Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 14:07:23 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/07/t12444052782fr3u51ebywvawp.htm/, Retrieved Mon, 13 May 2024 11:35:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42253, Retrieved Mon, 13 May 2024 11:35:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsthomas cammaert
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht 10 oefen...] [2009-06-07 20:07:23] [61792449e3c1c0e0abc5b9baf921991f] [Current]
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Dataseries X:
8.9722
8.8284
8.7446
8.7519
8.6337
8.7272
8.6330
8.5865
8.5968
8.5114
8.3884
8.2671
8.2410
8.3177
8.4070
8.3917
8.4145
8.5245
8.6289
8.6622
8.9055
8.9770
9.1264
9.1120
9.0576
9.2106
9.2637
9.3107
9.6744
9.5780
9.4166
9.4359
9.2275
9.1828
9.0594
9.1358
9.2208
9.1137
9.2689
9.2489
9.1679
9.1051
9.0818
9.0961
9.1733
9.1455
9.2265
9.1541
9.1559
9.1182
9.1856
9.2378
9.0682
9.0105
8.9939
9.0228
9.1368
9.1763
9.2346
9.1653
9.1277
9.1430
9.1962
9.1861
9.0920
9.0620
8.9981
8.9819
9.0476
9.0852
9.0884
9.1670
9.1931
9.2628
9.4276
9.3398
9.3342
9.4223
9.5614
9.4316
9.3111
9.3414
9.4017
9.3346
9.3310
9.2349
9.2170
9.2098
9.2665
9.2533
9.1008
9.0377
9.0795
9.1896
9.2992
9.2372
9.2061
9.3290
9.1842
9.3231
9.2835
9.1735
9.2889
9.4319
9.4314
9.3642
9.4020
9.3699
9.3106
9.3739
9.4566
9.3984
9.5637
9.8506




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42253&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42253&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.992290585513234
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.992290585513234 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42253&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]0.992290585513234[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42253&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
alpha0.992290585513234
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.2418.3819770181997-0.140977018199701
148.31778.315857442628180.00184255737182326
158.4078.39106707799660.0159329220033975
168.39178.359692876371220.0320071236287838
178.41458.364847998521580.0496520014784192
188.52458.458794431489340.0657055685106567
198.62898.6333521255316-0.00445212553160879
208.66228.634370832968790.0278291670312107
218.90558.70835732203790.197142677962091
228.9778.845717976519060.131282023480942
239.12648.87150011872770.254899881272301
249.1129.011202746638950.100797253361051
259.05769.09053184558146-0.0329318455814551
269.21069.140146861394650.0704531386053482
279.26379.29143080129675-0.0277308012967481
289.31079.21205559402780.098644405972209
299.67449.28057148559820.393828514401807
309.5789.72285221171003-0.144852211710033
319.41669.7013970074293-0.284797007429304
329.43599.425000694806780.0108993051932167
339.22759.48771479612216-0.260214796122158
349.18289.168582756460350.0142172435396475
359.05949.07672762191811-0.0173276219181133
369.13588.945943274606250.189856725393746
379.22089.112560110556280.108239889443716
389.11379.30454081328385-0.190840813283854
399.26899.194952402777940.0739475972220642
409.24899.2174125609460.0314874390540094
419.16799.2216235892913-0.0537235892913053
429.10519.21315757624781-0.108057576247809
439.08189.2210982165426-0.139298216542608
449.09619.091057836697030.00504216330296714
459.17339.144021831865210.0292781681347876
469.14559.114613337846430.0308866621535682
479.22659.039489821990620.187010178009382
489.15419.11098659881980.0431134011802037
499.15599.13130839230650.0245916076934929
509.11829.23736886492803-0.119168864928033
519.18569.20098535062063-0.0153853506206261
529.23789.134932992433160.102867007566836
539.06829.20934956930592-0.141149569305922
549.01059.1132251529313-0.102725152931301
558.99399.12501604266818-0.131116042668175
569.02289.00411857027580.0186814297242055
579.13689.070414062915540.0663859370844566
589.17639.078074688581070.0982253114189255
599.23469.070601699754210.163998300245789
609.16539.118067757906680.0472322420933189
619.12779.14230658597763-0.0146065859776243
629.1439.20810377195893-0.0651037719589294
639.19629.22639784314708-0.0301978431470857
649.18619.14649125300140.0396087469986046
659.0929.1564056091722-0.0644056091722032
669.0629.13683926387122-0.074839263871219
678.99819.17672348946052-0.178623489460515
688.98199.00984580539766-0.0279458053976569
699.04769.030020628422260.0175793715777353
709.08528.990055241722920.095144758277078
719.08848.981055602071070.107344397928927
729.1678.973252052350570.193747947649433
739.19319.142399595572670.0507004044273334
749.26289.27317649362574-0.0103764936257349
759.42769.347134696118210.0804653038817857
769.33989.37633515005932-0.0365351500593238
779.33429.309381121561260.0248188784387384
789.42239.37944426734170.0428557326583068
799.56149.539790271661880.0216097283381256
809.43169.57348466577655-0.141884665776550
819.31119.48337166335031-0.17227166335031
829.34149.253946123791340.0874538762086576
839.40179.234493136009970.167206863990032
849.33469.282822433726590.0517775662734099
859.3319.309547545104250.021452454895746
869.23499.4120295595693-0.177129559569302
879.2179.32097199836443-0.103971998364429
889.20989.16740107741330.0423989225866954
899.26659.179666884740670.0868331152593314
909.25339.31106993029959-0.0577699302995889
919.10089.36929712285692-0.268497122856916
929.03779.11331815031477-0.0756181503147708
939.07959.0865995592292-0.00709955922919292
949.18969.024473484301680.165126515698322
959.29929.084417503036240.214782496963759
969.23729.180376140003640.0568238599963564
979.20619.21213532599548-0.0060353259954784
989.3299.28471894023210.0442810597678989
999.18429.41478571155857-0.230585711558568
1009.32319.136869979358320.186230020641679
1019.28359.29183641964926-0.00833641964926457
1029.17359.32776731824655-0.154267318246552
1039.28899.287588548808380.00131145119162390
1049.43199.30106679744720.130833202552795
1059.43149.48186116181237-0.0504611618123718
1069.36429.37592629508195-0.0117262950819512
1079.4029.25875707708690.143242922913091
1089.36999.28121253394210.0886874660579018
1099.31069.34374615358706-0.0331461535870563
1109.37399.39071271615963-0.0168127161596257
1119.45669.45839864756825-0.00179864756824522
1129.39849.409328986761-0.0109289867609910
1139.56379.366903039935560.196796960064443
1149.85069.606533544416930.244066455583072

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.241 & 8.3819770181997 & -0.140977018199701 \tabularnewline
14 & 8.3177 & 8.31585744262818 & 0.00184255737182326 \tabularnewline
15 & 8.407 & 8.3910670779966 & 0.0159329220033975 \tabularnewline
16 & 8.3917 & 8.35969287637122 & 0.0320071236287838 \tabularnewline
17 & 8.4145 & 8.36484799852158 & 0.0496520014784192 \tabularnewline
18 & 8.5245 & 8.45879443148934 & 0.0657055685106567 \tabularnewline
19 & 8.6289 & 8.6333521255316 & -0.00445212553160879 \tabularnewline
20 & 8.6622 & 8.63437083296879 & 0.0278291670312107 \tabularnewline
21 & 8.9055 & 8.7083573220379 & 0.197142677962091 \tabularnewline
22 & 8.977 & 8.84571797651906 & 0.131282023480942 \tabularnewline
23 & 9.1264 & 8.8715001187277 & 0.254899881272301 \tabularnewline
24 & 9.112 & 9.01120274663895 & 0.100797253361051 \tabularnewline
25 & 9.0576 & 9.09053184558146 & -0.0329318455814551 \tabularnewline
26 & 9.2106 & 9.14014686139465 & 0.0704531386053482 \tabularnewline
27 & 9.2637 & 9.29143080129675 & -0.0277308012967481 \tabularnewline
28 & 9.3107 & 9.2120555940278 & 0.098644405972209 \tabularnewline
29 & 9.6744 & 9.2805714855982 & 0.393828514401807 \tabularnewline
30 & 9.578 & 9.72285221171003 & -0.144852211710033 \tabularnewline
31 & 9.4166 & 9.7013970074293 & -0.284797007429304 \tabularnewline
32 & 9.4359 & 9.42500069480678 & 0.0108993051932167 \tabularnewline
33 & 9.2275 & 9.48771479612216 & -0.260214796122158 \tabularnewline
34 & 9.1828 & 9.16858275646035 & 0.0142172435396475 \tabularnewline
35 & 9.0594 & 9.07672762191811 & -0.0173276219181133 \tabularnewline
36 & 9.1358 & 8.94594327460625 & 0.189856725393746 \tabularnewline
37 & 9.2208 & 9.11256011055628 & 0.108239889443716 \tabularnewline
38 & 9.1137 & 9.30454081328385 & -0.190840813283854 \tabularnewline
39 & 9.2689 & 9.19495240277794 & 0.0739475972220642 \tabularnewline
40 & 9.2489 & 9.217412560946 & 0.0314874390540094 \tabularnewline
41 & 9.1679 & 9.2216235892913 & -0.0537235892913053 \tabularnewline
42 & 9.1051 & 9.21315757624781 & -0.108057576247809 \tabularnewline
43 & 9.0818 & 9.2210982165426 & -0.139298216542608 \tabularnewline
44 & 9.0961 & 9.09105783669703 & 0.00504216330296714 \tabularnewline
45 & 9.1733 & 9.14402183186521 & 0.0292781681347876 \tabularnewline
46 & 9.1455 & 9.11461333784643 & 0.0308866621535682 \tabularnewline
47 & 9.2265 & 9.03948982199062 & 0.187010178009382 \tabularnewline
48 & 9.1541 & 9.1109865988198 & 0.0431134011802037 \tabularnewline
49 & 9.1559 & 9.1313083923065 & 0.0245916076934929 \tabularnewline
50 & 9.1182 & 9.23736886492803 & -0.119168864928033 \tabularnewline
51 & 9.1856 & 9.20098535062063 & -0.0153853506206261 \tabularnewline
52 & 9.2378 & 9.13493299243316 & 0.102867007566836 \tabularnewline
53 & 9.0682 & 9.20934956930592 & -0.141149569305922 \tabularnewline
54 & 9.0105 & 9.1132251529313 & -0.102725152931301 \tabularnewline
55 & 8.9939 & 9.12501604266818 & -0.131116042668175 \tabularnewline
56 & 9.0228 & 9.0041185702758 & 0.0186814297242055 \tabularnewline
57 & 9.1368 & 9.07041406291554 & 0.0663859370844566 \tabularnewline
58 & 9.1763 & 9.07807468858107 & 0.0982253114189255 \tabularnewline
59 & 9.2346 & 9.07060169975421 & 0.163998300245789 \tabularnewline
60 & 9.1653 & 9.11806775790668 & 0.0472322420933189 \tabularnewline
61 & 9.1277 & 9.14230658597763 & -0.0146065859776243 \tabularnewline
62 & 9.143 & 9.20810377195893 & -0.0651037719589294 \tabularnewline
63 & 9.1962 & 9.22639784314708 & -0.0301978431470857 \tabularnewline
64 & 9.1861 & 9.1464912530014 & 0.0396087469986046 \tabularnewline
65 & 9.092 & 9.1564056091722 & -0.0644056091722032 \tabularnewline
66 & 9.062 & 9.13683926387122 & -0.074839263871219 \tabularnewline
67 & 8.9981 & 9.17672348946052 & -0.178623489460515 \tabularnewline
68 & 8.9819 & 9.00984580539766 & -0.0279458053976569 \tabularnewline
69 & 9.0476 & 9.03002062842226 & 0.0175793715777353 \tabularnewline
70 & 9.0852 & 8.99005524172292 & 0.095144758277078 \tabularnewline
71 & 9.0884 & 8.98105560207107 & 0.107344397928927 \tabularnewline
72 & 9.167 & 8.97325205235057 & 0.193747947649433 \tabularnewline
73 & 9.1931 & 9.14239959557267 & 0.0507004044273334 \tabularnewline
74 & 9.2628 & 9.27317649362574 & -0.0103764936257349 \tabularnewline
75 & 9.4276 & 9.34713469611821 & 0.0804653038817857 \tabularnewline
76 & 9.3398 & 9.37633515005932 & -0.0365351500593238 \tabularnewline
77 & 9.3342 & 9.30938112156126 & 0.0248188784387384 \tabularnewline
78 & 9.4223 & 9.3794442673417 & 0.0428557326583068 \tabularnewline
79 & 9.5614 & 9.53979027166188 & 0.0216097283381256 \tabularnewline
80 & 9.4316 & 9.57348466577655 & -0.141884665776550 \tabularnewline
81 & 9.3111 & 9.48337166335031 & -0.17227166335031 \tabularnewline
82 & 9.3414 & 9.25394612379134 & 0.0874538762086576 \tabularnewline
83 & 9.4017 & 9.23449313600997 & 0.167206863990032 \tabularnewline
84 & 9.3346 & 9.28282243372659 & 0.0517775662734099 \tabularnewline
85 & 9.331 & 9.30954754510425 & 0.021452454895746 \tabularnewline
86 & 9.2349 & 9.4120295595693 & -0.177129559569302 \tabularnewline
87 & 9.217 & 9.32097199836443 & -0.103971998364429 \tabularnewline
88 & 9.2098 & 9.1674010774133 & 0.0423989225866954 \tabularnewline
89 & 9.2665 & 9.17966688474067 & 0.0868331152593314 \tabularnewline
90 & 9.2533 & 9.31106993029959 & -0.0577699302995889 \tabularnewline
91 & 9.1008 & 9.36929712285692 & -0.268497122856916 \tabularnewline
92 & 9.0377 & 9.11331815031477 & -0.0756181503147708 \tabularnewline
93 & 9.0795 & 9.0865995592292 & -0.00709955922919292 \tabularnewline
94 & 9.1896 & 9.02447348430168 & 0.165126515698322 \tabularnewline
95 & 9.2992 & 9.08441750303624 & 0.214782496963759 \tabularnewline
96 & 9.2372 & 9.18037614000364 & 0.0568238599963564 \tabularnewline
97 & 9.2061 & 9.21213532599548 & -0.0060353259954784 \tabularnewline
98 & 9.329 & 9.2847189402321 & 0.0442810597678989 \tabularnewline
99 & 9.1842 & 9.41478571155857 & -0.230585711558568 \tabularnewline
100 & 9.3231 & 9.13686997935832 & 0.186230020641679 \tabularnewline
101 & 9.2835 & 9.29183641964926 & -0.00833641964926457 \tabularnewline
102 & 9.1735 & 9.32776731824655 & -0.154267318246552 \tabularnewline
103 & 9.2889 & 9.28758854880838 & 0.00131145119162390 \tabularnewline
104 & 9.4319 & 9.3010667974472 & 0.130833202552795 \tabularnewline
105 & 9.4314 & 9.48186116181237 & -0.0504611618123718 \tabularnewline
106 & 9.3642 & 9.37592629508195 & -0.0117262950819512 \tabularnewline
107 & 9.402 & 9.2587570770869 & 0.143242922913091 \tabularnewline
108 & 9.3699 & 9.2812125339421 & 0.0886874660579018 \tabularnewline
109 & 9.3106 & 9.34374615358706 & -0.0331461535870563 \tabularnewline
110 & 9.3739 & 9.39071271615963 & -0.0168127161596257 \tabularnewline
111 & 9.4566 & 9.45839864756825 & -0.00179864756824522 \tabularnewline
112 & 9.3984 & 9.409328986761 & -0.0109289867609910 \tabularnewline
113 & 9.5637 & 9.36690303993556 & 0.196796960064443 \tabularnewline
114 & 9.8506 & 9.60653354441693 & 0.244066455583072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42253&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]8.241[/C][C]8.3819770181997[/C][C]-0.140977018199701[/C][/ROW]
[ROW][C]14[/C][C]8.3177[/C][C]8.31585744262818[/C][C]0.00184255737182326[/C][/ROW]
[ROW][C]15[/C][C]8.407[/C][C]8.3910670779966[/C][C]0.0159329220033975[/C][/ROW]
[ROW][C]16[/C][C]8.3917[/C][C]8.35969287637122[/C][C]0.0320071236287838[/C][/ROW]
[ROW][C]17[/C][C]8.4145[/C][C]8.36484799852158[/C][C]0.0496520014784192[/C][/ROW]
[ROW][C]18[/C][C]8.5245[/C][C]8.45879443148934[/C][C]0.0657055685106567[/C][/ROW]
[ROW][C]19[/C][C]8.6289[/C][C]8.6333521255316[/C][C]-0.00445212553160879[/C][/ROW]
[ROW][C]20[/C][C]8.6622[/C][C]8.63437083296879[/C][C]0.0278291670312107[/C][/ROW]
[ROW][C]21[/C][C]8.9055[/C][C]8.7083573220379[/C][C]0.197142677962091[/C][/ROW]
[ROW][C]22[/C][C]8.977[/C][C]8.84571797651906[/C][C]0.131282023480942[/C][/ROW]
[ROW][C]23[/C][C]9.1264[/C][C]8.8715001187277[/C][C]0.254899881272301[/C][/ROW]
[ROW][C]24[/C][C]9.112[/C][C]9.01120274663895[/C][C]0.100797253361051[/C][/ROW]
[ROW][C]25[/C][C]9.0576[/C][C]9.09053184558146[/C][C]-0.0329318455814551[/C][/ROW]
[ROW][C]26[/C][C]9.2106[/C][C]9.14014686139465[/C][C]0.0704531386053482[/C][/ROW]
[ROW][C]27[/C][C]9.2637[/C][C]9.29143080129675[/C][C]-0.0277308012967481[/C][/ROW]
[ROW][C]28[/C][C]9.3107[/C][C]9.2120555940278[/C][C]0.098644405972209[/C][/ROW]
[ROW][C]29[/C][C]9.6744[/C][C]9.2805714855982[/C][C]0.393828514401807[/C][/ROW]
[ROW][C]30[/C][C]9.578[/C][C]9.72285221171003[/C][C]-0.144852211710033[/C][/ROW]
[ROW][C]31[/C][C]9.4166[/C][C]9.7013970074293[/C][C]-0.284797007429304[/C][/ROW]
[ROW][C]32[/C][C]9.4359[/C][C]9.42500069480678[/C][C]0.0108993051932167[/C][/ROW]
[ROW][C]33[/C][C]9.2275[/C][C]9.48771479612216[/C][C]-0.260214796122158[/C][/ROW]
[ROW][C]34[/C][C]9.1828[/C][C]9.16858275646035[/C][C]0.0142172435396475[/C][/ROW]
[ROW][C]35[/C][C]9.0594[/C][C]9.07672762191811[/C][C]-0.0173276219181133[/C][/ROW]
[ROW][C]36[/C][C]9.1358[/C][C]8.94594327460625[/C][C]0.189856725393746[/C][/ROW]
[ROW][C]37[/C][C]9.2208[/C][C]9.11256011055628[/C][C]0.108239889443716[/C][/ROW]
[ROW][C]38[/C][C]9.1137[/C][C]9.30454081328385[/C][C]-0.190840813283854[/C][/ROW]
[ROW][C]39[/C][C]9.2689[/C][C]9.19495240277794[/C][C]0.0739475972220642[/C][/ROW]
[ROW][C]40[/C][C]9.2489[/C][C]9.217412560946[/C][C]0.0314874390540094[/C][/ROW]
[ROW][C]41[/C][C]9.1679[/C][C]9.2216235892913[/C][C]-0.0537235892913053[/C][/ROW]
[ROW][C]42[/C][C]9.1051[/C][C]9.21315757624781[/C][C]-0.108057576247809[/C][/ROW]
[ROW][C]43[/C][C]9.0818[/C][C]9.2210982165426[/C][C]-0.139298216542608[/C][/ROW]
[ROW][C]44[/C][C]9.0961[/C][C]9.09105783669703[/C][C]0.00504216330296714[/C][/ROW]
[ROW][C]45[/C][C]9.1733[/C][C]9.14402183186521[/C][C]0.0292781681347876[/C][/ROW]
[ROW][C]46[/C][C]9.1455[/C][C]9.11461333784643[/C][C]0.0308866621535682[/C][/ROW]
[ROW][C]47[/C][C]9.2265[/C][C]9.03948982199062[/C][C]0.187010178009382[/C][/ROW]
[ROW][C]48[/C][C]9.1541[/C][C]9.1109865988198[/C][C]0.0431134011802037[/C][/ROW]
[ROW][C]49[/C][C]9.1559[/C][C]9.1313083923065[/C][C]0.0245916076934929[/C][/ROW]
[ROW][C]50[/C][C]9.1182[/C][C]9.23736886492803[/C][C]-0.119168864928033[/C][/ROW]
[ROW][C]51[/C][C]9.1856[/C][C]9.20098535062063[/C][C]-0.0153853506206261[/C][/ROW]
[ROW][C]52[/C][C]9.2378[/C][C]9.13493299243316[/C][C]0.102867007566836[/C][/ROW]
[ROW][C]53[/C][C]9.0682[/C][C]9.20934956930592[/C][C]-0.141149569305922[/C][/ROW]
[ROW][C]54[/C][C]9.0105[/C][C]9.1132251529313[/C][C]-0.102725152931301[/C][/ROW]
[ROW][C]55[/C][C]8.9939[/C][C]9.12501604266818[/C][C]-0.131116042668175[/C][/ROW]
[ROW][C]56[/C][C]9.0228[/C][C]9.0041185702758[/C][C]0.0186814297242055[/C][/ROW]
[ROW][C]57[/C][C]9.1368[/C][C]9.07041406291554[/C][C]0.0663859370844566[/C][/ROW]
[ROW][C]58[/C][C]9.1763[/C][C]9.07807468858107[/C][C]0.0982253114189255[/C][/ROW]
[ROW][C]59[/C][C]9.2346[/C][C]9.07060169975421[/C][C]0.163998300245789[/C][/ROW]
[ROW][C]60[/C][C]9.1653[/C][C]9.11806775790668[/C][C]0.0472322420933189[/C][/ROW]
[ROW][C]61[/C][C]9.1277[/C][C]9.14230658597763[/C][C]-0.0146065859776243[/C][/ROW]
[ROW][C]62[/C][C]9.143[/C][C]9.20810377195893[/C][C]-0.0651037719589294[/C][/ROW]
[ROW][C]63[/C][C]9.1962[/C][C]9.22639784314708[/C][C]-0.0301978431470857[/C][/ROW]
[ROW][C]64[/C][C]9.1861[/C][C]9.1464912530014[/C][C]0.0396087469986046[/C][/ROW]
[ROW][C]65[/C][C]9.092[/C][C]9.1564056091722[/C][C]-0.0644056091722032[/C][/ROW]
[ROW][C]66[/C][C]9.062[/C][C]9.13683926387122[/C][C]-0.074839263871219[/C][/ROW]
[ROW][C]67[/C][C]8.9981[/C][C]9.17672348946052[/C][C]-0.178623489460515[/C][/ROW]
[ROW][C]68[/C][C]8.9819[/C][C]9.00984580539766[/C][C]-0.0279458053976569[/C][/ROW]
[ROW][C]69[/C][C]9.0476[/C][C]9.03002062842226[/C][C]0.0175793715777353[/C][/ROW]
[ROW][C]70[/C][C]9.0852[/C][C]8.99005524172292[/C][C]0.095144758277078[/C][/ROW]
[ROW][C]71[/C][C]9.0884[/C][C]8.98105560207107[/C][C]0.107344397928927[/C][/ROW]
[ROW][C]72[/C][C]9.167[/C][C]8.97325205235057[/C][C]0.193747947649433[/C][/ROW]
[ROW][C]73[/C][C]9.1931[/C][C]9.14239959557267[/C][C]0.0507004044273334[/C][/ROW]
[ROW][C]74[/C][C]9.2628[/C][C]9.27317649362574[/C][C]-0.0103764936257349[/C][/ROW]
[ROW][C]75[/C][C]9.4276[/C][C]9.34713469611821[/C][C]0.0804653038817857[/C][/ROW]
[ROW][C]76[/C][C]9.3398[/C][C]9.37633515005932[/C][C]-0.0365351500593238[/C][/ROW]
[ROW][C]77[/C][C]9.3342[/C][C]9.30938112156126[/C][C]0.0248188784387384[/C][/ROW]
[ROW][C]78[/C][C]9.4223[/C][C]9.3794442673417[/C][C]0.0428557326583068[/C][/ROW]
[ROW][C]79[/C][C]9.5614[/C][C]9.53979027166188[/C][C]0.0216097283381256[/C][/ROW]
[ROW][C]80[/C][C]9.4316[/C][C]9.57348466577655[/C][C]-0.141884665776550[/C][/ROW]
[ROW][C]81[/C][C]9.3111[/C][C]9.48337166335031[/C][C]-0.17227166335031[/C][/ROW]
[ROW][C]82[/C][C]9.3414[/C][C]9.25394612379134[/C][C]0.0874538762086576[/C][/ROW]
[ROW][C]83[/C][C]9.4017[/C][C]9.23449313600997[/C][C]0.167206863990032[/C][/ROW]
[ROW][C]84[/C][C]9.3346[/C][C]9.28282243372659[/C][C]0.0517775662734099[/C][/ROW]
[ROW][C]85[/C][C]9.331[/C][C]9.30954754510425[/C][C]0.021452454895746[/C][/ROW]
[ROW][C]86[/C][C]9.2349[/C][C]9.4120295595693[/C][C]-0.177129559569302[/C][/ROW]
[ROW][C]87[/C][C]9.217[/C][C]9.32097199836443[/C][C]-0.103971998364429[/C][/ROW]
[ROW][C]88[/C][C]9.2098[/C][C]9.1674010774133[/C][C]0.0423989225866954[/C][/ROW]
[ROW][C]89[/C][C]9.2665[/C][C]9.17966688474067[/C][C]0.0868331152593314[/C][/ROW]
[ROW][C]90[/C][C]9.2533[/C][C]9.31106993029959[/C][C]-0.0577699302995889[/C][/ROW]
[ROW][C]91[/C][C]9.1008[/C][C]9.36929712285692[/C][C]-0.268497122856916[/C][/ROW]
[ROW][C]92[/C][C]9.0377[/C][C]9.11331815031477[/C][C]-0.0756181503147708[/C][/ROW]
[ROW][C]93[/C][C]9.0795[/C][C]9.0865995592292[/C][C]-0.00709955922919292[/C][/ROW]
[ROW][C]94[/C][C]9.1896[/C][C]9.02447348430168[/C][C]0.165126515698322[/C][/ROW]
[ROW][C]95[/C][C]9.2992[/C][C]9.08441750303624[/C][C]0.214782496963759[/C][/ROW]
[ROW][C]96[/C][C]9.2372[/C][C]9.18037614000364[/C][C]0.0568238599963564[/C][/ROW]
[ROW][C]97[/C][C]9.2061[/C][C]9.21213532599548[/C][C]-0.0060353259954784[/C][/ROW]
[ROW][C]98[/C][C]9.329[/C][C]9.2847189402321[/C][C]0.0442810597678989[/C][/ROW]
[ROW][C]99[/C][C]9.1842[/C][C]9.41478571155857[/C][C]-0.230585711558568[/C][/ROW]
[ROW][C]100[/C][C]9.3231[/C][C]9.13686997935832[/C][C]0.186230020641679[/C][/ROW]
[ROW][C]101[/C][C]9.2835[/C][C]9.29183641964926[/C][C]-0.00833641964926457[/C][/ROW]
[ROW][C]102[/C][C]9.1735[/C][C]9.32776731824655[/C][C]-0.154267318246552[/C][/ROW]
[ROW][C]103[/C][C]9.2889[/C][C]9.28758854880838[/C][C]0.00131145119162390[/C][/ROW]
[ROW][C]104[/C][C]9.4319[/C][C]9.3010667974472[/C][C]0.130833202552795[/C][/ROW]
[ROW][C]105[/C][C]9.4314[/C][C]9.48186116181237[/C][C]-0.0504611618123718[/C][/ROW]
[ROW][C]106[/C][C]9.3642[/C][C]9.37592629508195[/C][C]-0.0117262950819512[/C][/ROW]
[ROW][C]107[/C][C]9.402[/C][C]9.2587570770869[/C][C]0.143242922913091[/C][/ROW]
[ROW][C]108[/C][C]9.3699[/C][C]9.2812125339421[/C][C]0.0886874660579018[/C][/ROW]
[ROW][C]109[/C][C]9.3106[/C][C]9.34374615358706[/C][C]-0.0331461535870563[/C][/ROW]
[ROW][C]110[/C][C]9.3739[/C][C]9.39071271615963[/C][C]-0.0168127161596257[/C][/ROW]
[ROW][C]111[/C][C]9.4566[/C][C]9.45839864756825[/C][C]-0.00179864756824522[/C][/ROW]
[ROW][C]112[/C][C]9.3984[/C][C]9.409328986761[/C][C]-0.0109289867609910[/C][/ROW]
[ROW][C]113[/C][C]9.5637[/C][C]9.36690303993556[/C][C]0.196796960064443[/C][/ROW]
[ROW][C]114[/C][C]9.8506[/C][C]9.60653354441693[/C][C]0.244066455583072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42253&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42253&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
138.2418.3819770181997-0.140977018199701
148.31778.315857442628180.00184255737182326
158.4078.39106707799660.0159329220033975
168.39178.359692876371220.0320071236287838
178.41458.364847998521580.0496520014784192
188.52458.458794431489340.0657055685106567
198.62898.6333521255316-0.00445212553160879
208.66228.634370832968790.0278291670312107
218.90558.70835732203790.197142677962091
228.9778.845717976519060.131282023480942
239.12648.87150011872770.254899881272301
249.1129.011202746638950.100797253361051
259.05769.09053184558146-0.0329318455814551
269.21069.140146861394650.0704531386053482
279.26379.29143080129675-0.0277308012967481
289.31079.21205559402780.098644405972209
299.67449.28057148559820.393828514401807
309.5789.72285221171003-0.144852211710033
319.41669.7013970074293-0.284797007429304
329.43599.425000694806780.0108993051932167
339.22759.48771479612216-0.260214796122158
349.18289.168582756460350.0142172435396475
359.05949.07672762191811-0.0173276219181133
369.13588.945943274606250.189856725393746
379.22089.112560110556280.108239889443716
389.11379.30454081328385-0.190840813283854
399.26899.194952402777940.0739475972220642
409.24899.2174125609460.0314874390540094
419.16799.2216235892913-0.0537235892913053
429.10519.21315757624781-0.108057576247809
439.08189.2210982165426-0.139298216542608
449.09619.091057836697030.00504216330296714
459.17339.144021831865210.0292781681347876
469.14559.114613337846430.0308866621535682
479.22659.039489821990620.187010178009382
489.15419.11098659881980.0431134011802037
499.15599.13130839230650.0245916076934929
509.11829.23736886492803-0.119168864928033
519.18569.20098535062063-0.0153853506206261
529.23789.134932992433160.102867007566836
539.06829.20934956930592-0.141149569305922
549.01059.1132251529313-0.102725152931301
558.99399.12501604266818-0.131116042668175
569.02289.00411857027580.0186814297242055
579.13689.070414062915540.0663859370844566
589.17639.078074688581070.0982253114189255
599.23469.070601699754210.163998300245789
609.16539.118067757906680.0472322420933189
619.12779.14230658597763-0.0146065859776243
629.1439.20810377195893-0.0651037719589294
639.19629.22639784314708-0.0301978431470857
649.18619.14649125300140.0396087469986046
659.0929.1564056091722-0.0644056091722032
669.0629.13683926387122-0.074839263871219
678.99819.17672348946052-0.178623489460515
688.98199.00984580539766-0.0279458053976569
699.04769.030020628422260.0175793715777353
709.08528.990055241722920.095144758277078
719.08848.981055602071070.107344397928927
729.1678.973252052350570.193747947649433
739.19319.142399595572670.0507004044273334
749.26289.27317649362574-0.0103764936257349
759.42769.347134696118210.0804653038817857
769.33989.37633515005932-0.0365351500593238
779.33429.309381121561260.0248188784387384
789.42239.37944426734170.0428557326583068
799.56149.539790271661880.0216097283381256
809.43169.57348466577655-0.141884665776550
819.31119.48337166335031-0.17227166335031
829.34149.253946123791340.0874538762086576
839.40179.234493136009970.167206863990032
849.33469.282822433726590.0517775662734099
859.3319.309547545104250.021452454895746
869.23499.4120295595693-0.177129559569302
879.2179.32097199836443-0.103971998364429
889.20989.16740107741330.0423989225866954
899.26659.179666884740670.0868331152593314
909.25339.31106993029959-0.0577699302995889
919.10089.36929712285692-0.268497122856916
929.03779.11331815031477-0.0756181503147708
939.07959.0865995592292-0.00709955922919292
949.18969.024473484301680.165126515698322
959.29929.084417503036240.214782496963759
969.23729.180376140003640.0568238599963564
979.20619.21213532599548-0.0060353259954784
989.3299.28471894023210.0442810597678989
999.18429.41478571155857-0.230585711558568
1009.32319.136869979358320.186230020641679
1019.28359.29183641964926-0.00833641964926457
1029.17359.32776731824655-0.154267318246552
1039.28899.287588548808380.00131145119162390
1049.43199.30106679744720.130833202552795
1059.43149.48186116181237-0.0504611618123718
1069.36429.37592629508195-0.0117262950819512
1079.4029.25875707708690.143242922913091
1089.36999.28121253394210.0886874660579018
1099.31069.34374615358706-0.0331461535870563
1109.37399.39071271615963-0.0168127161596257
1119.45669.45839864756825-0.00179864756824522
1129.39849.409328986761-0.0109289867609910
1139.56379.366903039935560.196796960064443
1149.85069.606533544416930.244066455583072







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1159.971215316516259.7367605693080310.2056700637245
1169.98534365763089.6541878417674710.3164994734941
11710.03782239353749.6346965020829410.4409482849918
1189.978685492016789.517109863878110.4402611201554
1199.867482321838999.355828591922210.3791360517558
1209.741425644708649.1806713906139310.3021798988033
1219.713968164634489.102428138051510.3255081912175
1229.7974161750669.1379753181244310.4568570320076
1239.885718006187749.189549174040610.5818868383349
1249.836213765785639.1043046510364510.5681228805348
1259.804804994020769.0335569523537810.5760530356877
1269.8506NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 9.97121531651625 & 9.73676056930803 & 10.2056700637245 \tabularnewline
116 & 9.9853436576308 & 9.65418784176747 & 10.3164994734941 \tabularnewline
117 & 10.0378223935374 & 9.63469650208294 & 10.4409482849918 \tabularnewline
118 & 9.97868549201678 & 9.5171098638781 & 10.4402611201554 \tabularnewline
119 & 9.86748232183899 & 9.3558285919222 & 10.3791360517558 \tabularnewline
120 & 9.74142564470864 & 9.18067139061393 & 10.3021798988033 \tabularnewline
121 & 9.71396816463448 & 9.1024281380515 & 10.3255081912175 \tabularnewline
122 & 9.797416175066 & 9.13797531812443 & 10.4568570320076 \tabularnewline
123 & 9.88571800618774 & 9.1895491740406 & 10.5818868383349 \tabularnewline
124 & 9.83621376578563 & 9.10430465103645 & 10.5681228805348 \tabularnewline
125 & 9.80480499402076 & 9.03355695235378 & 10.5760530356877 \tabularnewline
126 & 9.8506 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42253&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]115[/C][C]9.97121531651625[/C][C]9.73676056930803[/C][C]10.2056700637245[/C][/ROW]
[ROW][C]116[/C][C]9.9853436576308[/C][C]9.65418784176747[/C][C]10.3164994734941[/C][/ROW]
[ROW][C]117[/C][C]10.0378223935374[/C][C]9.63469650208294[/C][C]10.4409482849918[/C][/ROW]
[ROW][C]118[/C][C]9.97868549201678[/C][C]9.5171098638781[/C][C]10.4402611201554[/C][/ROW]
[ROW][C]119[/C][C]9.86748232183899[/C][C]9.3558285919222[/C][C]10.3791360517558[/C][/ROW]
[ROW][C]120[/C][C]9.74142564470864[/C][C]9.18067139061393[/C][C]10.3021798988033[/C][/ROW]
[ROW][C]121[/C][C]9.71396816463448[/C][C]9.1024281380515[/C][C]10.3255081912175[/C][/ROW]
[ROW][C]122[/C][C]9.797416175066[/C][C]9.13797531812443[/C][C]10.4568570320076[/C][/ROW]
[ROW][C]123[/C][C]9.88571800618774[/C][C]9.1895491740406[/C][C]10.5818868383349[/C][/ROW]
[ROW][C]124[/C][C]9.83621376578563[/C][C]9.10430465103645[/C][C]10.5681228805348[/C][/ROW]
[ROW][C]125[/C][C]9.80480499402076[/C][C]9.03355695235378[/C][C]10.5760530356877[/C][/ROW]
[ROW][C]126[/C][C]9.8506[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42253&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42253&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
1159.971215316516259.7367605693080310.2056700637245
1169.98534365763089.6541878417674710.3164994734941
11710.03782239353749.6346965020829410.4409482849918
1189.978685492016789.517109863878110.4402611201554
1199.867482321838999.355828591922210.3791360517558
1209.741425644708649.1806713906139310.3021798988033
1219.713968164634489.102428138051510.3255081912175
1229.7974161750669.1379753181244310.4568570320076
1239.885718006187749.189549174040610.5818868383349
1249.836213765785639.1043046510364510.5681228805348
1259.804804994020769.0335569523537810.5760530356877
1269.8506NANA



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')