
2394.793.7911340058050.908865994194954
2494.595.3449473329827-0.844947332982741
2598.794.53601818619164.16398181380839
2688.686.08916971430362.5108302856964
2795.289.14489918960646.05510081039355
2891.384.90398500411526.39601499588476
2991.794.0522684529454-2.35226845294537
3089.390.7950480007364-1.49504800073643
3188.787.34187443261081.35812556738922
3291.290.50637753799960.693622462000405
3388.694.5984373121041-5.99843731210412
3494.697.2946367118852-2.69463671188525
359697.0532611437824-1.05326114378244
3694.397.1555740886016-2.8555740886016
3710296.84524165163655.15475834836347
3893.488.22044913531455.17955086468547
3996.793.68110563871923.01889436128079
4093.787.90296728226385.79703271773622
4191.694.1970342377097-2.59703423770972
4289.691.0647203059072-1.46472030590719
4392.988.46238399012864.43761600987143
4494.193.01062671759611.08937328240394
459295.3205816450594-3.32058164505938
4697.5100.601334845667-3.10133484566715
4792.7100.735520114048-8.03552011404807
48100.796.88317500137383.81682499862617
49105.9102.3384554860523.5615445139485
5095.392.56465765699122.73534234300882
5199.896.22788477166933.57211522833073
5291.391.3738249263312-0.0738249263312127
5390.892.2844395287589-1.48443952875891
5487.190.0408769686152-2.94087696861524
5591.488.43497263806682.9650273619332
5686.191.2326418068929-5.13264180689295
5787.189.1298090634055-2.02980906340548
5892.694.7323667350736-2.1323667350736
5996.693.76169942822452.83830057177545
60105.398.75959992905516.5404000709449
61102.4105.543588219864-3.1435882198643
6298.292.35891847172045.84108152827956
6398.697.79265675784370.807343242156293
6492.690.57194371622362.02805628377644
6587.992.0972753288122-4.19727532881222
6684.188.1032829640416-4.0032829640416
6786.787.682445241045-0.982445241044985
6884.486.1366700164529-1.73667001645288
698686.5753722568462-0.575372256846165
7090.492.7582436940753-2.35824369407534
7192.993.1121559226043-0.212155922604296
72105.897.4996158936828.30038410631799
73106102.2402198601453.75978013985491
7499.194.966434348214.13356565179001
7599.998.07766847221041.82233152778956
7688.191.67621937329-3.57621937328996
7787.888.6126873188204-0.812687318820409
7887.186.32036163772280.779638362277154
7985.989.1974776731827-3.29747767318271
8086.586.28797401378960.212025986210449
8184.188.0681023259726-3.96810232597265
8292.192.05868154839620.0413184516037575
8393.394.2618624101664-0.961862410166418
8498.9100.779911384024-1.87991138402366
8510399.18611463692183.81388536307821
8698.492.36701907143916.03298092856092
87100.795.69822020291615.00177979708393
8892.389.35356162051052.94643837948945
898990.3031568368486-1.30315683684856
9088.988.22666115700470.673338842995264
9185.589.8614009634956-4.36140096349557
9290.187.47779398773562.62220601226441
938789.198651312998-2.198651312998
9497.195.53097310031751.56902689968253
95101.598.29491059158153.20508940841846
96103107.069802110009-4.06980211000864
97106.1106.16234995582-0.0623499558202241
9896.197.7582967070002-1.65829670700016
9994.296.9865602010526-2.78656020105264
10089.186.57351357645722.52648642354278
10185.286.1165909518759-0.916590951875918
10286.584.83699062282531.66300937717472
1038885.43052890751962.56947109248041
10488.488.5084187977972-0.108418797797199
10587.987.46769154293660.432308457063371
10695.796.2266593398136-0.526659339813634
10794.898.4157473340678-3.61574733406781
108105.2101.4511144489423.74888555105822
109108.7105.5476800555043.1523199444965
11096.198.1672562870916-2.06725628709165
11198.396.85496452141621.44503547858383
11288.689.8749736633895-1.27497366338952
11390.886.52176008976324.27823991023678
11488.188.5608882070516-0.460888207051568
11591.988.38770320195523.51229679804476
11698.591.18091048633877.31908951366132
11798.693.90855590411144.69144409588861
118100.3105.303581723062-5.00358172306214
11998.7104.514343245628-5.81434324562805
120110.7109.1156497765661.58435022343396
121115.4112.1016132940943.2983867059059
122105.4102.7145144541592.68548554584102
123108104.8614971990683.13850280093205
12494.597.210762337359-2.710762337359
12596.594.71763970984721.78236029015279
1269194.0658222963437-3.06582229634371
12794.193.85820174575660.241798254243392
12896.496.17866068992440.221339310075621
12993.194.6321919255452-1.53219192554516
13097.599.8243824732456-2.32438247324562
131102.5100.0136625649072.48633743509293
132105.7111.000747568092-5.30074756809171
133109.1111.058535138485-1.95853513848537
13497.299.3412155788951-2.14121557889509
135100.399.16348070183481.13651929816521
13691.389.53841936941281.76158063058723
13794.390.53693355534443.76306644465562
13889.589.5070904910066-0.00709049100660764
13989.391.7174477303793-2.41744773037932
14093.492.6366857260670.763314273933005
14191.990.89751968557471.0024803144253
14292.996.9576581225063-4.05765812250627
14393.797.6213435727307-3.92134357273069
144100.1102.646515690114-2.54651569011358
145105.5104.8327760288330.66722397116682
146110.594.757260747402915.7427392525971
14789.5104.418030315439-14.9180303154393
14890.487.40160534867492.99839465132507
14989.989.55508980806330.344910191936748
15084.685.8839785608697-1.28397856086968
15186.286.6602311803804-0.460231180380404
15283.489.3531804863035-5.95318048630348
15382.984.5202135669407-1.62021356694072
15481.887.3893132973817-5.58931329738166
15587.687.02446949595310.57553050404691
15694.694.05673829210060.543261707899376
15799.698.40670382759561.19329617240435
15896.793.06319155046453.63680844953555
15999.888.192467326734411.6075326732656
16083.889.4065786031964-5.60657860319644
16182.486.5560772138836-4.15607721388355
16286.880.43380639001686.36619360998323
1639185.17047206067395.82952793932607
16485.389.2909970753235-3.99099707532349
16583.686.6941693216046-3.09416932160464
1669487.68199665897166.3180033410284
167100.395.40824365134374.89175634865634
168107.1105.3963987306641.70360126933639
169100.7111.099503936517-10.399503936517
17095.5100.469951476688-4.96995147668768
17192.993.4551866696006-0.555186669600559
17279.283.9579893130804-4.75798931308039
1738281.89984276693470.100157233065289
17479.380.92308798005-1.62308798005
17581.581.42697522830510.0730247716948753
1767679.9160971122756-3.91609711227555
17773.177.610780569764-4.51078056976397
17880.480.04323451267470.356765487325262
17982.183.7816924238721-1.68169242387206
18090.588.44433856729392.05566143270615
18198.190.33297761272627.76702238727376
18289.590.4740019218478-0.974001921847787
18386.586.9219460673339-0.421946067333892
1847776.89565839786740.104341602132649
18574.778.5763317880713-3.87633178807133
18673.475.2179137283244-1.81791372832437
18772.575.9879845580986-3.48798455809862
18869.371.7391658464558-2.43916584645582
18975.269.96535158748725.23464841251283
19083.578.48024590552715.01975409447287
19190.583.92279671758866.57720328241136
19292.294.1332344389086-1.93323443890864
193110.595.777178471427414.7228215285726
194101.896.34044009276435.45955990723566
195107.495.846532114799311.5534678852007
19695.590.24106449830065.25893550169937
19784.593.4036385161438-8.90363851614376
19881.188.1045493395617-7.00454933956166
19986.286.04474358458420.155256415415792
20091.583.55062559843877.94937440156129
20184.789.591441475169-4.89144147516897
20292.294.150957443425-1.950957443425
20399.297.07061309585032.1293869041497
204104.5103.0761339992771.42386600072253
205113111.9248966661381.07510333386209
206100.4102.595018792916-2.19501879291558
20710199.96341180631431.03658819368574
20884.887.8482452934544-3.04824529345437
20986.582.90876165984293.5912383401571
21091.784.20882813287997.49117186712014
21194.891.6149283764713.18507162352897
2129592.81189492074522.18810507925477

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 97.2 & 98.5406902105951 & -1.34069021059513 \tabularnewline
14 & 86.6 & 87.0283710321231 & -0.428371032123081 \tabularnewline
15 & 88.4 & 88.5362752897322 & -0.136275289732211 \tabularnewline
16 & 81.4 & 81.5279709764879 & -0.127970976487887 \tabularnewline
17 & 86.9 & 86.9768580107083 & -0.0768580107083352 \tabularnewline
18 & 84.9 & 84.9172526075208 & -0.0172526075207884 \tabularnewline
19 & 83.7 & 81.7316600558183 & 1.96833994418172 \tabularnewline
20 & 86.8 & 85.122193113331 & 1.67780688666898 \tabularnewline
21 & 88.3 & 90.7055617471191 & -2.40556174711909 \tabularnewline
22 & 92.5 & 95.0023707788639 & -2.50237077886389 \tabularnewline
23 & 94.7 & 93.791134005805 & 0.908865994194954 \tabularnewline
24 & 94.5 & 95.3449473329827 & -0.844947332982741 \tabularnewline
25 & 98.7 & 94.5360181861916 & 4.16398181380839 \tabularnewline
26 & 88.6 & 86.0891697143036 & 2.5108302856964 \tabularnewline
27 & 95.2 & 89.1448991896064 & 6.05510081039355 \tabularnewline
28 & 91.3 & 84.9039850041152 & 6.39601499588476 \tabularnewline
29 & 91.7 & 94.0522684529454 & -2.35226845294537 \tabularnewline
30 & 89.3 & 90.7950480007364 & -1.49504800073643 \tabularnewline
31 & 88.7 & 87.3418744326108 & 1.35812556738922 \tabularnewline
32 & 91.2 & 90.5063775379996 & 0.693622462000405 \tabularnewline
33 & 88.6 & 94.5984373121041 & -5.99843731210412 \tabularnewline
34 & 94.6 & 97.2946367118852 & -2.69463671188525 \tabularnewline
35 & 96 & 97.0532611437824 & -1.05326114378244 \tabularnewline
36 & 94.3 & 97.1555740886016 & -2.8555740886016 \tabularnewline
37 & 102 & 96.8452416516365 & 5.15475834836347 \tabularnewline
38 & 93.4 & 88.2204491353145 & 5.17955086468547 \tabularnewline
39 & 96.7 & 93.6811056387192 & 3.01889436128079 \tabularnewline
40 & 93.7 & 87.9029672822638 & 5.79703271773622 \tabularnewline
41 & 91.6 & 94.1970342377097 & -2.59703423770972 \tabularnewline
42 & 89.6 & 91.0647203059072 & -1.46472030590719 \tabularnewline
43 & 92.9 & 88.4623839901286 & 4.43761600987143 \tabularnewline
44 & 94.1 & 93.0106267175961 & 1.08937328240394 \tabularnewline
45 & 92 & 95.3205816450594 & -3.32058164505938 \tabularnewline
46 & 97.5 & 100.601334845667 & -3.10133484566715 \tabularnewline
47 & 92.7 & 100.735520114048 & -8.03552011404807 \tabularnewline
48 & 100.7 & 96.8831750013738 & 3.81682499862617 \tabularnewline
49 & 105.9 & 102.338455486052 & 3.5615445139485 \tabularnewline
50 & 95.3 & 92.5646576569912 & 2.73534234300882 \tabularnewline
51 & 99.8 & 96.2278847716693 & 3.57211522833073 \tabularnewline
52 & 91.3 & 91.3738249263312 & -0.0738249263312127 \tabularnewline
53 & 90.8 & 92.2844395287589 & -1.48443952875891 \tabularnewline
54 & 87.1 & 90.0408769686152 & -2.94087696861524 \tabularnewline
55 & 91.4 & 88.4349726380668 & 2.9650273619332 \tabularnewline
56 & 86.1 & 91.2326418068929 & -5.13264180689295 \tabularnewline
57 & 87.1 & 89.1298090634055 & -2.02980906340548 \tabularnewline
58 & 92.6 & 94.7323667350736 & -2.1323667350736 \tabularnewline
59 & 96.6 & 93.7616994282245 & 2.83830057177545 \tabularnewline
60 & 105.3 & 98.7595999290551 & 6.5404000709449 \tabularnewline
61 & 102.4 & 105.543588219864 & -3.1435882198643 \tabularnewline
62 & 98.2 & 92.3589184717204 & 5.84108152827956 \tabularnewline
63 & 98.6 & 97.7926567578437 & 0.807343242156293 \tabularnewline
64 & 92.6 & 90.5719437162236 & 2.02805628377644 \tabularnewline
65 & 87.9 & 92.0972753288122 & -4.19727532881222 \tabularnewline
66 & 84.1 & 88.1032829640416 & -4.0032829640416 \tabularnewline
67 & 86.7 & 87.682445241045 & -0.982445241044985 \tabularnewline
68 & 84.4 & 86.1366700164529 & -1.73667001645288 \tabularnewline
69 & 86 & 86.5753722568462 & -0.575372256846165 \tabularnewline
70 & 90.4 & 92.7582436940753 & -2.35824369407534 \tabularnewline
71 & 92.9 & 93.1121559226043 & -0.212155922604296 \tabularnewline
72 & 105.8 & 97.499615893682 & 8.30038410631799 \tabularnewline
73 & 106 & 102.240219860145 & 3.75978013985491 \tabularnewline
74 & 99.1 & 94.96643434821 & 4.13356565179001 \tabularnewline
75 & 99.9 & 98.0776684722104 & 1.82233152778956 \tabularnewline
76 & 88.1 & 91.67621937329 & -3.57621937328996 \tabularnewline
77 & 87.8 & 88.6126873188204 & -0.812687318820409 \tabularnewline
78 & 87.1 & 86.3203616377228 & 0.779638362277154 \tabularnewline
79 & 85.9 & 89.1974776731827 & -3.29747767318271 \tabularnewline
80 & 86.5 & 86.2879740137896 & 0.212025986210449 \tabularnewline
81 & 84.1 & 88.0681023259726 & -3.96810232597265 \tabularnewline
82 & 92.1 & 92.0586815483962 & 0.0413184516037575 \tabularnewline
83 & 93.3 & 94.2618624101664 & -0.961862410166418 \tabularnewline
84 & 98.9 & 100.779911384024 & -1.87991138402366 \tabularnewline
85 & 103 & 99.1861146369218 & 3.81388536307821 \tabularnewline
86 & 98.4 & 92.3670190714391 & 6.03298092856092 \tabularnewline
87 & 100.7 & 95.6982202029161 & 5.00177979708393 \tabularnewline
88 & 92.3 & 89.3535616205105 & 2.94643837948945 \tabularnewline
89 & 89 & 90.3031568368486 & -1.30315683684856 \tabularnewline
90 & 88.9 & 88.2266611570047 & 0.673338842995264 \tabularnewline
91 & 85.5 & 89.8614009634956 & -4.36140096349557 \tabularnewline
92 & 90.1 & 87.4777939877356 & 2.62220601226441 \tabularnewline
93 & 87 & 89.198651312998 & -2.198651312998 \tabularnewline
94 & 97.1 & 95.5309731003175 & 1.56902689968253 \tabularnewline
95 & 101.5 & 98.2949105915815 & 3.20508940841846 \tabularnewline
96 & 103 & 107.069802110009 & -4.06980211000864 \tabularnewline
97 & 106.1 & 106.16234995582 & -0.0623499558202241 \tabularnewline
98 & 96.1 & 97.7582967070002 & -1.65829670700016 \tabularnewline
99 & 94.2 & 96.9865602010526 & -2.78656020105264 \tabularnewline
100 & 89.1 & 86.5735135764572 & 2.52648642354278 \tabularnewline
101 & 85.2 & 86.1165909518759 & -0.916590951875918 \tabularnewline
102 & 86.5 & 84.8369906228253 & 1.66300937717472 \tabularnewline
103 & 88 & 85.4305289075196 & 2.56947109248041 \tabularnewline
104 & 88.4 & 88.5084187977972 & -0.108418797797199 \tabularnewline
105 & 87.9 & 87.4676915429366 & 0.432308457063371 \tabularnewline
106 & 95.7 & 96.2266593398136 & -0.526659339813634 \tabularnewline
107 & 94.8 & 98.4157473340678 & -3.61574733406781 \tabularnewline
108 & 105.2 & 101.451114448942 & 3.74888555105822 \tabularnewline
109 & 108.7 & 105.547680055504 & 3.1523199444965 \tabularnewline
110 & 96.1 & 98.1672562870916 & -2.06725628709165 \tabularnewline
111 & 98.3 & 96.8549645214162 & 1.44503547858383 \tabularnewline
112 & 88.6 & 89.8749736633895 & -1.27497366338952 \tabularnewline
113 & 90.8 & 86.5217600897632 & 4.27823991023678 \tabularnewline
114 & 88.1 & 88.5608882070516 & -0.460888207051568 \tabularnewline
115 & 91.9 & 88.3877032019552 & 3.51229679804476 \tabularnewline
116 & 98.5 & 91.1809104863387 & 7.31908951366132 \tabularnewline
117 & 98.6 & 93.9085559041114 & 4.69144409588861 \tabularnewline
118 & 100.3 & 105.303581723062 & -5.00358172306214 \tabularnewline
119 & 98.7 & 104.514343245628 & -5.81434324562805 \tabularnewline
120 & 110.7 & 109.115649776566 & 1.58435022343396 \tabularnewline
121 & 115.4 & 112.101613294094 & 3.2983867059059 \tabularnewline
122 & 105.4 & 102.714514454159 & 2.68548554584102 \tabularnewline
123 & 108 & 104.861497199068 & 3.13850280093205 \tabularnewline
124 & 94.5 & 97.210762337359 & -2.710762337359 \tabularnewline
125 & 96.5 & 94.7176397098472 & 1.78236029015279 \tabularnewline
126 & 91 & 94.0658222963437 & -3.06582229634371 \tabularnewline
127 & 94.1 & 93.8582017457566 & 0.241798254243392 \tabularnewline
128 & 96.4 & 96.1786606899244 & 0.221339310075621 \tabularnewline
129 & 93.1 & 94.6321919255452 & -1.53219192554516 \tabularnewline
130 & 97.5 & 99.8243824732456 & -2.32438247324562 \tabularnewline
131 & 102.5 & 100.013662564907 & 2.48633743509293 \tabularnewline
132 & 105.7 & 111.000747568092 & -5.30074756809171 \tabularnewline
133 & 109.1 & 111.058535138485 & -1.95853513848537 \tabularnewline
134 & 97.2 & 99.3412155788951 & -2.14121557889509 \tabularnewline
135 & 100.3 & 99.1634807018348 & 1.13651929816521 \tabularnewline
136 & 91.3 & 89.5384193694128 & 1.76158063058723 \tabularnewline
137 & 94.3 & 90.5369335553444 & 3.76306644465562 \tabularnewline
138 & 89.5 & 89.5070904910066 & -0.00709049100660764 \tabularnewline
139 & 89.3 & 91.7174477303793 & -2.41744773037932 \tabularnewline
140 & 93.4 & 92.636685726067 & 0.763314273933005 \tabularnewline
141 & 91.9 & 90.8975196855747 & 1.0024803144253 \tabularnewline
142 & 92.9 & 96.9576581225063 & -4.05765812250627 \tabularnewline
143 & 93.7 & 97.6213435727307 & -3.92134357273069 \tabularnewline
144 & 100.1 & 102.646515690114 & -2.54651569011358 \tabularnewline
145 & 105.5 & 104.832776028833 & 0.66722397116682 \tabularnewline
146 & 110.5 & 94.7572607474029 & 15.7427392525971 \tabularnewline
147 & 89.5 & 104.418030315439 & -14.9180303154393 \tabularnewline
148 & 90.4 & 87.4016053486749 & 2.99839465132507 \tabularnewline
149 & 89.9 & 89.5550898080633 & 0.344910191936748 \tabularnewline
150 & 84.6 & 85.8839785608697 & -1.28397856086968 \tabularnewline
151 & 86.2 & 86.6602311803804 & -0.460231180380404 \tabularnewline
152 & 83.4 & 89.3531804863035 & -5.95318048630348 \tabularnewline
153 & 82.9 & 84.5202135669407 & -1.62021356694072 \tabularnewline
154 & 81.8 & 87.3893132973817 & -5.58931329738166 \tabularnewline
155 & 87.6 & 87.0244694959531 & 0.57553050404691 \tabularnewline
156 & 94.6 & 94.0567382921006 & 0.543261707899376 \tabularnewline
157 & 99.6 & 98.4067038275956 & 1.19329617240435 \tabularnewline
158 & 96.7 & 93.0631915504645 & 3.63680844953555 \tabularnewline
159 & 99.8 & 88.1924673267344 & 11.6075326732656 \tabularnewline
160 & 83.8 & 89.4065786031964 & -5.60657860319644 \tabularnewline
161 & 82.4 & 86.5560772138836 & -4.15607721388355 \tabularnewline
162 & 86.8 & 80.4338063900168 & 6.36619360998323 \tabularnewline
163 & 91 & 85.1704720606739 & 5.82952793932607 \tabularnewline
164 & 85.3 & 89.2909970753235 & -3.99099707532349 \tabularnewline
165 & 83.6 & 86.6941693216046 & -3.09416932160464 \tabularnewline
166 & 94 & 87.6819966589716 & 6.3180033410284 \tabularnewline
167 & 100.3 & 95.4082436513437 & 4.89175634865634 \tabularnewline
168 & 107.1 & 105.396398730664 & 1.70360126933639 \tabularnewline
169 & 100.7 & 111.099503936517 & -10.399503936517 \tabularnewline
170 & 95.5 & 100.469951476688 & -4.96995147668768 \tabularnewline
171 & 92.9 & 93.4551866696006 & -0.555186669600559 \tabularnewline
172 & 79.2 & 83.9579893130804 & -4.75798931308039 \tabularnewline
173 & 82 & 81.8998427669347 & 0.100157233065289 \tabularnewline
174 & 79.3 & 80.92308798005 & -1.62308798005 \tabularnewline
175 & 81.5 & 81.4269752283051 & 0.0730247716948753 \tabularnewline
176 & 76 & 79.9160971122756 & -3.91609711227555 \tabularnewline
177 & 73.1 & 77.610780569764 & -4.51078056976397 \tabularnewline
178 & 80.4 & 80.0432345126747 & 0.356765487325262 \tabularnewline
179 & 82.1 & 83.7816924238721 & -1.68169242387206 \tabularnewline
180 & 90.5 & 88.4443385672939 & 2.05566143270615 \tabularnewline
181 & 98.1 & 90.3329776127262 & 7.76702238727376 \tabularnewline
182 & 89.5 & 90.4740019218478 & -0.974001921847787 \tabularnewline
183 & 86.5 & 86.9219460673339 & -0.421946067333892 \tabularnewline
184 & 77 & 76.8956583978674 & 0.104341602132649 \tabularnewline
185 & 74.7 & 78.5763317880713 & -3.87633178807133 \tabularnewline
186 & 73.4 & 75.2179137283244 & -1.81791372832437 \tabularnewline
187 & 72.5 & 75.9879845580986 & -3.48798455809862 \tabularnewline
188 & 69.3 & 71.7391658464558 & -2.43916584645582 \tabularnewline
189 & 75.2 & 69.9653515874872 & 5.23464841251283 \tabularnewline
190 & 83.5 & 78.4802459055271 & 5.01975409447287 \tabularnewline
191 & 90.5 & 83.9227967175886 & 6.57720328241136 \tabularnewline
192 & 92.2 & 94.1332344389086 & -1.93323443890864 \tabularnewline
193 & 110.5 & 95.7771784714274 & 14.7228215285726 \tabularnewline
194 & 101.8 & 96.3404400927643 & 5.45955990723566 \tabularnewline
195 & 107.4 & 95.8465321147993 & 11.5534678852007 \tabularnewline
196 & 95.5 & 90.2410644983006 & 5.25893550169937 \tabularnewline
197 & 84.5 & 93.4036385161438 & -8.90363851614376 \tabularnewline
198 & 81.1 & 88.1045493395617 & -7.00454933956166 \tabularnewline
199 & 86.2 & 86.0447435845842 & 0.155256415415792 \tabularnewline
200 & 91.5 & 83.5506255984387 & 7.94937440156129 \tabularnewline
201 & 84.7 & 89.591441475169 & -4.89144147516897 \tabularnewline
202 & 92.2 & 94.150957443425 & -1.950957443425 \tabularnewline
203 & 99.2 & 97.0706130958503 & 2.1293869041497 \tabularnewline
204 & 104.5 & 103.076133999277 & 1.42386600072253 \tabularnewline
205 & 113 & 111.924896666138 & 1.07510333386209 \tabularnewline
206 & 100.4 & 102.595018792916 & -2.19501879291558 \tabularnewline
207 & 101 & 99.9634118063143 & 1.03658819368574 \tabularnewline
208 & 84.8 & 87.8482452934544 & -3.04824529345437 \tabularnewline
209 & 86.5 & 82.9087616598429 & 3.5912383401571 \tabularnewline
210 & 91.7 & 84.2088281328799 & 7.49117186712014 \tabularnewline
211 & 94.8 & 91.614928376471 & 3.18507162352897 \tabularnewline
212 & 95 & 92.8118949207452 & 2.18810507925477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309169&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]97.2[/C][C]98.5406902105951[/C][C]-1.34069021059513[/C][/ROW]
[ROW][C]14[/C][C]86.6[/C][C]87.0283710321231[/C][C]-0.428371032123081[/C][/ROW]
[ROW][C]15[/C][C]88.4[/C][C]88.5362752897322[/C][C]-0.136275289732211[/C][/ROW]
[ROW][C]16[/C][C]81.4[/C][C]81.5279709764879[/C][C]-0.127970976487887[/C][/ROW]
[ROW][C]17[/C][C]86.9[/C][C]86.9768580107083[/C][C]-0.0768580107083352[/C][/ROW]
[ROW][C]18[/C][C]84.9[/C][C]84.9172526075208[/C][C]-0.0172526075207884[/C][/ROW]
[ROW][C]19[/C][C]83.7[/C][C]81.7316600558183[/C][C]1.96833994418172[/C][/ROW]
[ROW][C]20[/C][C]86.8[/C][C]85.122193113331[/C][C]1.67780688666898[/C][/ROW]
[ROW][C]21[/C][C]88.3[/C][C]90.7055617471191[/C][C]-2.40556174711909[/C][/ROW]
[ROW][C]22[/C][C]92.5[/C][C]95.0023707788639[/C][C]-2.50237077886389[/C][/ROW]
[ROW][C]23[/C][C]94.7[/C][C]93.791134005805[/C][C]0.908865994194954[/C][/ROW]
[ROW][C]24[/C][C]94.5[/C][C]95.3449473329827[/C][C]-0.844947332982741[/C][/ROW]
[ROW][C]25[/C][C]98.7[/C][C]94.5360181861916[/C][C]4.16398181380839[/C][/ROW]
[ROW][C]26[/C][C]88.6[/C][C]86.0891697143036[/C][C]2.5108302856964[/C][/ROW]
[ROW][C]27[/C][C]95.2[/C][C]89.1448991896064[/C][C]6.05510081039355[/C][/ROW]
[ROW][C]28[/C][C]91.3[/C][C]84.9039850041152[/C][C]6.39601499588476[/C][/ROW]
[ROW][C]29[/C][C]91.7[/C][C]94.0522684529454[/C][C]-2.35226845294537[/C][/ROW]
[ROW][C]30[/C][C]89.3[/C][C]90.7950480007364[/C][C]-1.49504800073643[/C][/ROW]
[ROW][C]31[/C][C]88.7[/C][C]87.3418744326108[/C][C]1.35812556738922[/C][/ROW]
[ROW][C]32[/C][C]91.2[/C][C]90.5063775379996[/C][C]0.693622462000405[/C][/ROW]
[ROW][C]33[/C][C]88.6[/C][C]94.5984373121041[/C][C]-5.99843731210412[/C][/ROW]
[ROW][C]34[/C][C]94.6[/C][C]97.2946367118852[/C][C]-2.69463671188525[/C][/ROW]
[ROW][C]35[/C][C]96[/C][C]97.0532611437824[/C][C]-1.05326114378244[/C][/ROW]
[ROW][C]36[/C][C]94.3[/C][C]97.1555740886016[/C][C]-2.8555740886016[/C][/ROW]
[ROW][C]37[/C][C]102[/C][C]96.8452416516365[/C][C]5.15475834836347[/C][/ROW]
[ROW][C]38[/C][C]93.4[/C][C]88.2204491353145[/C][C]5.17955086468547[/C][/ROW]
[ROW][C]39[/C][C]96.7[/C][C]93.6811056387192[/C][C]3.01889436128079[/C][/ROW]
[ROW][C]40[/C][C]93.7[/C][C]87.9029672822638[/C][C]5.79703271773622[/C][/ROW]
[ROW][C]41[/C][C]91.6[/C][C]94.1970342377097[/C][C]-2.59703423770972[/C][/ROW]
[ROW][C]42[/C][C]89.6[/C][C]91.0647203059072[/C][C]-1.46472030590719[/C][/ROW]
[ROW][C]43[/C][C]92.9[/C][C]88.4623839901286[/C][C]4.43761600987143[/C][/ROW]
[ROW][C]44[/C][C]94.1[/C][C]93.0106267175961[/C][C]1.08937328240394[/C][/ROW]
[ROW][C]45[/C][C]92[/C][C]95.3205816450594[/C][C]-3.32058164505938[/C][/ROW]
[ROW][C]46[/C][C]97.5[/C][C]100.601334845667[/C][C]-3.10133484566715[/C][/ROW]
[ROW][C]47[/C][C]92.7[/C][C]100.735520114048[/C][C]-8.03552011404807[/C][/ROW]
[ROW][C]48[/C][C]100.7[/C][C]96.8831750013738[/C][C]3.81682499862617[/C][/ROW]
[ROW][C]49[/C][C]105.9[/C][C]102.338455486052[/C][C]3.5615445139485[/C][/ROW]
[ROW][C]50[/C][C]95.3[/C][C]92.5646576569912[/C][C]2.73534234300882[/C][/ROW]
[ROW][C]51[/C][C]99.8[/C][C]96.2278847716693[/C][C]3.57211522833073[/C][/ROW]
[ROW][C]52[/C][C]91.3[/C][C]91.3738249263312[/C][C]-0.0738249263312127[/C][/ROW]
[ROW][C]53[/C][C]90.8[/C][C]92.2844395287589[/C][C]-1.48443952875891[/C][/ROW]
[ROW][C]54[/C][C]87.1[/C][C]90.0408769686152[/C][C]-2.94087696861524[/C][/ROW]
[ROW][C]55[/C][C]91.4[/C][C]88.4349726380668[/C][C]2.9650273619332[/C][/ROW]
[ROW][C]56[/C][C]86.1[/C][C]91.2326418068929[/C][C]-5.13264180689295[/C][/ROW]
[ROW][C]57[/C][C]87.1[/C][C]89.1298090634055[/C][C]-2.02980906340548[/C][/ROW]
[ROW][C]58[/C][C]92.6[/C][C]94.7323667350736[/C][C]-2.1323667350736[/C][/ROW]
[ROW][C]59[/C][C]96.6[/C][C]93.7616994282245[/C][C]2.83830057177545[/C][/ROW]
[ROW][C]60[/C][C]105.3[/C][C]98.7595999290551[/C][C]6.5404000709449[/C][/ROW]
[ROW][C]61[/C][C]102.4[/C][C]105.543588219864[/C][C]-3.1435882198643[/C][/ROW]
[ROW][C]62[/C][C]98.2[/C][C]92.3589184717204[/C][C]5.84108152827956[/C][/ROW]
[ROW][C]63[/C][C]98.6[/C][C]97.7926567578437[/C][C]0.807343242156293[/C][/ROW]
[ROW][C]64[/C][C]92.6[/C][C]90.5719437162236[/C][C]2.02805628377644[/C][/ROW]
[ROW][C]65[/C][C]87.9[/C][C]92.0972753288122[/C][C]-4.19727532881222[/C][/ROW]
[ROW][C]66[/C][C]84.1[/C][C]88.1032829640416[/C][C]-4.0032829640416[/C][/ROW]
[ROW][C]67[/C][C]86.7[/C][C]87.682445241045[/C][C]-0.982445241044985[/C][/ROW]
[ROW][C]68[/C][C]84.4[/C][C]86.1366700164529[/C][C]-1.73667001645288[/C][/ROW]
[ROW][C]69[/C][C]86[/C][C]86.5753722568462[/C][C]-0.575372256846165[/C][/ROW]
[ROW][C]70[/C][C]90.4[/C][C]92.7582436940753[/C][C]-2.35824369407534[/C][/ROW]
[ROW][C]71[/C][C]92.9[/C][C]93.1121559226043[/C][C]-0.212155922604296[/C][/ROW]
[ROW][C]72[/C][C]105.8[/C][C]97.499615893682[/C][C]8.30038410631799[/C][/ROW]
[ROW][C]73[/C][C]106[/C][C]102.240219860145[/C][C]3.75978013985491[/C][/ROW]
[ROW][C]74[/C][C]99.1[/C][C]94.96643434821[/C][C]4.13356565179001[/C][/ROW]
[ROW][C]75[/C][C]99.9[/C][C]98.0776684722104[/C][C]1.82233152778956[/C][/ROW]
[ROW][C]76[/C][C]88.1[/C][C]91.67621937329[/C][C]-3.57621937328996[/C][/ROW]
[ROW][C]77[/C][C]87.8[/C][C]88.6126873188204[/C][C]-0.812687318820409[/C][/ROW]
[ROW][C]78[/C][C]87.1[/C][C]86.3203616377228[/C][C]0.779638362277154[/C][/ROW]
[ROW][C]79[/C][C]85.9[/C][C]89.1974776731827[/C][C]-3.29747767318271[/C][/ROW]
[ROW][C]80[/C][C]86.5[/C][C]86.2879740137896[/C][C]0.212025986210449[/C][/ROW]
[ROW][C]81[/C][C]84.1[/C][C]88.0681023259726[/C][C]-3.96810232597265[/C][/ROW]
[ROW][C]82[/C][C]92.1[/C][C]92.0586815483962[/C][C]0.0413184516037575[/C][/ROW]
[ROW][C]83[/C][C]93.3[/C][C]94.2618624101664[/C][C]-0.961862410166418[/C][/ROW]
[ROW][C]84[/C][C]98.9[/C][C]100.779911384024[/C][C]-1.87991138402366[/C][/ROW]
[ROW][C]85[/C][C]103[/C][C]99.1861146369218[/C][C]3.81388536307821[/C][/ROW]
[ROW][C]86[/C][C]98.4[/C][C]92.3670190714391[/C][C]6.03298092856092[/C][/ROW]
[ROW][C]87[/C][C]100.7[/C][C]95.6982202029161[/C][C]5.00177979708393[/C][/ROW]
[ROW][C]88[/C][C]92.3[/C][C]89.3535616205105[/C][C]2.94643837948945[/C][/ROW]
[ROW][C]89[/C][C]89[/C][C]90.3031568368486[/C][C]-1.30315683684856[/C][/ROW]
[ROW][C]90[/C][C]88.9[/C][C]88.2266611570047[/C][C]0.673338842995264[/C][/ROW]
[ROW][C]91[/C][C]85.5[/C][C]89.8614009634956[/C][C]-4.36140096349557[/C][/ROW]
[ROW][C]92[/C][C]90.1[/C][C]87.4777939877356[/C][C]2.62220601226441[/C][/ROW]
[ROW][C]93[/C][C]87[/C][C]89.198651312998[/C][C]-2.198651312998[/C][/ROW]
[ROW][C]94[/C][C]97.1[/C][C]95.5309731003175[/C][C]1.56902689968253[/C][/ROW]
[ROW][C]95[/C][C]101.5[/C][C]98.2949105915815[/C][C]3.20508940841846[/C][/ROW]
[ROW][C]96[/C][C]103[/C][C]107.069802110009[/C][C]-4.06980211000864[/C][/ROW]
[ROW][C]97[/C][C]106.1[/C][C]106.16234995582[/C][C]-0.0623499558202241[/C][/ROW]
[ROW][C]98[/C][C]96.1[/C][C]97.7582967070002[/C][C]-1.65829670700016[/C][/ROW]
[ROW][C]99[/C][C]94.2[/C][C]96.9865602010526[/C][C]-2.78656020105264[/C][/ROW]
[ROW][C]100[/C][C]89.1[/C][C]86.5735135764572[/C][C]2.52648642354278[/C][/ROW]
[ROW][C]101[/C][C]85.2[/C][C]86.1165909518759[/C][C]-0.916590951875918[/C][/ROW]
[ROW][C]102[/C][C]86.5[/C][C]84.8369906228253[/C][C]1.66300937717472[/C][/ROW]
[ROW][C]103[/C][C]88[/C][C]85.4305289075196[/C][C]2.56947109248041[/C][/ROW]
[ROW][C]104[/C][C]88.4[/C][C]88.5084187977972[/C][C]-0.108418797797199[/C][/ROW]
[ROW][C]105[/C][C]87.9[/C][C]87.4676915429366[/C][C]0.432308457063371[/C][/ROW]
[ROW][C]106[/C][C]95.7[/C][C]96.2266593398136[/C][C]-0.526659339813634[/C][/ROW]
[ROW][C]107[/C][C]94.8[/C][C]98.4157473340678[/C][C]-3.61574733406781[/C][/ROW]
[ROW][C]108[/C][C]105.2[/C][C]101.451114448942[/C][C]3.74888555105822[/C][/ROW]
[ROW][C]109[/C][C]108.7[/C][C]105.547680055504[/C][C]3.1523199444965[/C][/ROW]
[ROW][C]110[/C][C]96.1[/C][C]98.1672562870916[/C][C]-2.06725628709165[/C][/ROW]
[ROW][C]111[/C][C]98.3[/C][C]96.8549645214162[/C][C]1.44503547858383[/C][/ROW]
[ROW][C]112[/C][C]88.6[/C][C]89.8749736633895[/C][C]-1.27497366338952[/C][/ROW]
[ROW][C]113[/C][C]90.8[/C][C]86.5217600897632[/C][C]4.27823991023678[/C][/ROW]
[ROW][C]114[/C][C]88.1[/C][C]88.5608882070516[/C][C]-0.460888207051568[/C][/ROW]
[ROW][C]115[/C][C]91.9[/C][C]88.3877032019552[/C][C]3.51229679804476[/C][/ROW]
[ROW][C]116[/C][C]98.5[/C][C]91.1809104863387[/C][C]7.31908951366132[/C][/ROW]
[ROW][C]117[/C][C]98.6[/C][C]93.9085559041114[/C][C]4.69144409588861[/C][/ROW]
[ROW][C]118[/C][C]100.3[/C][C]105.303581723062[/C][C]-5.00358172306214[/C][/ROW]
[ROW][C]119[/C][C]98.7[/C][C]104.514343245628[/C][C]-5.81434324562805[/C][/ROW]
[ROW][C]120[/C][C]110.7[/C][C]109.115649776566[/C][C]1.58435022343396[/C][/ROW]
[ROW][C]121[/C][C]115.4[/C][C]112.101613294094[/C][C]3.2983867059059[/C][/ROW]
[ROW][C]122[/C][C]105.4[/C][C]102.714514454159[/C][C]2.68548554584102[/C][/ROW]
[ROW][C]123[/C][C]108[/C][C]104.861497199068[/C][C]3.13850280093205[/C][/ROW]
[ROW][C]124[/C][C]94.5[/C][C]97.210762337359[/C][C]-2.710762337359[/C][/ROW]
[ROW][C]125[/C][C]96.5[/C][C]94.7176397098472[/C][C]1.78236029015279[/C][/ROW]
[ROW][C]126[/C][C]91[/C][C]94.0658222963437[/C][C]-3.06582229634371[/C][/ROW]
[ROW][C]127[/C][C]94.1[/C][C]93.8582017457566[/C][C]0.241798254243392[/C][/ROW]
[ROW][C]128[/C][C]96.4[/C][C]96.1786606899244[/C][C]0.221339310075621[/C][/ROW]
[ROW][C]129[/C][C]93.1[/C][C]94.6321919255452[/C][C]-1.53219192554516[/C][/ROW]
[ROW][C]130[/C][C]97.5[/C][C]99.8243824732456[/C][C]-2.32438247324562[/C][/ROW]
[ROW][C]131[/C][C]102.5[/C][C]100.013662564907[/C][C]2.48633743509293[/C][/ROW]
[ROW][C]132[/C][C]105.7[/C][C]111.000747568092[/C][C]-5.30074756809171[/C][/ROW]
[ROW][C]133[/C][C]109.1[/C][C]111.058535138485[/C][C]-1.95853513848537[/C][/ROW]
[ROW][C]134[/C][C]97.2[/C][C]99.3412155788951[/C][C]-2.14121557889509[/C][/ROW]
[ROW][C]135[/C][C]100.3[/C][C]99.1634807018348[/C][C]1.13651929816521[/C][/ROW]
[ROW][C]136[/C][C]91.3[/C][C]89.5384193694128[/C][C]1.76158063058723[/C][/ROW]
[ROW][C]137[/C][C]94.3[/C][C]90.5369335553444[/C][C]3.76306644465562[/C][/ROW]
[ROW][C]138[/C][C]89.5[/C][C]89.5070904910066[/C][C]-0.00709049100660764[/C][/ROW]
[ROW][C]139[/C][C]89.3[/C][C]91.7174477303793[/C][C]-2.41744773037932[/C][/ROW]
[ROW][C]140[/C][C]93.4[/C][C]92.636685726067[/C][C]0.763314273933005[/C][/ROW]
[ROW][C]141[/C][C]91.9[/C][C]90.8975196855747[/C][C]1.0024803144253[/C][/ROW]
[ROW][C]142[/C][C]92.9[/C][C]96.9576581225063[/C][C]-4.05765812250627[/C][/ROW]
[ROW][C]143[/C][C]93.7[/C][C]97.6213435727307[/C][C]-3.92134357273069[/C][/ROW]
[ROW][C]144[/C][C]100.1[/C][C]102.646515690114[/C][C]-2.54651569011358[/C][/ROW]
[ROW][C]145[/C][C]105.5[/C][C]104.832776028833[/C][C]0.66722397116682[/C][/ROW]
[ROW][C]146[/C][C]110.5[/C][C]94.7572607474029[/C][C]15.7427392525971[/C][/ROW]
[ROW][C]147[/C][C]89.5[/C][C]104.418030315439[/C][C]-14.9180303154393[/C][/ROW]
[ROW][C]148[/C][C]90.4[/C][C]87.4016053486749[/C][C]2.99839465132507[/C][/ROW]
[ROW][C]149[/C][C]89.9[/C][C]89.5550898080633[/C][C]0.344910191936748[/C][/ROW]
[ROW][C]150[/C][C]84.6[/C][C]85.8839785608697[/C][C]-1.28397856086968[/C][/ROW]
[ROW][C]151[/C][C]86.2[/C][C]86.6602311803804[/C][C]-0.460231180380404[/C][/ROW]
[ROW][C]152[/C][C]83.4[/C][C]89.3531804863035[/C][C]-5.95318048630348[/C][/ROW]
[ROW][C]153[/C][C]82.9[/C][C]84.5202135669407[/C][C]-1.62021356694072[/C][/ROW]
[ROW][C]154[/C][C]81.8[/C][C]87.3893132973817[/C][C]-5.58931329738166[/C][/ROW]
[ROW][C]155[/C][C]87.6[/C][C]87.0244694959531[/C][C]0.57553050404691[/C][/ROW]
[ROW][C]156[/C][C]94.6[/C][C]94.0567382921006[/C][C]0.543261707899376[/C][/ROW]
[ROW][C]157[/C][C]99.6[/C][C]98.4067038275956[/C][C]1.19329617240435[/C][/ROW]
[ROW][C]158[/C][C]96.7[/C][C]93.0631915504645[/C][C]3.63680844953555[/C][/ROW]
[ROW][C]159[/C][C]99.8[/C][C]88.1924673267344[/C][C]11.6075326732656[/C][/ROW]
[ROW][C]160[/C][C]83.8[/C][C]89.4065786031964[/C][C]-5.60657860319644[/C][/ROW]
[ROW][C]161[/C][C]82.4[/C][C]86.5560772138836[/C][C]-4.15607721388355[/C][/ROW]
[ROW][C]162[/C][C]86.8[/C][C]80.4338063900168[/C][C]6.36619360998323[/C][/ROW]
[ROW][C]163[/C][C]91[/C][C]85.1704720606739[/C][C]5.82952793932607[/C][/ROW]
[ROW][C]164[/C][C]85.3[/C][C]89.2909970753235[/C][C]-3.99099707532349[/C][/ROW]
[ROW][C]165[/C][C]83.6[/C][C]86.6941693216046[/C][C]-3.09416932160464[/C][/ROW]
[ROW][C]166[/C][C]94[/C][C]87.6819966589716[/C][C]6.3180033410284[/C][/ROW]
[ROW][C]167[/C][C]100.3[/C][C]95.4082436513437[/C][C]4.89175634865634[/C][/ROW]
[ROW][C]168[/C][C]107.1[/C][C]105.396398730664[/C][C]1.70360126933639[/C][/ROW]
[ROW][C]169[/C][C]100.7[/C][C]111.099503936517[/C][C]-10.399503936517[/C][/ROW]
[ROW][C]170[/C][C]95.5[/C][C]100.469951476688[/C][C]-4.96995147668768[/C][/ROW]
[ROW][C]171[/C][C]92.9[/C][C]93.4551866696006[/C][C]-0.555186669600559[/C][/ROW]
[ROW][C]172[/C][C]79.2[/C][C]83.9579893130804[/C][C]-4.75798931308039[/C][/ROW]
[ROW][C]173[/C][C]82[/C][C]81.8998427669347[/C][C]0.100157233065289[/C][/ROW]
[ROW][C]174[/C][C]79.3[/C][C]80.92308798005[/C][C]-1.62308798005[/C][/ROW]
[ROW][C]175[/C][C]81.5[/C][C]81.4269752283051[/C][C]0.0730247716948753[/C][/ROW]
[ROW][C]176[/C][C]76[/C][C]79.9160971122756[/C][C]-3.91609711227555[/C][/ROW]
[ROW][C]177[/C][C]73.1[/C][C]77.610780569764[/C][C]-4.51078056976397[/C][/ROW]
[ROW][C]178[/C][C]80.4[/C][C]80.0432345126747[/C][C]0.356765487325262[/C][/ROW]
[ROW][C]179[/C][C]82.1[/C][C]83.7816924238721[/C][C]-1.68169242387206[/C][/ROW]
[ROW][C]180[/C][C]90.5[/C][C]88.4443385672939[/C][C]2.05566143270615[/C][/ROW]
[ROW][C]181[/C][C]98.1[/C][C]90.3329776127262[/C][C]7.76702238727376[/C][/ROW]
[ROW][C]182[/C][C]89.5[/C][C]90.4740019218478[/C][C]-0.974001921847787[/C][/ROW]
[ROW][C]183[/C][C]86.5[/C][C]86.9219460673339[/C][C]-0.421946067333892[/C][/ROW]
[ROW][C]184[/C][C]77[/C][C]76.8956583978674[/C][C]0.104341602132649[/C][/ROW]
[ROW][C]185[/C][C]74.7[/C][C]78.5763317880713[/C][C]-3.87633178807133[/C][/ROW]
[ROW][C]186[/C][C]73.4[/C][C]75.2179137283244[/C][C]-1.81791372832437[/C][/ROW]
[ROW][C]187[/C][C]72.5[/C][C]75.9879845580986[/C][C]-3.48798455809862[/C][/ROW]
[ROW][C]188[/C][C]69.3[/C][C]71.7391658464558[/C][C]-2.43916584645582[/C][/ROW]
[ROW][C]189[/C][C]75.2[/C][C]69.9653515874872[/C][C]5.23464841251283[/C][/ROW]
[ROW][C]190[/C][C]83.5[/C][C]78.4802459055271[/C][C]5.01975409447287[/C][/ROW]
[ROW][C]191[/C][C]90.5[/C][C]83.9227967175886[/C][C]6.57720328241136[/C][/ROW]
[ROW][C]192[/C][C]92.2[/C][C]94.1332344389086[/C][C]-1.93323443890864[/C][/ROW]
[ROW][C]193[/C][C]110.5[/C][C]95.7771784714274[/C][C]14.7228215285726[/C][/ROW]
[ROW][C]194[/C][C]101.8[/C][C]96.3404400927643[/C][C]5.45955990723566[/C][/ROW]
[ROW][C]195[/C][C]107.4[/C][C]95.8465321147993[/C][C]11.5534678852007[/C][/ROW]
[ROW][C]196[/C][C]95.5[/C][C]90.2410644983006[/C][C]5.25893550169937[/C][/ROW]
[ROW][C]197[/C][C]84.5[/C][C]93.4036385161438[/C][C]-8.90363851614376[/C][/ROW]
[ROW][C]198[/C][C]81.1[/C][C]88.1045493395617[/C][C]-7.00454933956166[/C][/ROW]
[ROW][C]199[/C][C]86.2[/C][C]86.0447435845842[/C][C]0.155256415415792[/C][/ROW]
[ROW][C]200[/C][C]91.5[/C][C]83.5506255984387[/C][C]7.94937440156129[/C][/ROW]
[ROW][C]201[/C][C]84.7[/C][C]89.591441475169[/C][C]-4.89144147516897[/C][/ROW]
[ROW][C]202[/C][C]92.2[/C][C]94.150957443425[/C][C]-1.950957443425[/C][/ROW]
[ROW][C]203[/C][C]99.2[/C][C]97.0706130958503[/C][C]2.1293869041497[/C][/ROW]
[ROW][C]204[/C][C]104.5[/C][C]103.076133999277[/C][C]1.42386600072253[/C][/ROW]
[ROW][C]205[/C][C]113[/C][C]111.924896666138[/C][C]1.07510333386209[/C][/ROW]
[ROW][C]206[/C][C]100.4[/C][C]102.595018792916[/C][C]-2.19501879291558[/C][/ROW]
[ROW][C]207[/C][C]101[/C][C]99.9634118063143[/C][C]1.03658819368574[/C][/ROW]
[ROW][C]208[/C][C]84.8[/C][C]87.8482452934544[/C][C]-3.04824529345437[/C][/ROW]
[ROW][C]209[/C][C]86.5[/C][C]82.9087616598429[/C][C]3.5912383401571[/C][/ROW]
[ROW][C]210[/C][C]91.7[/C][C]84.2088281328799[/C][C]7.49117186712014[/C][/ROW]
[ROW][C]211[/C][C]94.8[/C][C]91.614928376471[/C][C]3.18507162352897[/C][/ROW]
[ROW][C]212[/C][C]95[/C][C]92.8118949207452[/C][C]2.18810507925477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309169&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397.298.5406902105951-1.34069021059513
1486.687.0283710321231-0.428371032123081
1588.488.5362752897322-0.136275289732211
1681.481.5279709764879-0.127970976487887
1786.986.9768580107083-0.0768580107083352
1884.984.9172526075208-0.0172526075207884
1983.781.73166005581831.96833994418172
2086.885.1221931133311.67780688666898
2188.390.7055617471191-2.40556174711909
2292.595.0023707788639-2.50237077886389
2394.793.7911340058050.908865994194954
2494.595.3449473329827-0.844947332982741
2598.794.53601818619164.16398181380839
2688.686.08916971430362.5108302856964
2795.289.14489918960646.05510081039355
2891.384.90398500411526.39601499588476
2991.794.0522684529454-2.35226845294537
3089.390.7950480007364-1.49504800073643
3188.787.34187443261081.35812556738922
3291.290.50637753799960.693622462000405
3388.694.5984373121041-5.99843731210412
3494.697.2946367118852-2.69463671188525
359697.0532611437824-1.05326114378244
3694.397.1555740886016-2.8555740886016
3710296.84524165163655.15475834836347
3893.488.22044913531455.17955086468547
3996.793.68110563871923.01889436128079
4093.787.90296728226385.79703271773622
4191.694.1970342377097-2.59703423770972
4289.691.0647203059072-1.46472030590719
4392.988.46238399012864.43761600987143
4494.193.01062671759611.08937328240394
459295.3205816450594-3.32058164505938
4697.5100.601334845667-3.10133484566715
4792.7100.735520114048-8.03552011404807
48100.796.88317500137383.81682499862617
49105.9102.3384554860523.5615445139485
5095.392.56465765699122.73534234300882
5199.896.22788477166933.57211522833073
5291.391.3738249263312-0.0738249263312127
5390.892.2844395287589-1.48443952875891
5487.190.0408769686152-2.94087696861524
5591.488.43497263806682.9650273619332
5686.191.2326418068929-5.13264180689295
5787.189.1298090634055-2.02980906340548
5892.694.7323667350736-2.1323667350736
5996.693.76169942822452.83830057177545
60105.398.75959992905516.5404000709449
61102.4105.543588219864-3.1435882198643
6298.292.35891847172045.84108152827956
6398.697.79265675784370.807343242156293
6492.690.57194371622362.02805628377644
6587.992.0972753288122-4.19727532881222
6684.188.1032829640416-4.0032829640416
6786.787.682445241045-0.982445241044985
6884.486.1366700164529-1.73667001645288
698686.5753722568462-0.575372256846165
7090.492.7582436940753-2.35824369407534
7192.993.1121559226043-0.212155922604296
72105.897.4996158936828.30038410631799
73106102.2402198601453.75978013985491
7499.194.966434348214.13356565179001
7599.998.07766847221041.82233152778956
7688.191.67621937329-3.57621937328996
7787.888.6126873188204-0.812687318820409
7887.186.32036163772280.779638362277154
7985.989.1974776731827-3.29747767318271
8086.586.28797401378960.212025986210449
8184.188.0681023259726-3.96810232597265
8292.192.05868154839620.0413184516037575
8393.394.2618624101664-0.961862410166418
8498.9100.779911384024-1.87991138402366
8510399.18611463692183.81388536307821
8698.492.36701907143916.03298092856092
87100.795.69822020291615.00177979708393
8892.389.35356162051052.94643837948945
898990.3031568368486-1.30315683684856
9088.988.22666115700470.673338842995264
9185.589.8614009634956-4.36140096349557
9290.187.47779398773562.62220601226441
938789.198651312998-2.198651312998
9497.195.53097310031751.56902689968253
95101.598.29491059158153.20508940841846
96103107.069802110009-4.06980211000864
97106.1106.16234995582-0.0623499558202241
9896.197.7582967070002-1.65829670700016
9994.296.9865602010526-2.78656020105264
10089.186.57351357645722.52648642354278
10185.286.1165909518759-0.916590951875918
10286.584.83699062282531.66300937717472
1038885.43052890751962.56947109248041
10488.488.5084187977972-0.108418797797199
10587.987.46769154293660.432308457063371
10695.796.2266593398136-0.526659339813634
10794.898.4157473340678-3.61574733406781
108105.2101.4511144489423.74888555105822
109108.7105.5476800555043.1523199444965
11096.198.1672562870916-2.06725628709165
11198.396.85496452141621.44503547858383
11288.689.8749736633895-1.27497366338952
11390.886.52176008976324.27823991023678
11488.188.5608882070516-0.460888207051568
11591.988.38770320195523.51229679804476
11698.591.18091048633877.31908951366132
11798.693.90855590411144.69144409588861
118100.3105.303581723062-5.00358172306214
11998.7104.514343245628-5.81434324562805
120110.7109.1156497765661.58435022343396
121115.4112.1016132940943.2983867059059
122105.4102.7145144541592.68548554584102
123108104.8614971990683.13850280093205
12494.597.210762337359-2.710762337359
12596.594.71763970984721.78236029015279
1269194.0658222963437-3.06582229634371
12794.193.85820174575660.241798254243392
12896.496.17866068992440.221339310075621
12993.194.6321919255452-1.53219192554516
13097.599.8243824732456-2.32438247324562
131102.5100.0136625649072.48633743509293
132105.7111.000747568092-5.30074756809171
133109.1111.058535138485-1.95853513848537
13497.299.3412155788951-2.14121557889509
135100.399.16348070183481.13651929816521
13691.389.53841936941281.76158063058723
13794.390.53693355534443.76306644465562
13889.589.5070904910066-0.00709049100660764
13989.391.7174477303793-2.41744773037932
14093.492.6366857260670.763314273933005
14191.990.89751968557471.0024803144253
14292.996.9576581225063-4.05765812250627
14393.797.6213435727307-3.92134357273069
144100.1102.646515690114-2.54651569011358
145105.5104.8327760288330.66722397116682
146110.594.757260747402915.7427392525971
14789.5104.418030315439-14.9180303154393
14890.487.40160534867492.99839465132507
14989.989.55508980806330.344910191936748
15084.685.8839785608697-1.28397856086968
15186.286.6602311803804-0.460231180380404
15283.489.3531804863035-5.95318048630348
15382.984.5202135669407-1.62021356694072
15481.887.3893132973817-5.58931329738166
15587.687.02446949595310.57553050404691
15694.694.05673829210060.543261707899376
15799.698.40670382759561.19329617240435
15896.793.06319155046453.63680844953555
15999.888.192467326734411.6075326732656
16083.889.4065786031964-5.60657860319644
16182.486.5560772138836-4.15607721388355
16286.880.43380639001686.36619360998323
1639185.17047206067395.82952793932607
16485.389.2909970753235-3.99099707532349
16583.686.6941693216046-3.09416932160464
1669487.68199665897166.3180033410284
167100.395.40824365134374.89175634865634
168107.1105.3963987306641.70360126933639
169100.7111.099503936517-10.399503936517
17095.5100.469951476688-4.96995147668768
17192.993.4551866696006-0.555186669600559
17279.283.9579893130804-4.75798931308039
1738281.89984276693470.100157233065289
17479.380.92308798005-1.62308798005
17581.581.42697522830510.0730247716948753
1767679.9160971122756-3.91609711227555
17773.177.610780569764-4.51078056976397
17880.480.04323451267470.356765487325262
17982.183.7816924238721-1.68169242387206
18090.588.44433856729392.05566143270615
18198.190.33297761272627.76702238727376
18289.590.4740019218478-0.974001921847787
18386.586.9219460673339-0.421946067333892
1847776.89565839786740.104341602132649
18574.778.5763317880713-3.87633178807133
18673.475.2179137283244-1.81791372832437
18772.575.9879845580986-3.48798455809862
18869.371.7391658464558-2.43916584645582
18975.269.96535158748725.23464841251283
19083.578.48024590552715.01975409447287
19190.583.92279671758866.57720328241136
19292.294.1332344389086-1.93323443890864
193110.595.777178471427414.7228215285726
194101.896.34044009276435.45955990723566
195107.495.846532114799311.5534678852007
19695.590.24106449830065.25893550169937
19784.593.4036385161438-8.90363851614376
19881.188.1045493395617-7.00454933956166
19986.286.04474358458420.155256415415792
20091.583.55062559843877.94937440156129
20184.789.591441475169-4.89144147516897
20292.294.150957443425-1.950957443425
20399.297.07061309585032.1293869041497
204104.5103.0761339992771.42386600072253
205113111.9248966661381.07510333386209
206100.4102.595018792916-2.19501879291558
20710199.96341180631431.03658819368574
20884.887.8482452934544-3.04824529345437
20986.582.90876165984293.5912383401571
21091.784.20882813287997.49117186712014
21194.891.6149283764713.18507162352897
2129592.81189492074522.18810507925477







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21392.129673297240385.794095467256398.4652511272244
214100.56293274599592.892435333149108.233430158842
215106.11420715689397.2489843732066114.97942994058
216111.255860230273101.256538639547121.255181820999
217119.883221397953108.552457877397131.21398491851
218108.39741494554497.1869919210837119.607837970005
219107.78563453869195.9163938833138119.654875194068
22093.001512045890681.7143802400945104.288643851687
22191.400605801197279.5588912189527103.242320383442
22292.072172074717679.48619697896104.658147170475
22394.583843876880881.0758561147179108.091831639044
22493.9196730481715-18.5478532963533206.387199392696
22591.533273638475521.8597515489728161.206795727978
22699.911589173577223.5297307800016176.293447567153
227105.42653695194924.4586964683366186.394377435562
228110.53448011013725.2569800877006195.811980132573
229119.1054814540126.8240961358147211.386866772205
230107.69380854975623.7891369869122191.5984801126

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 92.1296732972403 & 85.7940954672563 & 98.4652511272244 \tabularnewline
214 & 100.562932745995 & 92.892435333149 & 108.233430158842 \tabularnewline
215 & 106.114207156893 & 97.2489843732066 & 114.97942994058 \tabularnewline
216 & 111.255860230273 & 101.256538639547 & 121.255181820999 \tabularnewline
217 & 119.883221397953 & 108.552457877397 & 131.21398491851 \tabularnewline
218 & 108.397414945544 & 97.1869919210837 & 119.607837970005 \tabularnewline
219 & 107.785634538691 & 95.9163938833138 & 119.654875194068 \tabularnewline
220 & 93.0015120458906 & 81.7143802400945 & 104.288643851687 \tabularnewline
221 & 91.4006058011972 & 79.5588912189527 & 103.242320383442 \tabularnewline
222 & 92.0721720747176 & 79.48619697896 & 104.658147170475 \tabularnewline
223 & 94.5838438768808 & 81.0758561147179 & 108.091831639044 \tabularnewline
224 & 93.9196730481715 & -18.5478532963533 & 206.387199392696 \tabularnewline
225 & 91.5332736384755 & 21.8597515489728 & 161.206795727978 \tabularnewline
226 & 99.9115891735772 & 23.5297307800016 & 176.293447567153 \tabularnewline
227 & 105.426536951949 & 24.4586964683366 & 186.394377435562 \tabularnewline
228 & 110.534480110137 & 25.2569800877006 & 195.811980132573 \tabularnewline
229 & 119.10548145401 & 26.8240961358147 & 211.386866772205 \tabularnewline
230 & 107.693808549756 & 23.7891369869122 & 191.5984801126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309169&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]213[/C][C]92.1296732972403[/C][C]85.7940954672563[/C][C]98.4652511272244[/C][/ROW]
[ROW][C]214[/C][C]100.562932745995[/C][C]92.892435333149[/C][C]108.233430158842[/C][/ROW]
[ROW][C]215[/C][C]106.114207156893[/C][C]97.2489843732066[/C][C]114.97942994058[/C][/ROW]
[ROW][C]216[/C][C]111.255860230273[/C][C]101.256538639547[/C][C]121.255181820999[/C][/ROW]
[ROW][C]217[/C][C]119.883221397953[/C][C]108.552457877397[/C][C]131.21398491851[/C][/ROW]
[ROW][C]218[/C][C]108.397414945544[/C][C]97.1869919210837[/C][C]119.607837970005[/C][/ROW]
[ROW][C]219[/C][C]107.785634538691[/C][C]95.9163938833138[/C][C]119.654875194068[/C][/ROW]
[ROW][C]220[/C][C]93.0015120458906[/C][C]81.7143802400945[/C][C]104.288643851687[/C][/ROW]
[ROW][C]221[/C][C]91.4006058011972[/C][C]79.5588912189527[/C][C]103.242320383442[/C][/ROW]
[ROW][C]222[/C][C]92.0721720747176[/C][C]79.48619697896[/C][C]104.658147170475[/C][/ROW]
[ROW][C]223[/C][C]94.5838438768808[/C][C]81.0758561147179[/C][C]108.091831639044[/C][/ROW]
[ROW][C]224[/C][C]93.9196730481715[/C][C]-18.5478532963533[/C][C]206.387199392696[/C][/ROW]
[ROW][C]225[/C][C]91.5332736384755[/C][C]21.8597515489728[/C][C]161.206795727978[/C][/ROW]
[ROW][C]226[/C][C]99.9115891735772[/C][C]23.5297307800016[/C][C]176.293447567153[/C][/ROW]
[ROW][C]227[/C][C]105.426536951949[/C][C]24.4586964683366[/C][C]186.394377435562[/C][/ROW]
[ROW][C]228[/C][C]110.534480110137[/C][C]25.2569800877006[/C][C]195.811980132573[/C][/ROW]
[ROW][C]229[/C][C]119.10548145401[/C][C]26.8240961358147[/C][C]211.386866772205[/C][/ROW]
[ROW][C]230[/C][C]107.693808549756[/C][C]23.7891369869122[/C][C]191.5984801126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309169&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309169&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21392.129673297240385.794095467256398.4652511272244
214100.56293274599592.892435333149108.233430158842
215106.11420715689397.2489843732066114.97942994058
216111.255860230273101.256538639547121.255181820999
217119.883221397953108.552457877397131.21398491851
218108.39741494554497.1869919210837119.607837970005
219107.78563453869195.9163938833138119.654875194068
22093.001512045890681.7143802400945104.288643851687
22191.400605801197279.5588912189527103.242320383442
22292.072172074717679.48619697896104.658147170475
22394.583843876880881.0758561147179108.091831639044
22493.9196730481715-18.5478532963533206.387199392696
22591.533273638475521.8597515489728161.206795727978
22699.911589173577223.5297307800016176.293447567153
227105.42653695194924.4586964683366186.394377435562
228110.53448011013725.2569800877006195.811980132573
229119.1054814540126.8240961358147211.386866772205
230107.69380854975623.7891369869122191.5984801126



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'multiplicative'
par2 <- 'Double'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')