Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 14:15:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/19/t1282227325fggc7xi7gz5k8v1.htm/, Retrieved Fri, 03 May 2024 09:59:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79303, Retrieved Fri, 03 May 2024 09:59:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTrouillard Olivier
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [aantal bezoekers] [2010-08-19 14:15:28] [b58dfa1c2951471c561e0016df4afa08] [Current]
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Dataseries X:
80
79
78
76
74
73
74
76
77
77
78
80
90
90
89
82
78
76
74
78
81
82
88
99
117
113
106
100
97
96
100
104
104
111
117
118
140
147
134
126
116
114
120
122
117
119
132
134
154
152
132
130
123
129
124
128
128
129
141
138
155
160
142
133
131
140
134
134
134
136
145
137
152
168
160
157
147
161
159
164
163
158
175
163




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79303&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79303&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.635952506179521
beta0.0081533707107304
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.635952506179521 \tabularnewline
beta & 0.0081533707107304 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79303&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]0.635952506179521[/C][/ROW]
[ROW][C]beta[/C][C]0.0081533707107304[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79303&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
alpha0.635952506179521
beta0.0081533707107304
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139087.03659188034192.9634081196581
149089.279638841450.720361158550062
158988.93328298486680.0667170151332073
168282.0465864352953-0.0465864352952963
177877.83759271450550.162407285494538
187675.17901784809250.820982151907529
197480.026855572787-6.02685557278697
207877.73854354497870.261456455021275
218178.40898833687432.59101166312571
228279.7826877360442.21731226395599
238882.22189584360135.77810415639867
249988.08055885368110.9194411463190
25117106.51097498505310.4890250149470
26113112.8683238784300.131676121570166
27106112.051524992776-6.05152499277558
28100101.342835432956-1.34283543295587
299796.48901746504860.510982534951424
309694.39712476026381.60287523973615
3110097.3585777585522.64142224144796
32104103.0263759090160.973624090983776
33104105.155739873687-1.15573987368684
34111104.1491570646926.85084293530817
35117110.9939117128806.00608828712024
36118119.032978514998-1.03297851499829
37140129.80728219364710.1927178063528
38147132.30584116832914.6941588316715
39134138.674833841784-4.67483384178433
40126130.738702515116-4.73870251511588
41116124.565405460484-8.56540546048375
42114117.217052682704-3.21705268270378
43120117.5845396085852.41546039141502
44122122.593506106066-0.593506106066314
45117123.034961352979-6.03496135297878
46119121.898803567889-2.89880356788905
47132122.2437635783219.75623642167893
48134130.1326852650093.86731473499103
49154148.1629315247595.83706847524084
50152149.5605601871042.43943981289641
51132141.051675182987-9.05167518298674
52130130.252909633819-0.252909633819399
53123125.506601953726-2.50660195372575
54129123.957170486285.04282951371998
55124131.669636857380-7.66963685738028
56128129.158845357211-1.15884535721102
57128127.2461837578110.753816242189373
58129131.590637567348-2.59063756734781
59141136.7617710866934.23822891330735
60138138.992202131415-0.992202131414672
61155154.6184602615300.381539738469741
62160151.2507956690348.74920433096602
63142142.545088842174-0.54508884217401
64133140.377163958185-7.37716395818461
65131130.260664686880.73933531311988
66140133.5216242994526.47837570054782
67134137.524309409594-3.52430940959385
68134140.046701855386-6.04670185538649
69134135.723266265022-1.72326626502209
70136137.263400095077-1.26340009507683
71145145.760034149733-0.760034149733315
72137142.87717399375-5.87717399375009
73152155.84109200071-3.84109200071012
74168152.75652917889615.2434708211038
75160144.75324473792715.2467552620727
76157150.1788075215516.82119247844921
77147152.158025184662-5.15802518466199
78161153.8386934980597.16130650194052
79159154.7186454394374.28135456056282
80164161.4116801130522.58831988694789
81163164.323299383372-1.32329938337179
82158166.456935423119-8.4569354231188
83175170.6965013040174.30349869598297
84163169.331610361607-6.331610361607

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 90 & 87.0365918803419 & 2.9634081196581 \tabularnewline
14 & 90 & 89.27963884145 & 0.720361158550062 \tabularnewline
15 & 89 & 88.9332829848668 & 0.0667170151332073 \tabularnewline
16 & 82 & 82.0465864352953 & -0.0465864352952963 \tabularnewline
17 & 78 & 77.8375927145055 & 0.162407285494538 \tabularnewline
18 & 76 & 75.1790178480925 & 0.820982151907529 \tabularnewline
19 & 74 & 80.026855572787 & -6.02685557278697 \tabularnewline
20 & 78 & 77.7385435449787 & 0.261456455021275 \tabularnewline
21 & 81 & 78.4089883368743 & 2.59101166312571 \tabularnewline
22 & 82 & 79.782687736044 & 2.21731226395599 \tabularnewline
23 & 88 & 82.2218958436013 & 5.77810415639867 \tabularnewline
24 & 99 & 88.080558853681 & 10.9194411463190 \tabularnewline
25 & 117 & 106.510974985053 & 10.4890250149470 \tabularnewline
26 & 113 & 112.868323878430 & 0.131676121570166 \tabularnewline
27 & 106 & 112.051524992776 & -6.05152499277558 \tabularnewline
28 & 100 & 101.342835432956 & -1.34283543295587 \tabularnewline
29 & 97 & 96.4890174650486 & 0.510982534951424 \tabularnewline
30 & 96 & 94.3971247602638 & 1.60287523973615 \tabularnewline
31 & 100 & 97.358577758552 & 2.64142224144796 \tabularnewline
32 & 104 & 103.026375909016 & 0.973624090983776 \tabularnewline
33 & 104 & 105.155739873687 & -1.15573987368684 \tabularnewline
34 & 111 & 104.149157064692 & 6.85084293530817 \tabularnewline
35 & 117 & 110.993911712880 & 6.00608828712024 \tabularnewline
36 & 118 & 119.032978514998 & -1.03297851499829 \tabularnewline
37 & 140 & 129.807282193647 & 10.1927178063528 \tabularnewline
38 & 147 & 132.305841168329 & 14.6941588316715 \tabularnewline
39 & 134 & 138.674833841784 & -4.67483384178433 \tabularnewline
40 & 126 & 130.738702515116 & -4.73870251511588 \tabularnewline
41 & 116 & 124.565405460484 & -8.56540546048375 \tabularnewline
42 & 114 & 117.217052682704 & -3.21705268270378 \tabularnewline
43 & 120 & 117.584539608585 & 2.41546039141502 \tabularnewline
44 & 122 & 122.593506106066 & -0.593506106066314 \tabularnewline
45 & 117 & 123.034961352979 & -6.03496135297878 \tabularnewline
46 & 119 & 121.898803567889 & -2.89880356788905 \tabularnewline
47 & 132 & 122.243763578321 & 9.75623642167893 \tabularnewline
48 & 134 & 130.132685265009 & 3.86731473499103 \tabularnewline
49 & 154 & 148.162931524759 & 5.83706847524084 \tabularnewline
50 & 152 & 149.560560187104 & 2.43943981289641 \tabularnewline
51 & 132 & 141.051675182987 & -9.05167518298674 \tabularnewline
52 & 130 & 130.252909633819 & -0.252909633819399 \tabularnewline
53 & 123 & 125.506601953726 & -2.50660195372575 \tabularnewline
54 & 129 & 123.95717048628 & 5.04282951371998 \tabularnewline
55 & 124 & 131.669636857380 & -7.66963685738028 \tabularnewline
56 & 128 & 129.158845357211 & -1.15884535721102 \tabularnewline
57 & 128 & 127.246183757811 & 0.753816242189373 \tabularnewline
58 & 129 & 131.590637567348 & -2.59063756734781 \tabularnewline
59 & 141 & 136.761771086693 & 4.23822891330735 \tabularnewline
60 & 138 & 138.992202131415 & -0.992202131414672 \tabularnewline
61 & 155 & 154.618460261530 & 0.381539738469741 \tabularnewline
62 & 160 & 151.250795669034 & 8.74920433096602 \tabularnewline
63 & 142 & 142.545088842174 & -0.54508884217401 \tabularnewline
64 & 133 & 140.377163958185 & -7.37716395818461 \tabularnewline
65 & 131 & 130.26066468688 & 0.73933531311988 \tabularnewline
66 & 140 & 133.521624299452 & 6.47837570054782 \tabularnewline
67 & 134 & 137.524309409594 & -3.52430940959385 \tabularnewline
68 & 134 & 140.046701855386 & -6.04670185538649 \tabularnewline
69 & 134 & 135.723266265022 & -1.72326626502209 \tabularnewline
70 & 136 & 137.263400095077 & -1.26340009507683 \tabularnewline
71 & 145 & 145.760034149733 & -0.760034149733315 \tabularnewline
72 & 137 & 142.87717399375 & -5.87717399375009 \tabularnewline
73 & 152 & 155.84109200071 & -3.84109200071012 \tabularnewline
74 & 168 & 152.756529178896 & 15.2434708211038 \tabularnewline
75 & 160 & 144.753244737927 & 15.2467552620727 \tabularnewline
76 & 157 & 150.178807521551 & 6.82119247844921 \tabularnewline
77 & 147 & 152.158025184662 & -5.15802518466199 \tabularnewline
78 & 161 & 153.838693498059 & 7.16130650194052 \tabularnewline
79 & 159 & 154.718645439437 & 4.28135456056282 \tabularnewline
80 & 164 & 161.411680113052 & 2.58831988694789 \tabularnewline
81 & 163 & 164.323299383372 & -1.32329938337179 \tabularnewline
82 & 158 & 166.456935423119 & -8.4569354231188 \tabularnewline
83 & 175 & 170.696501304017 & 4.30349869598297 \tabularnewline
84 & 163 & 169.331610361607 & -6.331610361607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79303&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]90[/C][C]87.0365918803419[/C][C]2.9634081196581[/C][/ROW]
[ROW][C]14[/C][C]90[/C][C]89.27963884145[/C][C]0.720361158550062[/C][/ROW]
[ROW][C]15[/C][C]89[/C][C]88.9332829848668[/C][C]0.0667170151332073[/C][/ROW]
[ROW][C]16[/C][C]82[/C][C]82.0465864352953[/C][C]-0.0465864352952963[/C][/ROW]
[ROW][C]17[/C][C]78[/C][C]77.8375927145055[/C][C]0.162407285494538[/C][/ROW]
[ROW][C]18[/C][C]76[/C][C]75.1790178480925[/C][C]0.820982151907529[/C][/ROW]
[ROW][C]19[/C][C]74[/C][C]80.026855572787[/C][C]-6.02685557278697[/C][/ROW]
[ROW][C]20[/C][C]78[/C][C]77.7385435449787[/C][C]0.261456455021275[/C][/ROW]
[ROW][C]21[/C][C]81[/C][C]78.4089883368743[/C][C]2.59101166312571[/C][/ROW]
[ROW][C]22[/C][C]82[/C][C]79.782687736044[/C][C]2.21731226395599[/C][/ROW]
[ROW][C]23[/C][C]88[/C][C]82.2218958436013[/C][C]5.77810415639867[/C][/ROW]
[ROW][C]24[/C][C]99[/C][C]88.080558853681[/C][C]10.9194411463190[/C][/ROW]
[ROW][C]25[/C][C]117[/C][C]106.510974985053[/C][C]10.4890250149470[/C][/ROW]
[ROW][C]26[/C][C]113[/C][C]112.868323878430[/C][C]0.131676121570166[/C][/ROW]
[ROW][C]27[/C][C]106[/C][C]112.051524992776[/C][C]-6.05152499277558[/C][/ROW]
[ROW][C]28[/C][C]100[/C][C]101.342835432956[/C][C]-1.34283543295587[/C][/ROW]
[ROW][C]29[/C][C]97[/C][C]96.4890174650486[/C][C]0.510982534951424[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]94.3971247602638[/C][C]1.60287523973615[/C][/ROW]
[ROW][C]31[/C][C]100[/C][C]97.358577758552[/C][C]2.64142224144796[/C][/ROW]
[ROW][C]32[/C][C]104[/C][C]103.026375909016[/C][C]0.973624090983776[/C][/ROW]
[ROW][C]33[/C][C]104[/C][C]105.155739873687[/C][C]-1.15573987368684[/C][/ROW]
[ROW][C]34[/C][C]111[/C][C]104.149157064692[/C][C]6.85084293530817[/C][/ROW]
[ROW][C]35[/C][C]117[/C][C]110.993911712880[/C][C]6.00608828712024[/C][/ROW]
[ROW][C]36[/C][C]118[/C][C]119.032978514998[/C][C]-1.03297851499829[/C][/ROW]
[ROW][C]37[/C][C]140[/C][C]129.807282193647[/C][C]10.1927178063528[/C][/ROW]
[ROW][C]38[/C][C]147[/C][C]132.305841168329[/C][C]14.6941588316715[/C][/ROW]
[ROW][C]39[/C][C]134[/C][C]138.674833841784[/C][C]-4.67483384178433[/C][/ROW]
[ROW][C]40[/C][C]126[/C][C]130.738702515116[/C][C]-4.73870251511588[/C][/ROW]
[ROW][C]41[/C][C]116[/C][C]124.565405460484[/C][C]-8.56540546048375[/C][/ROW]
[ROW][C]42[/C][C]114[/C][C]117.217052682704[/C][C]-3.21705268270378[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]117.584539608585[/C][C]2.41546039141502[/C][/ROW]
[ROW][C]44[/C][C]122[/C][C]122.593506106066[/C][C]-0.593506106066314[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]123.034961352979[/C][C]-6.03496135297878[/C][/ROW]
[ROW][C]46[/C][C]119[/C][C]121.898803567889[/C][C]-2.89880356788905[/C][/ROW]
[ROW][C]47[/C][C]132[/C][C]122.243763578321[/C][C]9.75623642167893[/C][/ROW]
[ROW][C]48[/C][C]134[/C][C]130.132685265009[/C][C]3.86731473499103[/C][/ROW]
[ROW][C]49[/C][C]154[/C][C]148.162931524759[/C][C]5.83706847524084[/C][/ROW]
[ROW][C]50[/C][C]152[/C][C]149.560560187104[/C][C]2.43943981289641[/C][/ROW]
[ROW][C]51[/C][C]132[/C][C]141.051675182987[/C][C]-9.05167518298674[/C][/ROW]
[ROW][C]52[/C][C]130[/C][C]130.252909633819[/C][C]-0.252909633819399[/C][/ROW]
[ROW][C]53[/C][C]123[/C][C]125.506601953726[/C][C]-2.50660195372575[/C][/ROW]
[ROW][C]54[/C][C]129[/C][C]123.95717048628[/C][C]5.04282951371998[/C][/ROW]
[ROW][C]55[/C][C]124[/C][C]131.669636857380[/C][C]-7.66963685738028[/C][/ROW]
[ROW][C]56[/C][C]128[/C][C]129.158845357211[/C][C]-1.15884535721102[/C][/ROW]
[ROW][C]57[/C][C]128[/C][C]127.246183757811[/C][C]0.753816242189373[/C][/ROW]
[ROW][C]58[/C][C]129[/C][C]131.590637567348[/C][C]-2.59063756734781[/C][/ROW]
[ROW][C]59[/C][C]141[/C][C]136.761771086693[/C][C]4.23822891330735[/C][/ROW]
[ROW][C]60[/C][C]138[/C][C]138.992202131415[/C][C]-0.992202131414672[/C][/ROW]
[ROW][C]61[/C][C]155[/C][C]154.618460261530[/C][C]0.381539738469741[/C][/ROW]
[ROW][C]62[/C][C]160[/C][C]151.250795669034[/C][C]8.74920433096602[/C][/ROW]
[ROW][C]63[/C][C]142[/C][C]142.545088842174[/C][C]-0.54508884217401[/C][/ROW]
[ROW][C]64[/C][C]133[/C][C]140.377163958185[/C][C]-7.37716395818461[/C][/ROW]
[ROW][C]65[/C][C]131[/C][C]130.26066468688[/C][C]0.73933531311988[/C][/ROW]
[ROW][C]66[/C][C]140[/C][C]133.521624299452[/C][C]6.47837570054782[/C][/ROW]
[ROW][C]67[/C][C]134[/C][C]137.524309409594[/C][C]-3.52430940959385[/C][/ROW]
[ROW][C]68[/C][C]134[/C][C]140.046701855386[/C][C]-6.04670185538649[/C][/ROW]
[ROW][C]69[/C][C]134[/C][C]135.723266265022[/C][C]-1.72326626502209[/C][/ROW]
[ROW][C]70[/C][C]136[/C][C]137.263400095077[/C][C]-1.26340009507683[/C][/ROW]
[ROW][C]71[/C][C]145[/C][C]145.760034149733[/C][C]-0.760034149733315[/C][/ROW]
[ROW][C]72[/C][C]137[/C][C]142.87717399375[/C][C]-5.87717399375009[/C][/ROW]
[ROW][C]73[/C][C]152[/C][C]155.84109200071[/C][C]-3.84109200071012[/C][/ROW]
[ROW][C]74[/C][C]168[/C][C]152.756529178896[/C][C]15.2434708211038[/C][/ROW]
[ROW][C]75[/C][C]160[/C][C]144.753244737927[/C][C]15.2467552620727[/C][/ROW]
[ROW][C]76[/C][C]157[/C][C]150.178807521551[/C][C]6.82119247844921[/C][/ROW]
[ROW][C]77[/C][C]147[/C][C]152.158025184662[/C][C]-5.15802518466199[/C][/ROW]
[ROW][C]78[/C][C]161[/C][C]153.838693498059[/C][C]7.16130650194052[/C][/ROW]
[ROW][C]79[/C][C]159[/C][C]154.718645439437[/C][C]4.28135456056282[/C][/ROW]
[ROW][C]80[/C][C]164[/C][C]161.411680113052[/C][C]2.58831988694789[/C][/ROW]
[ROW][C]81[/C][C]163[/C][C]164.323299383372[/C][C]-1.32329938337179[/C][/ROW]
[ROW][C]82[/C][C]158[/C][C]166.456935423119[/C][C]-8.4569354231188[/C][/ROW]
[ROW][C]83[/C][C]175[/C][C]170.696501304017[/C][C]4.30349869598297[/C][/ROW]
[ROW][C]84[/C][C]163[/C][C]169.331610361607[/C][C]-6.331610361607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79303&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
139087.03659188034192.9634081196581
149089.279638841450.720361158550062
158988.93328298486680.0667170151332073
168282.0465864352953-0.0465864352952963
177877.83759271450550.162407285494538
187675.17901784809250.820982151907529
197480.026855572787-6.02685557278697
207877.73854354497870.261456455021275
218178.40898833687432.59101166312571
228279.7826877360442.21731226395599
238882.22189584360135.77810415639867
249988.08055885368110.9194411463190
25117106.51097498505310.4890250149470
26113112.8683238784300.131676121570166
27106112.051524992776-6.05152499277558
28100101.342835432956-1.34283543295587
299796.48901746504860.510982534951424
309694.39712476026381.60287523973615
3110097.3585777585522.64142224144796
32104103.0263759090160.973624090983776
33104105.155739873687-1.15573987368684
34111104.1491570646926.85084293530817
35117110.9939117128806.00608828712024
36118119.032978514998-1.03297851499829
37140129.80728219364710.1927178063528
38147132.30584116832914.6941588316715
39134138.674833841784-4.67483384178433
40126130.738702515116-4.73870251511588
41116124.565405460484-8.56540546048375
42114117.217052682704-3.21705268270378
43120117.5845396085852.41546039141502
44122122.593506106066-0.593506106066314
45117123.034961352979-6.03496135297878
46119121.898803567889-2.89880356788905
47132122.2437635783219.75623642167893
48134130.1326852650093.86731473499103
49154148.1629315247595.83706847524084
50152149.5605601871042.43943981289641
51132141.051675182987-9.05167518298674
52130130.252909633819-0.252909633819399
53123125.506601953726-2.50660195372575
54129123.957170486285.04282951371998
55124131.669636857380-7.66963685738028
56128129.158845357211-1.15884535721102
57128127.2461837578110.753816242189373
58129131.590637567348-2.59063756734781
59141136.7617710866934.23822891330735
60138138.992202131415-0.992202131414672
61155154.6184602615300.381539738469741
62160151.2507956690348.74920433096602
63142142.545088842174-0.54508884217401
64133140.377163958185-7.37716395818461
65131130.260664686880.73933531311988
66140133.5216242994526.47837570054782
67134137.524309409594-3.52430940959385
68134140.046701855386-6.04670185538649
69134135.723266265022-1.72326626502209
70136137.263400095077-1.26340009507683
71145145.760034149733-0.760034149733315
72137142.87717399375-5.87717399375009
73152155.84109200071-3.84109200071012
74168152.75652917889615.2434708211038
75160144.75324473792715.2467552620727
76157150.1788075215516.82119247844921
77147152.158025184662-5.15802518466199
78161153.8386934980597.16130650194052
79159154.7186454394374.28135456056282
80164161.4116801130522.58831988694789
81163164.323299383372-1.32329938337179
82158166.456935423119-8.4569354231188
83175170.6965013040174.30349869598297
84163169.331610361607-6.331610361607







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85182.906087390566171.821759415369193.990415365763
86189.390209004566176.223363983176202.557054025955
87171.793202087721156.803556359497186.782847815944
88164.475396126374147.836888173477181.113904079272
89157.740434709181139.579382485922175.901486932441
90167.197708599443147.610781876616186.78463532227
91162.449362649276141.513312516008183.385412782543
92165.755506849255143.532952662492187.978061036018
93165.535834283631142.078949086234188.992719481029
94165.859676950106141.212659941159190.506693959053
95180.112340092594154.313144874029205.911535311159
96172.106113179352145.187696637166199.024529721538

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 182.906087390566 & 171.821759415369 & 193.990415365763 \tabularnewline
86 & 189.390209004566 & 176.223363983176 & 202.557054025955 \tabularnewline
87 & 171.793202087721 & 156.803556359497 & 186.782847815944 \tabularnewline
88 & 164.475396126374 & 147.836888173477 & 181.113904079272 \tabularnewline
89 & 157.740434709181 & 139.579382485922 & 175.901486932441 \tabularnewline
90 & 167.197708599443 & 147.610781876616 & 186.78463532227 \tabularnewline
91 & 162.449362649276 & 141.513312516008 & 183.385412782543 \tabularnewline
92 & 165.755506849255 & 143.532952662492 & 187.978061036018 \tabularnewline
93 & 165.535834283631 & 142.078949086234 & 188.992719481029 \tabularnewline
94 & 165.859676950106 & 141.212659941159 & 190.506693959053 \tabularnewline
95 & 180.112340092594 & 154.313144874029 & 205.911535311159 \tabularnewline
96 & 172.106113179352 & 145.187696637166 & 199.024529721538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79303&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]85[/C][C]182.906087390566[/C][C]171.821759415369[/C][C]193.990415365763[/C][/ROW]
[ROW][C]86[/C][C]189.390209004566[/C][C]176.223363983176[/C][C]202.557054025955[/C][/ROW]
[ROW][C]87[/C][C]171.793202087721[/C][C]156.803556359497[/C][C]186.782847815944[/C][/ROW]
[ROW][C]88[/C][C]164.475396126374[/C][C]147.836888173477[/C][C]181.113904079272[/C][/ROW]
[ROW][C]89[/C][C]157.740434709181[/C][C]139.579382485922[/C][C]175.901486932441[/C][/ROW]
[ROW][C]90[/C][C]167.197708599443[/C][C]147.610781876616[/C][C]186.78463532227[/C][/ROW]
[ROW][C]91[/C][C]162.449362649276[/C][C]141.513312516008[/C][C]183.385412782543[/C][/ROW]
[ROW][C]92[/C][C]165.755506849255[/C][C]143.532952662492[/C][C]187.978061036018[/C][/ROW]
[ROW][C]93[/C][C]165.535834283631[/C][C]142.078949086234[/C][C]188.992719481029[/C][/ROW]
[ROW][C]94[/C][C]165.859676950106[/C][C]141.212659941159[/C][C]190.506693959053[/C][/ROW]
[ROW][C]95[/C][C]180.112340092594[/C][C]154.313144874029[/C][C]205.911535311159[/C][/ROW]
[ROW][C]96[/C][C]172.106113179352[/C][C]145.187696637166[/C][C]199.024529721538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79303&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79303&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
85182.906087390566171.821759415369193.990415365763
86189.390209004566176.223363983176202.557054025955
87171.793202087721156.803556359497186.782847815944
88164.475396126374147.836888173477181.113904079272
89157.740434709181139.579382485922175.901486932441
90167.197708599443147.610781876616186.78463532227
91162.449362649276141.513312516008183.385412782543
92165.755506849255143.532952662492187.978061036018
93165.535834283631142.078949086234188.992719481029
94165.859676950106141.212659941159190.506693959053
95180.112340092594154.313144874029205.911535311159
96172.106113179352145.187696637166199.024529721538



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