Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 25 Nov 2015 20:53:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/25/t1448484873ls9rzwo1lv3p1oi.htm/, Retrieved Thu, 16 May 2024 00:09:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284160, Retrieved Thu, 16 May 2024 00:09:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-25 20:53:08] [30eae7c09eb039ed7d9b26159bd388f7] [Current]
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Dataseries X:
88.52
90.15
88.63
88.32
88.51
88.53
88.35
88.4
88.41
88.47
88.46
89.28
89.11
90.74
89.49
88.62
89.09
89.14
89.45
89.33
89.44
89.54
89.52
90.48
90.04
91.93
91.25
89.27
90.57
90.79
90.83
90.76
91.29
91.48
91.63
92.63
91.7
93.86
92.45
92.03
92.71
93.15
92.98
92.73
93.29
93.2
93.34
93.95
93.43
95.67
94.02
93.51
94.6
94.27
94.05
94.1
94.51
94.53
94.2
93.58
94.94
96.24
95.77
94.41
95.09
95.37
95.17
95.05
95.33
95.42
95.95
96.12
96.94
98.73
98.03
97.42
98.39
98.77
98.46
98.3
98.25
98.33
98.61
98.99
98.8
100.26
100.85
98.87
99.81
100.44
100.07
99.8
99.77
99.9
100.58
100.86
101.05
101.3
101.45
101.13
101.38
101.03
100.79
100.84
101.17
101.36
101.14
101.24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284160&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284160&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284160&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.394433694491101
beta0.0387270863158461
gamma0.460318220941388

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.394433694491101 \tabularnewline
beta & 0.0387270863158461 \tabularnewline
gamma & 0.460318220941388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284160&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]0.394433694491101[/C][/ROW]
[ROW][C]beta[/C][C]0.0387270863158461[/C][/ROW]
[ROW][C]gamma[/C][C]0.460318220941388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284160&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284160&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
alpha0.394433694491101
beta0.0387270863158461
gamma0.460318220941388







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1389.1188.80960470085470.300395299145265
1490.7490.54549111868610.194508881313851
1589.4989.3655002074410.124499792559035
1688.6288.53396378700090.0860362129991046
1789.0989.02732026095990.0626797390401066
1889.1489.08700493773350.0529950622664614
1989.4589.1499291654320.300070834568004
2089.3389.3536420651553-0.0236420651553431
2189.4489.37806055101140.0619394489886389
2289.5489.49926474467120.0407352553288405
2389.5289.554394198485-0.0343941984849891
2490.4890.3964480170090.0835519829910254
2590.0490.3583695481144-0.318369548114347
2691.9391.83031084088970.0996891591103264
2791.2590.60158893977780.648411060222173
2889.2789.9821661763549-0.712166176354884
2990.5790.15816853195020.411831468049769
3090.7990.36219865757130.42780134242868
3190.8390.65688541773260.173114582267374
3290.7690.73340033836790.0265996616320621
3391.2990.81537328392620.474626716073772
3491.4891.11362972105840.366370278941631
3591.6391.30141740343990.328582596560054
3692.6392.35022332315280.279776676847192
3791.792.311206902092-0.611206902091965
3893.8693.81340664234510.0465933576548707
3992.4592.7451170664077-0.295117066407741
4092.0391.38827421888360.641725781116435
4192.7192.44630065375890.263699346241111
4293.1592.62877690256030.521223097439702
4392.9892.92316741210040.0568325878995921
4492.7392.9450488657972-0.215048865797215
4593.2993.08497879437370.205021205626323
4693.293.2709809362323-0.070980936232317
4793.3493.2933124995830.046687500417022
4893.9594.2306020395964-0.280602039596417
4993.4393.7269062595054-0.296906259505377
5095.6795.54595913624790.1240408637521
5194.0294.4236660645556-0.403666064555594
5293.5193.29419913940460.215800860595436
5394.694.08138759599970.518612404000265
5494.2794.4426268217836-0.172626821783638
5594.0594.3297215653234-0.279721565323399
5694.194.1337583034274-0.0337583034274473
5794.5194.4557518875590.0542481124409733
5894.5394.49650513118480.0334948688151684
5994.294.5855993933837-0.385599393383657
6093.5895.2472975780092-1.66729757800924
6194.9494.15706552367390.782934476326062
6296.2496.5008472108088-0.260847210808805
6395.7795.05522492825830.714775071741713
6494.4194.5322553623956-0.12225536239562
6595.0995.258016942167-0.168016942167029
6695.3795.13275702199530.237242978004659
6795.1795.13494184591860.0350581540814261
6895.0595.1197863275408-0.0697863275408395
6995.3395.4396359461552-0.10963594615518
7095.4295.39499401975260.0250059802473999
7195.9595.34881769752110.601182302478932
7296.1296.04243329843280.0775667015672212
7396.9496.3500727563940.589927243605985
7498.7398.35044837192610.379551628073898
7598.0397.46284104488190.567158955118146
7697.4296.67952915534150.740470844658475
7798.3997.77720856936410.612791430635866
7898.7798.12920607474620.64079392525376
7998.4698.29668246392990.163317536070068
8098.398.3673273703989-0.0673273703989423
8198.2598.7415125750818-0.491512575081757
8298.3398.6424181391793-0.312418139179258
8398.6198.6772477589319-0.0672477589318987
8498.9999.0045284343193-0.0145284343193026
8598.899.4605337723813-0.660533772381299
86100.26100.931810587677-0.671810587676745
87100.8599.68851491695781.16148508304219
8898.8799.2037232088311-0.333723208831046
8999.8199.8414913326468-0.0314913326467803
90100.4499.936704285520.503295714479989
91100.0799.90428484494640.165715155053618
9299.899.899055241662-0.0990552416620005
9399.77100.129471063359-0.359471063358683
9499.9100.12138650966-0.221386509659979
95100.58100.2508597460020.32914025399802
96100.86100.7456354689960.114364531003787
97101.05101.07082393061-0.0208239306100069
98101.3102.799471606001-1.49947160600131
99101.45101.736304033446-0.286304033445646
100101.13100.2370944948150.892905505185482
101101.38101.435104582228-0.05510458222777
102101.03101.661886742383-0.631886742382775
103100.79101.062080678273-0.2720806782729
104100.84100.7781458514660.0618541485343087
105101.17100.9696777486210.200322251378921
106101.36101.199676779770.160323220229913
107101.14101.617791740642-0.477791740641919
108101.24101.706712218573-0.466712218573193

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 89.11 & 88.8096047008547 & 0.300395299145265 \tabularnewline
14 & 90.74 & 90.5454911186861 & 0.194508881313851 \tabularnewline
15 & 89.49 & 89.365500207441 & 0.124499792559035 \tabularnewline
16 & 88.62 & 88.5339637870009 & 0.0860362129991046 \tabularnewline
17 & 89.09 & 89.0273202609599 & 0.0626797390401066 \tabularnewline
18 & 89.14 & 89.0870049377335 & 0.0529950622664614 \tabularnewline
19 & 89.45 & 89.149929165432 & 0.300070834568004 \tabularnewline
20 & 89.33 & 89.3536420651553 & -0.0236420651553431 \tabularnewline
21 & 89.44 & 89.3780605510114 & 0.0619394489886389 \tabularnewline
22 & 89.54 & 89.4992647446712 & 0.0407352553288405 \tabularnewline
23 & 89.52 & 89.554394198485 & -0.0343941984849891 \tabularnewline
24 & 90.48 & 90.396448017009 & 0.0835519829910254 \tabularnewline
25 & 90.04 & 90.3583695481144 & -0.318369548114347 \tabularnewline
26 & 91.93 & 91.8303108408897 & 0.0996891591103264 \tabularnewline
27 & 91.25 & 90.6015889397778 & 0.648411060222173 \tabularnewline
28 & 89.27 & 89.9821661763549 & -0.712166176354884 \tabularnewline
29 & 90.57 & 90.1581685319502 & 0.411831468049769 \tabularnewline
30 & 90.79 & 90.3621986575713 & 0.42780134242868 \tabularnewline
31 & 90.83 & 90.6568854177326 & 0.173114582267374 \tabularnewline
32 & 90.76 & 90.7334003383679 & 0.0265996616320621 \tabularnewline
33 & 91.29 & 90.8153732839262 & 0.474626716073772 \tabularnewline
34 & 91.48 & 91.1136297210584 & 0.366370278941631 \tabularnewline
35 & 91.63 & 91.3014174034399 & 0.328582596560054 \tabularnewline
36 & 92.63 & 92.3502233231528 & 0.279776676847192 \tabularnewline
37 & 91.7 & 92.311206902092 & -0.611206902091965 \tabularnewline
38 & 93.86 & 93.8134066423451 & 0.0465933576548707 \tabularnewline
39 & 92.45 & 92.7451170664077 & -0.295117066407741 \tabularnewline
40 & 92.03 & 91.3882742188836 & 0.641725781116435 \tabularnewline
41 & 92.71 & 92.4463006537589 & 0.263699346241111 \tabularnewline
42 & 93.15 & 92.6287769025603 & 0.521223097439702 \tabularnewline
43 & 92.98 & 92.9231674121004 & 0.0568325878995921 \tabularnewline
44 & 92.73 & 92.9450488657972 & -0.215048865797215 \tabularnewline
45 & 93.29 & 93.0849787943737 & 0.205021205626323 \tabularnewline
46 & 93.2 & 93.2709809362323 & -0.070980936232317 \tabularnewline
47 & 93.34 & 93.293312499583 & 0.046687500417022 \tabularnewline
48 & 93.95 & 94.2306020395964 & -0.280602039596417 \tabularnewline
49 & 93.43 & 93.7269062595054 & -0.296906259505377 \tabularnewline
50 & 95.67 & 95.5459591362479 & 0.1240408637521 \tabularnewline
51 & 94.02 & 94.4236660645556 & -0.403666064555594 \tabularnewline
52 & 93.51 & 93.2941991394046 & 0.215800860595436 \tabularnewline
53 & 94.6 & 94.0813875959997 & 0.518612404000265 \tabularnewline
54 & 94.27 & 94.4426268217836 & -0.172626821783638 \tabularnewline
55 & 94.05 & 94.3297215653234 & -0.279721565323399 \tabularnewline
56 & 94.1 & 94.1337583034274 & -0.0337583034274473 \tabularnewline
57 & 94.51 & 94.455751887559 & 0.0542481124409733 \tabularnewline
58 & 94.53 & 94.4965051311848 & 0.0334948688151684 \tabularnewline
59 & 94.2 & 94.5855993933837 & -0.385599393383657 \tabularnewline
60 & 93.58 & 95.2472975780092 & -1.66729757800924 \tabularnewline
61 & 94.94 & 94.1570655236739 & 0.782934476326062 \tabularnewline
62 & 96.24 & 96.5008472108088 & -0.260847210808805 \tabularnewline
63 & 95.77 & 95.0552249282583 & 0.714775071741713 \tabularnewline
64 & 94.41 & 94.5322553623956 & -0.12225536239562 \tabularnewline
65 & 95.09 & 95.258016942167 & -0.168016942167029 \tabularnewline
66 & 95.37 & 95.1327570219953 & 0.237242978004659 \tabularnewline
67 & 95.17 & 95.1349418459186 & 0.0350581540814261 \tabularnewline
68 & 95.05 & 95.1197863275408 & -0.0697863275408395 \tabularnewline
69 & 95.33 & 95.4396359461552 & -0.10963594615518 \tabularnewline
70 & 95.42 & 95.3949940197526 & 0.0250059802473999 \tabularnewline
71 & 95.95 & 95.3488176975211 & 0.601182302478932 \tabularnewline
72 & 96.12 & 96.0424332984328 & 0.0775667015672212 \tabularnewline
73 & 96.94 & 96.350072756394 & 0.589927243605985 \tabularnewline
74 & 98.73 & 98.3504483719261 & 0.379551628073898 \tabularnewline
75 & 98.03 & 97.4628410448819 & 0.567158955118146 \tabularnewline
76 & 97.42 & 96.6795291553415 & 0.740470844658475 \tabularnewline
77 & 98.39 & 97.7772085693641 & 0.612791430635866 \tabularnewline
78 & 98.77 & 98.1292060747462 & 0.64079392525376 \tabularnewline
79 & 98.46 & 98.2966824639299 & 0.163317536070068 \tabularnewline
80 & 98.3 & 98.3673273703989 & -0.0673273703989423 \tabularnewline
81 & 98.25 & 98.7415125750818 & -0.491512575081757 \tabularnewline
82 & 98.33 & 98.6424181391793 & -0.312418139179258 \tabularnewline
83 & 98.61 & 98.6772477589319 & -0.0672477589318987 \tabularnewline
84 & 98.99 & 99.0045284343193 & -0.0145284343193026 \tabularnewline
85 & 98.8 & 99.4605337723813 & -0.660533772381299 \tabularnewline
86 & 100.26 & 100.931810587677 & -0.671810587676745 \tabularnewline
87 & 100.85 & 99.6885149169578 & 1.16148508304219 \tabularnewline
88 & 98.87 & 99.2037232088311 & -0.333723208831046 \tabularnewline
89 & 99.81 & 99.8414913326468 & -0.0314913326467803 \tabularnewline
90 & 100.44 & 99.93670428552 & 0.503295714479989 \tabularnewline
91 & 100.07 & 99.9042848449464 & 0.165715155053618 \tabularnewline
92 & 99.8 & 99.899055241662 & -0.0990552416620005 \tabularnewline
93 & 99.77 & 100.129471063359 & -0.359471063358683 \tabularnewline
94 & 99.9 & 100.12138650966 & -0.221386509659979 \tabularnewline
95 & 100.58 & 100.250859746002 & 0.32914025399802 \tabularnewline
96 & 100.86 & 100.745635468996 & 0.114364531003787 \tabularnewline
97 & 101.05 & 101.07082393061 & -0.0208239306100069 \tabularnewline
98 & 101.3 & 102.799471606001 & -1.49947160600131 \tabularnewline
99 & 101.45 & 101.736304033446 & -0.286304033445646 \tabularnewline
100 & 101.13 & 100.237094494815 & 0.892905505185482 \tabularnewline
101 & 101.38 & 101.435104582228 & -0.05510458222777 \tabularnewline
102 & 101.03 & 101.661886742383 & -0.631886742382775 \tabularnewline
103 & 100.79 & 101.062080678273 & -0.2720806782729 \tabularnewline
104 & 100.84 & 100.778145851466 & 0.0618541485343087 \tabularnewline
105 & 101.17 & 100.969677748621 & 0.200322251378921 \tabularnewline
106 & 101.36 & 101.19967677977 & 0.160323220229913 \tabularnewline
107 & 101.14 & 101.617791740642 & -0.477791740641919 \tabularnewline
108 & 101.24 & 101.706712218573 & -0.466712218573193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284160&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]89.11[/C][C]88.8096047008547[/C][C]0.300395299145265[/C][/ROW]
[ROW][C]14[/C][C]90.74[/C][C]90.5454911186861[/C][C]0.194508881313851[/C][/ROW]
[ROW][C]15[/C][C]89.49[/C][C]89.365500207441[/C][C]0.124499792559035[/C][/ROW]
[ROW][C]16[/C][C]88.62[/C][C]88.5339637870009[/C][C]0.0860362129991046[/C][/ROW]
[ROW][C]17[/C][C]89.09[/C][C]89.0273202609599[/C][C]0.0626797390401066[/C][/ROW]
[ROW][C]18[/C][C]89.14[/C][C]89.0870049377335[/C][C]0.0529950622664614[/C][/ROW]
[ROW][C]19[/C][C]89.45[/C][C]89.149929165432[/C][C]0.300070834568004[/C][/ROW]
[ROW][C]20[/C][C]89.33[/C][C]89.3536420651553[/C][C]-0.0236420651553431[/C][/ROW]
[ROW][C]21[/C][C]89.44[/C][C]89.3780605510114[/C][C]0.0619394489886389[/C][/ROW]
[ROW][C]22[/C][C]89.54[/C][C]89.4992647446712[/C][C]0.0407352553288405[/C][/ROW]
[ROW][C]23[/C][C]89.52[/C][C]89.554394198485[/C][C]-0.0343941984849891[/C][/ROW]
[ROW][C]24[/C][C]90.48[/C][C]90.396448017009[/C][C]0.0835519829910254[/C][/ROW]
[ROW][C]25[/C][C]90.04[/C][C]90.3583695481144[/C][C]-0.318369548114347[/C][/ROW]
[ROW][C]26[/C][C]91.93[/C][C]91.8303108408897[/C][C]0.0996891591103264[/C][/ROW]
[ROW][C]27[/C][C]91.25[/C][C]90.6015889397778[/C][C]0.648411060222173[/C][/ROW]
[ROW][C]28[/C][C]89.27[/C][C]89.9821661763549[/C][C]-0.712166176354884[/C][/ROW]
[ROW][C]29[/C][C]90.57[/C][C]90.1581685319502[/C][C]0.411831468049769[/C][/ROW]
[ROW][C]30[/C][C]90.79[/C][C]90.3621986575713[/C][C]0.42780134242868[/C][/ROW]
[ROW][C]31[/C][C]90.83[/C][C]90.6568854177326[/C][C]0.173114582267374[/C][/ROW]
[ROW][C]32[/C][C]90.76[/C][C]90.7334003383679[/C][C]0.0265996616320621[/C][/ROW]
[ROW][C]33[/C][C]91.29[/C][C]90.8153732839262[/C][C]0.474626716073772[/C][/ROW]
[ROW][C]34[/C][C]91.48[/C][C]91.1136297210584[/C][C]0.366370278941631[/C][/ROW]
[ROW][C]35[/C][C]91.63[/C][C]91.3014174034399[/C][C]0.328582596560054[/C][/ROW]
[ROW][C]36[/C][C]92.63[/C][C]92.3502233231528[/C][C]0.279776676847192[/C][/ROW]
[ROW][C]37[/C][C]91.7[/C][C]92.311206902092[/C][C]-0.611206902091965[/C][/ROW]
[ROW][C]38[/C][C]93.86[/C][C]93.8134066423451[/C][C]0.0465933576548707[/C][/ROW]
[ROW][C]39[/C][C]92.45[/C][C]92.7451170664077[/C][C]-0.295117066407741[/C][/ROW]
[ROW][C]40[/C][C]92.03[/C][C]91.3882742188836[/C][C]0.641725781116435[/C][/ROW]
[ROW][C]41[/C][C]92.71[/C][C]92.4463006537589[/C][C]0.263699346241111[/C][/ROW]
[ROW][C]42[/C][C]93.15[/C][C]92.6287769025603[/C][C]0.521223097439702[/C][/ROW]
[ROW][C]43[/C][C]92.98[/C][C]92.9231674121004[/C][C]0.0568325878995921[/C][/ROW]
[ROW][C]44[/C][C]92.73[/C][C]92.9450488657972[/C][C]-0.215048865797215[/C][/ROW]
[ROW][C]45[/C][C]93.29[/C][C]93.0849787943737[/C][C]0.205021205626323[/C][/ROW]
[ROW][C]46[/C][C]93.2[/C][C]93.2709809362323[/C][C]-0.070980936232317[/C][/ROW]
[ROW][C]47[/C][C]93.34[/C][C]93.293312499583[/C][C]0.046687500417022[/C][/ROW]
[ROW][C]48[/C][C]93.95[/C][C]94.2306020395964[/C][C]-0.280602039596417[/C][/ROW]
[ROW][C]49[/C][C]93.43[/C][C]93.7269062595054[/C][C]-0.296906259505377[/C][/ROW]
[ROW][C]50[/C][C]95.67[/C][C]95.5459591362479[/C][C]0.1240408637521[/C][/ROW]
[ROW][C]51[/C][C]94.02[/C][C]94.4236660645556[/C][C]-0.403666064555594[/C][/ROW]
[ROW][C]52[/C][C]93.51[/C][C]93.2941991394046[/C][C]0.215800860595436[/C][/ROW]
[ROW][C]53[/C][C]94.6[/C][C]94.0813875959997[/C][C]0.518612404000265[/C][/ROW]
[ROW][C]54[/C][C]94.27[/C][C]94.4426268217836[/C][C]-0.172626821783638[/C][/ROW]
[ROW][C]55[/C][C]94.05[/C][C]94.3297215653234[/C][C]-0.279721565323399[/C][/ROW]
[ROW][C]56[/C][C]94.1[/C][C]94.1337583034274[/C][C]-0.0337583034274473[/C][/ROW]
[ROW][C]57[/C][C]94.51[/C][C]94.455751887559[/C][C]0.0542481124409733[/C][/ROW]
[ROW][C]58[/C][C]94.53[/C][C]94.4965051311848[/C][C]0.0334948688151684[/C][/ROW]
[ROW][C]59[/C][C]94.2[/C][C]94.5855993933837[/C][C]-0.385599393383657[/C][/ROW]
[ROW][C]60[/C][C]93.58[/C][C]95.2472975780092[/C][C]-1.66729757800924[/C][/ROW]
[ROW][C]61[/C][C]94.94[/C][C]94.1570655236739[/C][C]0.782934476326062[/C][/ROW]
[ROW][C]62[/C][C]96.24[/C][C]96.5008472108088[/C][C]-0.260847210808805[/C][/ROW]
[ROW][C]63[/C][C]95.77[/C][C]95.0552249282583[/C][C]0.714775071741713[/C][/ROW]
[ROW][C]64[/C][C]94.41[/C][C]94.5322553623956[/C][C]-0.12225536239562[/C][/ROW]
[ROW][C]65[/C][C]95.09[/C][C]95.258016942167[/C][C]-0.168016942167029[/C][/ROW]
[ROW][C]66[/C][C]95.37[/C][C]95.1327570219953[/C][C]0.237242978004659[/C][/ROW]
[ROW][C]67[/C][C]95.17[/C][C]95.1349418459186[/C][C]0.0350581540814261[/C][/ROW]
[ROW][C]68[/C][C]95.05[/C][C]95.1197863275408[/C][C]-0.0697863275408395[/C][/ROW]
[ROW][C]69[/C][C]95.33[/C][C]95.4396359461552[/C][C]-0.10963594615518[/C][/ROW]
[ROW][C]70[/C][C]95.42[/C][C]95.3949940197526[/C][C]0.0250059802473999[/C][/ROW]
[ROW][C]71[/C][C]95.95[/C][C]95.3488176975211[/C][C]0.601182302478932[/C][/ROW]
[ROW][C]72[/C][C]96.12[/C][C]96.0424332984328[/C][C]0.0775667015672212[/C][/ROW]
[ROW][C]73[/C][C]96.94[/C][C]96.350072756394[/C][C]0.589927243605985[/C][/ROW]
[ROW][C]74[/C][C]98.73[/C][C]98.3504483719261[/C][C]0.379551628073898[/C][/ROW]
[ROW][C]75[/C][C]98.03[/C][C]97.4628410448819[/C][C]0.567158955118146[/C][/ROW]
[ROW][C]76[/C][C]97.42[/C][C]96.6795291553415[/C][C]0.740470844658475[/C][/ROW]
[ROW][C]77[/C][C]98.39[/C][C]97.7772085693641[/C][C]0.612791430635866[/C][/ROW]
[ROW][C]78[/C][C]98.77[/C][C]98.1292060747462[/C][C]0.64079392525376[/C][/ROW]
[ROW][C]79[/C][C]98.46[/C][C]98.2966824639299[/C][C]0.163317536070068[/C][/ROW]
[ROW][C]80[/C][C]98.3[/C][C]98.3673273703989[/C][C]-0.0673273703989423[/C][/ROW]
[ROW][C]81[/C][C]98.25[/C][C]98.7415125750818[/C][C]-0.491512575081757[/C][/ROW]
[ROW][C]82[/C][C]98.33[/C][C]98.6424181391793[/C][C]-0.312418139179258[/C][/ROW]
[ROW][C]83[/C][C]98.61[/C][C]98.6772477589319[/C][C]-0.0672477589318987[/C][/ROW]
[ROW][C]84[/C][C]98.99[/C][C]99.0045284343193[/C][C]-0.0145284343193026[/C][/ROW]
[ROW][C]85[/C][C]98.8[/C][C]99.4605337723813[/C][C]-0.660533772381299[/C][/ROW]
[ROW][C]86[/C][C]100.26[/C][C]100.931810587677[/C][C]-0.671810587676745[/C][/ROW]
[ROW][C]87[/C][C]100.85[/C][C]99.6885149169578[/C][C]1.16148508304219[/C][/ROW]
[ROW][C]88[/C][C]98.87[/C][C]99.2037232088311[/C][C]-0.333723208831046[/C][/ROW]
[ROW][C]89[/C][C]99.81[/C][C]99.8414913326468[/C][C]-0.0314913326467803[/C][/ROW]
[ROW][C]90[/C][C]100.44[/C][C]99.93670428552[/C][C]0.503295714479989[/C][/ROW]
[ROW][C]91[/C][C]100.07[/C][C]99.9042848449464[/C][C]0.165715155053618[/C][/ROW]
[ROW][C]92[/C][C]99.8[/C][C]99.899055241662[/C][C]-0.0990552416620005[/C][/ROW]
[ROW][C]93[/C][C]99.77[/C][C]100.129471063359[/C][C]-0.359471063358683[/C][/ROW]
[ROW][C]94[/C][C]99.9[/C][C]100.12138650966[/C][C]-0.221386509659979[/C][/ROW]
[ROW][C]95[/C][C]100.58[/C][C]100.250859746002[/C][C]0.32914025399802[/C][/ROW]
[ROW][C]96[/C][C]100.86[/C][C]100.745635468996[/C][C]0.114364531003787[/C][/ROW]
[ROW][C]97[/C][C]101.05[/C][C]101.07082393061[/C][C]-0.0208239306100069[/C][/ROW]
[ROW][C]98[/C][C]101.3[/C][C]102.799471606001[/C][C]-1.49947160600131[/C][/ROW]
[ROW][C]99[/C][C]101.45[/C][C]101.736304033446[/C][C]-0.286304033445646[/C][/ROW]
[ROW][C]100[/C][C]101.13[/C][C]100.237094494815[/C][C]0.892905505185482[/C][/ROW]
[ROW][C]101[/C][C]101.38[/C][C]101.435104582228[/C][C]-0.05510458222777[/C][/ROW]
[ROW][C]102[/C][C]101.03[/C][C]101.661886742383[/C][C]-0.631886742382775[/C][/ROW]
[ROW][C]103[/C][C]100.79[/C][C]101.062080678273[/C][C]-0.2720806782729[/C][/ROW]
[ROW][C]104[/C][C]100.84[/C][C]100.778145851466[/C][C]0.0618541485343087[/C][/ROW]
[ROW][C]105[/C][C]101.17[/C][C]100.969677748621[/C][C]0.200322251378921[/C][/ROW]
[ROW][C]106[/C][C]101.36[/C][C]101.19967677977[/C][C]0.160323220229913[/C][/ROW]
[ROW][C]107[/C][C]101.14[/C][C]101.617791740642[/C][C]-0.477791740641919[/C][/ROW]
[ROW][C]108[/C][C]101.24[/C][C]101.706712218573[/C][C]-0.466712218573193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284160&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284160&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
1389.1188.80960470085470.300395299145265
1490.7490.54549111868610.194508881313851
1589.4989.3655002074410.124499792559035
1688.6288.53396378700090.0860362129991046
1789.0989.02732026095990.0626797390401066
1889.1489.08700493773350.0529950622664614
1989.4589.1499291654320.300070834568004
2089.3389.3536420651553-0.0236420651553431
2189.4489.37806055101140.0619394489886389
2289.5489.49926474467120.0407352553288405
2389.5289.554394198485-0.0343941984849891
2490.4890.3964480170090.0835519829910254
2590.0490.3583695481144-0.318369548114347
2691.9391.83031084088970.0996891591103264
2791.2590.60158893977780.648411060222173
2889.2789.9821661763549-0.712166176354884
2990.5790.15816853195020.411831468049769
3090.7990.36219865757130.42780134242868
3190.8390.65688541773260.173114582267374
3290.7690.73340033836790.0265996616320621
3391.2990.81537328392620.474626716073772
3491.4891.11362972105840.366370278941631
3591.6391.30141740343990.328582596560054
3692.6392.35022332315280.279776676847192
3791.792.311206902092-0.611206902091965
3893.8693.81340664234510.0465933576548707
3992.4592.7451170664077-0.295117066407741
4092.0391.38827421888360.641725781116435
4192.7192.44630065375890.263699346241111
4293.1592.62877690256030.521223097439702
4392.9892.92316741210040.0568325878995921
4492.7392.9450488657972-0.215048865797215
4593.2993.08497879437370.205021205626323
4693.293.2709809362323-0.070980936232317
4793.3493.2933124995830.046687500417022
4893.9594.2306020395964-0.280602039596417
4993.4393.7269062595054-0.296906259505377
5095.6795.54595913624790.1240408637521
5194.0294.4236660645556-0.403666064555594
5293.5193.29419913940460.215800860595436
5394.694.08138759599970.518612404000265
5494.2794.4426268217836-0.172626821783638
5594.0594.3297215653234-0.279721565323399
5694.194.1337583034274-0.0337583034274473
5794.5194.4557518875590.0542481124409733
5894.5394.49650513118480.0334948688151684
5994.294.5855993933837-0.385599393383657
6093.5895.2472975780092-1.66729757800924
6194.9494.15706552367390.782934476326062
6296.2496.5008472108088-0.260847210808805
6395.7795.05522492825830.714775071741713
6494.4194.5322553623956-0.12225536239562
6595.0995.258016942167-0.168016942167029
6695.3795.13275702199530.237242978004659
6795.1795.13494184591860.0350581540814261
6895.0595.1197863275408-0.0697863275408395
6995.3395.4396359461552-0.10963594615518
7095.4295.39499401975260.0250059802473999
7195.9595.34881769752110.601182302478932
7296.1296.04243329843280.0775667015672212
7396.9496.3500727563940.589927243605985
7498.7398.35044837192610.379551628073898
7598.0397.46284104488190.567158955118146
7697.4296.67952915534150.740470844658475
7798.3997.77720856936410.612791430635866
7898.7798.12920607474620.64079392525376
7998.4698.29668246392990.163317536070068
8098.398.3673273703989-0.0673273703989423
8198.2598.7415125750818-0.491512575081757
8298.3398.6424181391793-0.312418139179258
8398.6198.6772477589319-0.0672477589318987
8498.9999.0045284343193-0.0145284343193026
8598.899.4605337723813-0.660533772381299
86100.26100.931810587677-0.671810587676745
87100.8599.68851491695781.16148508304219
8898.8799.2037232088311-0.333723208831046
8999.8199.8414913326468-0.0314913326467803
90100.4499.936704285520.503295714479989
91100.0799.90428484494640.165715155053618
9299.899.899055241662-0.0990552416620005
9399.77100.129471063359-0.359471063358683
9499.9100.12138650966-0.221386509659979
95100.58100.2508597460020.32914025399802
96100.86100.7456354689960.114364531003787
97101.05101.07082393061-0.0208239306100069
98101.3102.799471606001-1.49947160600131
99101.45101.736304033446-0.286304033445646
100101.13100.2370944948150.892905505185482
101101.38101.435104582228-0.05510458222777
102101.03101.661886742383-0.631886742382775
103100.79101.062080678273-0.2720806782729
104100.84100.7781458514660.0618541485343087
105101.17100.9696777486210.200322251378921
106101.36101.199676779770.160323220229913
107101.14101.617791740642-0.477791740641919
108101.24101.706712218573-0.466712218573193







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109101.728439455072100.86626783522102.590611074923
110103.016860344626102.085131841367103.948588847886
111102.869951407983101.868765206692103.871137609275
112101.803393797577100.732667776439102.874119818715
113102.362327180409101.221842150039103.50281221078
114102.428282468715101.217713850759103.638851086671
115102.165881058999100.88482215019103.446939967809
116102.074375666324100.722355087955103.426396244693
117102.271190035814100.847685058332103.694695013296
118102.399046792418100.903493667236103.8945999176
119102.561620732243100.993422809479104.129818655008
120102.834957669821101.19349184997104.476423489671

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 101.728439455072 & 100.86626783522 & 102.590611074923 \tabularnewline
110 & 103.016860344626 & 102.085131841367 & 103.948588847886 \tabularnewline
111 & 102.869951407983 & 101.868765206692 & 103.871137609275 \tabularnewline
112 & 101.803393797577 & 100.732667776439 & 102.874119818715 \tabularnewline
113 & 102.362327180409 & 101.221842150039 & 103.50281221078 \tabularnewline
114 & 102.428282468715 & 101.217713850759 & 103.638851086671 \tabularnewline
115 & 102.165881058999 & 100.88482215019 & 103.446939967809 \tabularnewline
116 & 102.074375666324 & 100.722355087955 & 103.426396244693 \tabularnewline
117 & 102.271190035814 & 100.847685058332 & 103.694695013296 \tabularnewline
118 & 102.399046792418 & 100.903493667236 & 103.8945999176 \tabularnewline
119 & 102.561620732243 & 100.993422809479 & 104.129818655008 \tabularnewline
120 & 102.834957669821 & 101.19349184997 & 104.476423489671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284160&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]109[/C][C]101.728439455072[/C][C]100.86626783522[/C][C]102.590611074923[/C][/ROW]
[ROW][C]110[/C][C]103.016860344626[/C][C]102.085131841367[/C][C]103.948588847886[/C][/ROW]
[ROW][C]111[/C][C]102.869951407983[/C][C]101.868765206692[/C][C]103.871137609275[/C][/ROW]
[ROW][C]112[/C][C]101.803393797577[/C][C]100.732667776439[/C][C]102.874119818715[/C][/ROW]
[ROW][C]113[/C][C]102.362327180409[/C][C]101.221842150039[/C][C]103.50281221078[/C][/ROW]
[ROW][C]114[/C][C]102.428282468715[/C][C]101.217713850759[/C][C]103.638851086671[/C][/ROW]
[ROW][C]115[/C][C]102.165881058999[/C][C]100.88482215019[/C][C]103.446939967809[/C][/ROW]
[ROW][C]116[/C][C]102.074375666324[/C][C]100.722355087955[/C][C]103.426396244693[/C][/ROW]
[ROW][C]117[/C][C]102.271190035814[/C][C]100.847685058332[/C][C]103.694695013296[/C][/ROW]
[ROW][C]118[/C][C]102.399046792418[/C][C]100.903493667236[/C][C]103.8945999176[/C][/ROW]
[ROW][C]119[/C][C]102.561620732243[/C][C]100.993422809479[/C][C]104.129818655008[/C][/ROW]
[ROW][C]120[/C][C]102.834957669821[/C][C]101.19349184997[/C][C]104.476423489671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284160&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284160&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
109101.728439455072100.86626783522102.590611074923
110103.016860344626102.085131841367103.948588847886
111102.869951407983101.868765206692103.871137609275
112101.803393797577100.732667776439102.874119818715
113102.362327180409101.221842150039103.50281221078
114102.428282468715101.217713850759103.638851086671
115102.165881058999100.88482215019103.446939967809
116102.074375666324100.722355087955103.426396244693
117102.271190035814100.847685058332103.694695013296
118102.399046792418100.903493667236103.8945999176
119102.561620732243100.993422809479104.129818655008
120102.834957669821101.19349184997104.476423489671



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