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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Dec 2011 14:19:54 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/27/t13250136125en3a0xuyhjrxns.htm/, Retrieved Sat, 18 May 2024 06:47:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160869, Retrieved Sat, 18 May 2024 06:47:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Bestellingen Boeing] [2011-12-27 19:19:54] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
20
32
11
14
199
162
88
89
24
36
142
193
39
25
95
144
33
131
31
24
160
52
57
210
13
52
96
133
74
131
129
74
127
55
175
185
34
115
95
58
63
56
70
32
32
14
6
23
18
4
6
17
20
20
44
32
20
14
9
59
10
47
43
34
5
49
130
10
117
108
17
55




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.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 & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160869&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160869&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.209275066505597
beta0
gamma0.709805286362768

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.209275066505597 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.709805286362768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160869&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]0.209275066505597[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.709805286362768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160869&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
alpha0.209275066505597
beta0
gamma0.709805286362768







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133945.0275106837607-6.02751068376068
142534.2977172036677-9.2977172036677
159598.8418843699674-3.84188436996745
16144140.1528213153833.84717868461675
173332.28122077624620.7187792237538
18131132.713257565214-1.71325756521435
193186.5529963600938-55.5529963600938
202474.8754202380308-50.8754202380308
21160-4.53158916333572164.531589163336
225232.432384320207219.5676156797928
2357143.475679278733-86.4756792787327
24210184.03508996567325.9649100343266
251335.2008406985811-22.2008406985811
265219.250933979724332.7490660202757
279695.65658926340740.34341073659256
28133142.15897332401-9.15897332400965
297429.80966166858244.190338331418
30131137.974205118246-6.97420511824623
3112960.494827242246268.5051727577538
327477.4048725385169-3.4048725385169
33127128.83176219938-1.83176219938002
345549.61744754289525.38255245710481
3517598.174224479302776.8257755206973
36185236.017046102348-51.0170461023483
373444.0388480494185-10.0388480494185
3811561.475368341044553.5246316589555
3995124.040809510318-29.0408095103181
4058159.060493835315-101.060493835315
416357.42135938660285.57864061339716
4256128.788787819955-72.7887878199549
437079.899670091399-9.89967009139905
443240.0412516040123-8.04125160401225
453291.3807877972671-59.3807877972671
46144.172008548655779.82799145134423
47693.7573811175102-87.7573811175102
4823125.403895296011-102.403895296011
4918-54.328835364354472.3288353643544
50416.0208728732382-12.0208728732382
51618.5285337905546-12.5285337905546
521716.58200455076340.417995449236635
5320-3.9678530193286523.9678530193287
542027.2634183571012-7.26341835710121
554427.384319299952316.6156807000477
5632-5.8820400556645237.8820400556645
572026.2532300889591-6.25323008895913
5814-10.99310547997324.993105479973
59926.9951091241155-17.9951091241155
605965.0206140588134-6.02061405881335
61103.529122326926836.47087767307317
624712.754222605622534.2457773943775
634324.659409693653218.3405903063468
643436.4393970059734-2.43939700597345
65528.5091688759118-23.5091688759118
664932.275796920899716.7242030791003
6713050.819109691207479.1808903087926
681042.5820612807816-32.5820612807816
6911735.199557645242781.8004423547573
7010833.918001589658174.0819984103419
711758.0517004787544-41.0517004787544
725597.9728496600885-42.9728496600885

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 39 & 45.0275106837607 & -6.02751068376068 \tabularnewline
14 & 25 & 34.2977172036677 & -9.2977172036677 \tabularnewline
15 & 95 & 98.8418843699674 & -3.84188436996745 \tabularnewline
16 & 144 & 140.152821315383 & 3.84717868461675 \tabularnewline
17 & 33 & 32.2812207762462 & 0.7187792237538 \tabularnewline
18 & 131 & 132.713257565214 & -1.71325756521435 \tabularnewline
19 & 31 & 86.5529963600938 & -55.5529963600938 \tabularnewline
20 & 24 & 74.8754202380308 & -50.8754202380308 \tabularnewline
21 & 160 & -4.53158916333572 & 164.531589163336 \tabularnewline
22 & 52 & 32.4323843202072 & 19.5676156797928 \tabularnewline
23 & 57 & 143.475679278733 & -86.4756792787327 \tabularnewline
24 & 210 & 184.035089965673 & 25.9649100343266 \tabularnewline
25 & 13 & 35.2008406985811 & -22.2008406985811 \tabularnewline
26 & 52 & 19.2509339797243 & 32.7490660202757 \tabularnewline
27 & 96 & 95.6565892634074 & 0.34341073659256 \tabularnewline
28 & 133 & 142.15897332401 & -9.15897332400965 \tabularnewline
29 & 74 & 29.809661668582 & 44.190338331418 \tabularnewline
30 & 131 & 137.974205118246 & -6.97420511824623 \tabularnewline
31 & 129 & 60.4948272422462 & 68.5051727577538 \tabularnewline
32 & 74 & 77.4048725385169 & -3.4048725385169 \tabularnewline
33 & 127 & 128.83176219938 & -1.83176219938002 \tabularnewline
34 & 55 & 49.6174475428952 & 5.38255245710481 \tabularnewline
35 & 175 & 98.1742244793027 & 76.8257755206973 \tabularnewline
36 & 185 & 236.017046102348 & -51.0170461023483 \tabularnewline
37 & 34 & 44.0388480494185 & -10.0388480494185 \tabularnewline
38 & 115 & 61.4753683410445 & 53.5246316589555 \tabularnewline
39 & 95 & 124.040809510318 & -29.0408095103181 \tabularnewline
40 & 58 & 159.060493835315 & -101.060493835315 \tabularnewline
41 & 63 & 57.4213593866028 & 5.57864061339716 \tabularnewline
42 & 56 & 128.788787819955 & -72.7887878199549 \tabularnewline
43 & 70 & 79.899670091399 & -9.89967009139905 \tabularnewline
44 & 32 & 40.0412516040123 & -8.04125160401225 \tabularnewline
45 & 32 & 91.3807877972671 & -59.3807877972671 \tabularnewline
46 & 14 & 4.17200854865577 & 9.82799145134423 \tabularnewline
47 & 6 & 93.7573811175102 & -87.7573811175102 \tabularnewline
48 & 23 & 125.403895296011 & -102.403895296011 \tabularnewline
49 & 18 & -54.3288353643544 & 72.3288353643544 \tabularnewline
50 & 4 & 16.0208728732382 & -12.0208728732382 \tabularnewline
51 & 6 & 18.5285337905546 & -12.5285337905546 \tabularnewline
52 & 17 & 16.5820045507634 & 0.417995449236635 \tabularnewline
53 & 20 & -3.96785301932865 & 23.9678530193287 \tabularnewline
54 & 20 & 27.2634183571012 & -7.26341835710121 \tabularnewline
55 & 44 & 27.3843192999523 & 16.6156807000477 \tabularnewline
56 & 32 & -5.88204005566452 & 37.8820400556645 \tabularnewline
57 & 20 & 26.2532300889591 & -6.25323008895913 \tabularnewline
58 & 14 & -10.993105479973 & 24.993105479973 \tabularnewline
59 & 9 & 26.9951091241155 & -17.9951091241155 \tabularnewline
60 & 59 & 65.0206140588134 & -6.02061405881335 \tabularnewline
61 & 10 & 3.52912232692683 & 6.47087767307317 \tabularnewline
62 & 47 & 12.7542226056225 & 34.2457773943775 \tabularnewline
63 & 43 & 24.6594096936532 & 18.3405903063468 \tabularnewline
64 & 34 & 36.4393970059734 & -2.43939700597345 \tabularnewline
65 & 5 & 28.5091688759118 & -23.5091688759118 \tabularnewline
66 & 49 & 32.2757969208997 & 16.7242030791003 \tabularnewline
67 & 130 & 50.8191096912074 & 79.1808903087926 \tabularnewline
68 & 10 & 42.5820612807816 & -32.5820612807816 \tabularnewline
69 & 117 & 35.1995576452427 & 81.8004423547573 \tabularnewline
70 & 108 & 33.9180015896581 & 74.0819984103419 \tabularnewline
71 & 17 & 58.0517004787544 & -41.0517004787544 \tabularnewline
72 & 55 & 97.9728496600885 & -42.9728496600885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160869&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]39[/C][C]45.0275106837607[/C][C]-6.02751068376068[/C][/ROW]
[ROW][C]14[/C][C]25[/C][C]34.2977172036677[/C][C]-9.2977172036677[/C][/ROW]
[ROW][C]15[/C][C]95[/C][C]98.8418843699674[/C][C]-3.84188436996745[/C][/ROW]
[ROW][C]16[/C][C]144[/C][C]140.152821315383[/C][C]3.84717868461675[/C][/ROW]
[ROW][C]17[/C][C]33[/C][C]32.2812207762462[/C][C]0.7187792237538[/C][/ROW]
[ROW][C]18[/C][C]131[/C][C]132.713257565214[/C][C]-1.71325756521435[/C][/ROW]
[ROW][C]19[/C][C]31[/C][C]86.5529963600938[/C][C]-55.5529963600938[/C][/ROW]
[ROW][C]20[/C][C]24[/C][C]74.8754202380308[/C][C]-50.8754202380308[/C][/ROW]
[ROW][C]21[/C][C]160[/C][C]-4.53158916333572[/C][C]164.531589163336[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]32.4323843202072[/C][C]19.5676156797928[/C][/ROW]
[ROW][C]23[/C][C]57[/C][C]143.475679278733[/C][C]-86.4756792787327[/C][/ROW]
[ROW][C]24[/C][C]210[/C][C]184.035089965673[/C][C]25.9649100343266[/C][/ROW]
[ROW][C]25[/C][C]13[/C][C]35.2008406985811[/C][C]-22.2008406985811[/C][/ROW]
[ROW][C]26[/C][C]52[/C][C]19.2509339797243[/C][C]32.7490660202757[/C][/ROW]
[ROW][C]27[/C][C]96[/C][C]95.6565892634074[/C][C]0.34341073659256[/C][/ROW]
[ROW][C]28[/C][C]133[/C][C]142.15897332401[/C][C]-9.15897332400965[/C][/ROW]
[ROW][C]29[/C][C]74[/C][C]29.809661668582[/C][C]44.190338331418[/C][/ROW]
[ROW][C]30[/C][C]131[/C][C]137.974205118246[/C][C]-6.97420511824623[/C][/ROW]
[ROW][C]31[/C][C]129[/C][C]60.4948272422462[/C][C]68.5051727577538[/C][/ROW]
[ROW][C]32[/C][C]74[/C][C]77.4048725385169[/C][C]-3.4048725385169[/C][/ROW]
[ROW][C]33[/C][C]127[/C][C]128.83176219938[/C][C]-1.83176219938002[/C][/ROW]
[ROW][C]34[/C][C]55[/C][C]49.6174475428952[/C][C]5.38255245710481[/C][/ROW]
[ROW][C]35[/C][C]175[/C][C]98.1742244793027[/C][C]76.8257755206973[/C][/ROW]
[ROW][C]36[/C][C]185[/C][C]236.017046102348[/C][C]-51.0170461023483[/C][/ROW]
[ROW][C]37[/C][C]34[/C][C]44.0388480494185[/C][C]-10.0388480494185[/C][/ROW]
[ROW][C]38[/C][C]115[/C][C]61.4753683410445[/C][C]53.5246316589555[/C][/ROW]
[ROW][C]39[/C][C]95[/C][C]124.040809510318[/C][C]-29.0408095103181[/C][/ROW]
[ROW][C]40[/C][C]58[/C][C]159.060493835315[/C][C]-101.060493835315[/C][/ROW]
[ROW][C]41[/C][C]63[/C][C]57.4213593866028[/C][C]5.57864061339716[/C][/ROW]
[ROW][C]42[/C][C]56[/C][C]128.788787819955[/C][C]-72.7887878199549[/C][/ROW]
[ROW][C]43[/C][C]70[/C][C]79.899670091399[/C][C]-9.89967009139905[/C][/ROW]
[ROW][C]44[/C][C]32[/C][C]40.0412516040123[/C][C]-8.04125160401225[/C][/ROW]
[ROW][C]45[/C][C]32[/C][C]91.3807877972671[/C][C]-59.3807877972671[/C][/ROW]
[ROW][C]46[/C][C]14[/C][C]4.17200854865577[/C][C]9.82799145134423[/C][/ROW]
[ROW][C]47[/C][C]6[/C][C]93.7573811175102[/C][C]-87.7573811175102[/C][/ROW]
[ROW][C]48[/C][C]23[/C][C]125.403895296011[/C][C]-102.403895296011[/C][/ROW]
[ROW][C]49[/C][C]18[/C][C]-54.3288353643544[/C][C]72.3288353643544[/C][/ROW]
[ROW][C]50[/C][C]4[/C][C]16.0208728732382[/C][C]-12.0208728732382[/C][/ROW]
[ROW][C]51[/C][C]6[/C][C]18.5285337905546[/C][C]-12.5285337905546[/C][/ROW]
[ROW][C]52[/C][C]17[/C][C]16.5820045507634[/C][C]0.417995449236635[/C][/ROW]
[ROW][C]53[/C][C]20[/C][C]-3.96785301932865[/C][C]23.9678530193287[/C][/ROW]
[ROW][C]54[/C][C]20[/C][C]27.2634183571012[/C][C]-7.26341835710121[/C][/ROW]
[ROW][C]55[/C][C]44[/C][C]27.3843192999523[/C][C]16.6156807000477[/C][/ROW]
[ROW][C]56[/C][C]32[/C][C]-5.88204005566452[/C][C]37.8820400556645[/C][/ROW]
[ROW][C]57[/C][C]20[/C][C]26.2532300889591[/C][C]-6.25323008895913[/C][/ROW]
[ROW][C]58[/C][C]14[/C][C]-10.993105479973[/C][C]24.993105479973[/C][/ROW]
[ROW][C]59[/C][C]9[/C][C]26.9951091241155[/C][C]-17.9951091241155[/C][/ROW]
[ROW][C]60[/C][C]59[/C][C]65.0206140588134[/C][C]-6.02061405881335[/C][/ROW]
[ROW][C]61[/C][C]10[/C][C]3.52912232692683[/C][C]6.47087767307317[/C][/ROW]
[ROW][C]62[/C][C]47[/C][C]12.7542226056225[/C][C]34.2457773943775[/C][/ROW]
[ROW][C]63[/C][C]43[/C][C]24.6594096936532[/C][C]18.3405903063468[/C][/ROW]
[ROW][C]64[/C][C]34[/C][C]36.4393970059734[/C][C]-2.43939700597345[/C][/ROW]
[ROW][C]65[/C][C]5[/C][C]28.5091688759118[/C][C]-23.5091688759118[/C][/ROW]
[ROW][C]66[/C][C]49[/C][C]32.2757969208997[/C][C]16.7242030791003[/C][/ROW]
[ROW][C]67[/C][C]130[/C][C]50.8191096912074[/C][C]79.1808903087926[/C][/ROW]
[ROW][C]68[/C][C]10[/C][C]42.5820612807816[/C][C]-32.5820612807816[/C][/ROW]
[ROW][C]69[/C][C]117[/C][C]35.1995576452427[/C][C]81.8004423547573[/C][/ROW]
[ROW][C]70[/C][C]108[/C][C]33.9180015896581[/C][C]74.0819984103419[/C][/ROW]
[ROW][C]71[/C][C]17[/C][C]58.0517004787544[/C][C]-41.0517004787544[/C][/ROW]
[ROW][C]72[/C][C]55[/C][C]97.9728496600885[/C][C]-42.9728496600885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160869&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160869&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
133945.0275106837607-6.02751068376068
142534.2977172036677-9.2977172036677
159598.8418843699674-3.84188436996745
16144140.1528213153833.84717868461675
173332.28122077624620.7187792237538
18131132.713257565214-1.71325756521435
193186.5529963600938-55.5529963600938
202474.8754202380308-50.8754202380308
21160-4.53158916333572164.531589163336
225232.432384320207219.5676156797928
2357143.475679278733-86.4756792787327
24210184.03508996567325.9649100343266
251335.2008406985811-22.2008406985811
265219.250933979724332.7490660202757
279695.65658926340740.34341073659256
28133142.15897332401-9.15897332400965
297429.80966166858244.190338331418
30131137.974205118246-6.97420511824623
3112960.494827242246268.5051727577538
327477.4048725385169-3.4048725385169
33127128.83176219938-1.83176219938002
345549.61744754289525.38255245710481
3517598.174224479302776.8257755206973
36185236.017046102348-51.0170461023483
373444.0388480494185-10.0388480494185
3811561.475368341044553.5246316589555
3995124.040809510318-29.0408095103181
4058159.060493835315-101.060493835315
416357.42135938660285.57864061339716
4256128.788787819955-72.7887878199549
437079.899670091399-9.89967009139905
443240.0412516040123-8.04125160401225
453291.3807877972671-59.3807877972671
46144.172008548655779.82799145134423
47693.7573811175102-87.7573811175102
4823125.403895296011-102.403895296011
4918-54.328835364354472.3288353643544
50416.0208728732382-12.0208728732382
51618.5285337905546-12.5285337905546
521716.58200455076340.417995449236635
5320-3.9678530193286523.9678530193287
542027.2634183571012-7.26341835710121
554427.384319299952316.6156807000477
5632-5.8820400556645237.8820400556645
572026.2532300889591-6.25323008895913
5814-10.99310547997324.993105479973
59926.9951091241155-17.9951091241155
605965.0206140588134-6.02061405881335
61103.529122326926836.47087767307317
624712.754222605622534.2457773943775
634324.659409693653218.3405903063468
643436.4393970059734-2.43939700597345
65528.5091688759118-23.5091688759118
664932.275796920899716.7242030791003
6713050.819109691207479.1808903087926
681042.5820612807816-32.5820612807816
6911735.199557645242781.8004423547573
7010833.918001589658174.0819984103419
711758.0517004787544-41.0517004787544
725597.9728496600885-42.9728496600885







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7335.7591602315401-57.6398756533544129.158196116435
7459.219027866231-36.2033464328468154.641402165309
7555.0304705717965-42.3732209882197152.434162131813
7651.3092386165117-48.0362632553108150.654740488334
7732.063879750989-69.1861985443377133.313958046316
7863.331802705766-39.787681231341166.451286642873
79113.4296431228448.47404498677133218.385241258917
8025.8938519532601-80.8662866413777132.653990547898
8189.5283697471222-19.0063104495401198.063049943785
8266.7959611342376-43.4847099647236177.076632233199
8310.8061200888825-101.193326475298122.805566653063
8458.2401010110342-55.4521398998047171.932341921873

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 35.7591602315401 & -57.6398756533544 & 129.158196116435 \tabularnewline
74 & 59.219027866231 & -36.2033464328468 & 154.641402165309 \tabularnewline
75 & 55.0304705717965 & -42.3732209882197 & 152.434162131813 \tabularnewline
76 & 51.3092386165117 & -48.0362632553108 & 150.654740488334 \tabularnewline
77 & 32.063879750989 & -69.1861985443377 & 133.313958046316 \tabularnewline
78 & 63.331802705766 & -39.787681231341 & 166.451286642873 \tabularnewline
79 & 113.429643122844 & 8.47404498677133 & 218.385241258917 \tabularnewline
80 & 25.8938519532601 & -80.8662866413777 & 132.653990547898 \tabularnewline
81 & 89.5283697471222 & -19.0063104495401 & 198.063049943785 \tabularnewline
82 & 66.7959611342376 & -43.4847099647236 & 177.076632233199 \tabularnewline
83 & 10.8061200888825 & -101.193326475298 & 122.805566653063 \tabularnewline
84 & 58.2401010110342 & -55.4521398998047 & 171.932341921873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160869&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]73[/C][C]35.7591602315401[/C][C]-57.6398756533544[/C][C]129.158196116435[/C][/ROW]
[ROW][C]74[/C][C]59.219027866231[/C][C]-36.2033464328468[/C][C]154.641402165309[/C][/ROW]
[ROW][C]75[/C][C]55.0304705717965[/C][C]-42.3732209882197[/C][C]152.434162131813[/C][/ROW]
[ROW][C]76[/C][C]51.3092386165117[/C][C]-48.0362632553108[/C][C]150.654740488334[/C][/ROW]
[ROW][C]77[/C][C]32.063879750989[/C][C]-69.1861985443377[/C][C]133.313958046316[/C][/ROW]
[ROW][C]78[/C][C]63.331802705766[/C][C]-39.787681231341[/C][C]166.451286642873[/C][/ROW]
[ROW][C]79[/C][C]113.429643122844[/C][C]8.47404498677133[/C][C]218.385241258917[/C][/ROW]
[ROW][C]80[/C][C]25.8938519532601[/C][C]-80.8662866413777[/C][C]132.653990547898[/C][/ROW]
[ROW][C]81[/C][C]89.5283697471222[/C][C]-19.0063104495401[/C][C]198.063049943785[/C][/ROW]
[ROW][C]82[/C][C]66.7959611342376[/C][C]-43.4847099647236[/C][C]177.076632233199[/C][/ROW]
[ROW][C]83[/C][C]10.8061200888825[/C][C]-101.193326475298[/C][C]122.805566653063[/C][/ROW]
[ROW][C]84[/C][C]58.2401010110342[/C][C]-55.4521398998047[/C][C]171.932341921873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160869&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160869&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
7335.7591602315401-57.6398756533544129.158196116435
7459.219027866231-36.2033464328468154.641402165309
7555.0304705717965-42.3732209882197152.434162131813
7651.3092386165117-48.0362632553108150.654740488334
7732.063879750989-69.1861985443377133.313958046316
7863.331802705766-39.787681231341166.451286642873
79113.4296431228448.47404498677133218.385241258917
8025.8938519532601-80.8662866413777132.653990547898
8189.5283697471222-19.0063104495401198.063049943785
8266.7959611342376-43.4847099647236177.076632233199
8310.8061200888825-101.193326475298122.805566653063
8458.2401010110342-55.4521398998047171.932341921873



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