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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 11:58:27 +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/2014/Nov/27/t1417089693jvje9a9jq9g6g45.htm/, Retrieved Sun, 19 May 2024 18:06:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=259831, Retrieved Sun, 19 May 2024 18:06:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-27 11:58:27] [25af208440423f5cc2d7fa35cacd4ca5] [Current]
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Dataseries X:
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6
2070.83
2293.41
2443.27
2513.17
2466.92
2502.66
2539.91
2482.6
2626.15
2656.32
2446.66
2467.38
2462.32
2504.58
2579.39
2649.24
2636.87
2613.94
2634.01
2711.94
2646.43
2717.79
2701.54
2572.98
2488.92
2204.91
2123.99
2149.1
2036.71
2048.32
2159.56
2267.79
2313.55
2247.3
2134.43
2114
2236.94
2345.39
2422.4
2385.96
2378.17
2457.13
2527.67
2530.03
2604.92
2596.8
2713.2
2574.82
2611.98
2768.46
2785.61
2859.27
2880.53
2824.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259831&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259831&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259831&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.848430731007457
beta0.0533755880386224
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.848430731007457 \tabularnewline
beta & 0.0533755880386224 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259831&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]0.848430731007457[/C][/ROW]
[ROW][C]beta[/C][C]0.0533755880386224[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259831&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259831&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
alpha0.848430731007457
beta0.0533755880386224
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131905.412769.22118589744-863.811185897438
141810.991882.81795529623-71.8279552962285
151670.071600.159038554169.910961445896
161864.441731.67130997699132.768690023011
172052.021875.25567174785176.764328252153
182029.61840.65214409664188.947855903362
192070.831958.57667513376112.253324866239
202293.412125.62048920049167.789510799507
212443.272250.98009017137192.289909828627
222513.171729.470775231783.699224768998
232466.922315.73441711852151.185582881485
242502.662382.35014385793120.309856142066
252539.912458.6880992169981.2219007830063
262482.62589.46043819004-106.860438190036
272626.152392.31582494991233.834175050088
282656.322773.60990578088-117.289905780883
292446.662801.55824870019-354.898248700188
302467.382383.4988923969483.8811076030588
312462.322461.675424052070.6445759479343
322504.582598.40866068852-93.8286606885176
332579.392549.6335017730429.75649822696
342649.242016.62154712634632.618452873664
352636.872408.74844625533228.121553744673
362613.942569.3577440498644.5822559501412
372634.012605.4907223679228.5192776320791
382711.942690.6235485235921.3164514764071
392646.432687.25404900687-40.8240490068702
402717.792803.24906778063-85.4590677806341
412701.542844.58006009391-143.040060093911
422572.982704.75778069466-131.777780694663
432488.922609.56497838556-120.64497838556
442204.912645.79892809771-440.888928097715
452123.992322.30782875082-198.317828750819
462149.11677.84643820057471.253561799427
472036.711855.13010378643181.579896213569
482048.321929.69844839365118.621551606351
492159.562010.83222882145148.72777117855
502267.792186.9238506228980.866149377111
512313.552217.4182344819996.1317655180137
522247.32441.80626886602-194.506268866016
532134.432375.91329083493-241.483290834926
5421142143.84024991036-29.8402499103595
552236.942131.00254825591105.937451744091
562345.392315.3785258131230.0114741868815
572422.42453.94675066021-31.5467506602072
582385.962085.78445130654300.175548693463
592378.172099.58623322057278.583766779433
602457.132276.87754589034180.252454109665
612527.672447.6194947595880.0505052404246
622530.032584.80283271027-54.7728327102745
632604.922526.0336119695278.8863880304821
642596.82714.46025620317-117.660256203167
652713.22732.84744575702-19.6474457570162
662574.822757.31320056299-182.493200562988
672611.982664.87467436357-52.8946743635688
682768.462725.1266625984343.3333374015674
692785.612888.41262999756-102.802629997556
702859.272529.59210146508329.677898534919
712880.532586.00650355944294.523496440564
722824.52783.4939765311541.0060234688544

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1905.41 & 2769.22118589744 & -863.811185897438 \tabularnewline
14 & 1810.99 & 1882.81795529623 & -71.8279552962285 \tabularnewline
15 & 1670.07 & 1600.1590385541 & 69.910961445896 \tabularnewline
16 & 1864.44 & 1731.67130997699 & 132.768690023011 \tabularnewline
17 & 2052.02 & 1875.25567174785 & 176.764328252153 \tabularnewline
18 & 2029.6 & 1840.65214409664 & 188.947855903362 \tabularnewline
19 & 2070.83 & 1958.57667513376 & 112.253324866239 \tabularnewline
20 & 2293.41 & 2125.62048920049 & 167.789510799507 \tabularnewline
21 & 2443.27 & 2250.98009017137 & 192.289909828627 \tabularnewline
22 & 2513.17 & 1729.470775231 & 783.699224768998 \tabularnewline
23 & 2466.92 & 2315.73441711852 & 151.185582881485 \tabularnewline
24 & 2502.66 & 2382.35014385793 & 120.309856142066 \tabularnewline
25 & 2539.91 & 2458.68809921699 & 81.2219007830063 \tabularnewline
26 & 2482.6 & 2589.46043819004 & -106.860438190036 \tabularnewline
27 & 2626.15 & 2392.31582494991 & 233.834175050088 \tabularnewline
28 & 2656.32 & 2773.60990578088 & -117.289905780883 \tabularnewline
29 & 2446.66 & 2801.55824870019 & -354.898248700188 \tabularnewline
30 & 2467.38 & 2383.49889239694 & 83.8811076030588 \tabularnewline
31 & 2462.32 & 2461.67542405207 & 0.6445759479343 \tabularnewline
32 & 2504.58 & 2598.40866068852 & -93.8286606885176 \tabularnewline
33 & 2579.39 & 2549.63350177304 & 29.75649822696 \tabularnewline
34 & 2649.24 & 2016.62154712634 & 632.618452873664 \tabularnewline
35 & 2636.87 & 2408.74844625533 & 228.121553744673 \tabularnewline
36 & 2613.94 & 2569.35774404986 & 44.5822559501412 \tabularnewline
37 & 2634.01 & 2605.49072236792 & 28.5192776320791 \tabularnewline
38 & 2711.94 & 2690.62354852359 & 21.3164514764071 \tabularnewline
39 & 2646.43 & 2687.25404900687 & -40.8240490068702 \tabularnewline
40 & 2717.79 & 2803.24906778063 & -85.4590677806341 \tabularnewline
41 & 2701.54 & 2844.58006009391 & -143.040060093911 \tabularnewline
42 & 2572.98 & 2704.75778069466 & -131.777780694663 \tabularnewline
43 & 2488.92 & 2609.56497838556 & -120.64497838556 \tabularnewline
44 & 2204.91 & 2645.79892809771 & -440.888928097715 \tabularnewline
45 & 2123.99 & 2322.30782875082 & -198.317828750819 \tabularnewline
46 & 2149.1 & 1677.84643820057 & 471.253561799427 \tabularnewline
47 & 2036.71 & 1855.13010378643 & 181.579896213569 \tabularnewline
48 & 2048.32 & 1929.69844839365 & 118.621551606351 \tabularnewline
49 & 2159.56 & 2010.83222882145 & 148.72777117855 \tabularnewline
50 & 2267.79 & 2186.92385062289 & 80.866149377111 \tabularnewline
51 & 2313.55 & 2217.41823448199 & 96.1317655180137 \tabularnewline
52 & 2247.3 & 2441.80626886602 & -194.506268866016 \tabularnewline
53 & 2134.43 & 2375.91329083493 & -241.483290834926 \tabularnewline
54 & 2114 & 2143.84024991036 & -29.8402499103595 \tabularnewline
55 & 2236.94 & 2131.00254825591 & 105.937451744091 \tabularnewline
56 & 2345.39 & 2315.37852581312 & 30.0114741868815 \tabularnewline
57 & 2422.4 & 2453.94675066021 & -31.5467506602072 \tabularnewline
58 & 2385.96 & 2085.78445130654 & 300.175548693463 \tabularnewline
59 & 2378.17 & 2099.58623322057 & 278.583766779433 \tabularnewline
60 & 2457.13 & 2276.87754589034 & 180.252454109665 \tabularnewline
61 & 2527.67 & 2447.61949475958 & 80.0505052404246 \tabularnewline
62 & 2530.03 & 2584.80283271027 & -54.7728327102745 \tabularnewline
63 & 2604.92 & 2526.03361196952 & 78.8863880304821 \tabularnewline
64 & 2596.8 & 2714.46025620317 & -117.660256203167 \tabularnewline
65 & 2713.2 & 2732.84744575702 & -19.6474457570162 \tabularnewline
66 & 2574.82 & 2757.31320056299 & -182.493200562988 \tabularnewline
67 & 2611.98 & 2664.87467436357 & -52.8946743635688 \tabularnewline
68 & 2768.46 & 2725.12666259843 & 43.3333374015674 \tabularnewline
69 & 2785.61 & 2888.41262999756 & -102.802629997556 \tabularnewline
70 & 2859.27 & 2529.59210146508 & 329.677898534919 \tabularnewline
71 & 2880.53 & 2586.00650355944 & 294.523496440564 \tabularnewline
72 & 2824.5 & 2783.49397653115 & 41.0060234688544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259831&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]1905.41[/C][C]2769.22118589744[/C][C]-863.811185897438[/C][/ROW]
[ROW][C]14[/C][C]1810.99[/C][C]1882.81795529623[/C][C]-71.8279552962285[/C][/ROW]
[ROW][C]15[/C][C]1670.07[/C][C]1600.1590385541[/C][C]69.910961445896[/C][/ROW]
[ROW][C]16[/C][C]1864.44[/C][C]1731.67130997699[/C][C]132.768690023011[/C][/ROW]
[ROW][C]17[/C][C]2052.02[/C][C]1875.25567174785[/C][C]176.764328252153[/C][/ROW]
[ROW][C]18[/C][C]2029.6[/C][C]1840.65214409664[/C][C]188.947855903362[/C][/ROW]
[ROW][C]19[/C][C]2070.83[/C][C]1958.57667513376[/C][C]112.253324866239[/C][/ROW]
[ROW][C]20[/C][C]2293.41[/C][C]2125.62048920049[/C][C]167.789510799507[/C][/ROW]
[ROW][C]21[/C][C]2443.27[/C][C]2250.98009017137[/C][C]192.289909828627[/C][/ROW]
[ROW][C]22[/C][C]2513.17[/C][C]1729.470775231[/C][C]783.699224768998[/C][/ROW]
[ROW][C]23[/C][C]2466.92[/C][C]2315.73441711852[/C][C]151.185582881485[/C][/ROW]
[ROW][C]24[/C][C]2502.66[/C][C]2382.35014385793[/C][C]120.309856142066[/C][/ROW]
[ROW][C]25[/C][C]2539.91[/C][C]2458.68809921699[/C][C]81.2219007830063[/C][/ROW]
[ROW][C]26[/C][C]2482.6[/C][C]2589.46043819004[/C][C]-106.860438190036[/C][/ROW]
[ROW][C]27[/C][C]2626.15[/C][C]2392.31582494991[/C][C]233.834175050088[/C][/ROW]
[ROW][C]28[/C][C]2656.32[/C][C]2773.60990578088[/C][C]-117.289905780883[/C][/ROW]
[ROW][C]29[/C][C]2446.66[/C][C]2801.55824870019[/C][C]-354.898248700188[/C][/ROW]
[ROW][C]30[/C][C]2467.38[/C][C]2383.49889239694[/C][C]83.8811076030588[/C][/ROW]
[ROW][C]31[/C][C]2462.32[/C][C]2461.67542405207[/C][C]0.6445759479343[/C][/ROW]
[ROW][C]32[/C][C]2504.58[/C][C]2598.40866068852[/C][C]-93.8286606885176[/C][/ROW]
[ROW][C]33[/C][C]2579.39[/C][C]2549.63350177304[/C][C]29.75649822696[/C][/ROW]
[ROW][C]34[/C][C]2649.24[/C][C]2016.62154712634[/C][C]632.618452873664[/C][/ROW]
[ROW][C]35[/C][C]2636.87[/C][C]2408.74844625533[/C][C]228.121553744673[/C][/ROW]
[ROW][C]36[/C][C]2613.94[/C][C]2569.35774404986[/C][C]44.5822559501412[/C][/ROW]
[ROW][C]37[/C][C]2634.01[/C][C]2605.49072236792[/C][C]28.5192776320791[/C][/ROW]
[ROW][C]38[/C][C]2711.94[/C][C]2690.62354852359[/C][C]21.3164514764071[/C][/ROW]
[ROW][C]39[/C][C]2646.43[/C][C]2687.25404900687[/C][C]-40.8240490068702[/C][/ROW]
[ROW][C]40[/C][C]2717.79[/C][C]2803.24906778063[/C][C]-85.4590677806341[/C][/ROW]
[ROW][C]41[/C][C]2701.54[/C][C]2844.58006009391[/C][C]-143.040060093911[/C][/ROW]
[ROW][C]42[/C][C]2572.98[/C][C]2704.75778069466[/C][C]-131.777780694663[/C][/ROW]
[ROW][C]43[/C][C]2488.92[/C][C]2609.56497838556[/C][C]-120.64497838556[/C][/ROW]
[ROW][C]44[/C][C]2204.91[/C][C]2645.79892809771[/C][C]-440.888928097715[/C][/ROW]
[ROW][C]45[/C][C]2123.99[/C][C]2322.30782875082[/C][C]-198.317828750819[/C][/ROW]
[ROW][C]46[/C][C]2149.1[/C][C]1677.84643820057[/C][C]471.253561799427[/C][/ROW]
[ROW][C]47[/C][C]2036.71[/C][C]1855.13010378643[/C][C]181.579896213569[/C][/ROW]
[ROW][C]48[/C][C]2048.32[/C][C]1929.69844839365[/C][C]118.621551606351[/C][/ROW]
[ROW][C]49[/C][C]2159.56[/C][C]2010.83222882145[/C][C]148.72777117855[/C][/ROW]
[ROW][C]50[/C][C]2267.79[/C][C]2186.92385062289[/C][C]80.866149377111[/C][/ROW]
[ROW][C]51[/C][C]2313.55[/C][C]2217.41823448199[/C][C]96.1317655180137[/C][/ROW]
[ROW][C]52[/C][C]2247.3[/C][C]2441.80626886602[/C][C]-194.506268866016[/C][/ROW]
[ROW][C]53[/C][C]2134.43[/C][C]2375.91329083493[/C][C]-241.483290834926[/C][/ROW]
[ROW][C]54[/C][C]2114[/C][C]2143.84024991036[/C][C]-29.8402499103595[/C][/ROW]
[ROW][C]55[/C][C]2236.94[/C][C]2131.00254825591[/C][C]105.937451744091[/C][/ROW]
[ROW][C]56[/C][C]2345.39[/C][C]2315.37852581312[/C][C]30.0114741868815[/C][/ROW]
[ROW][C]57[/C][C]2422.4[/C][C]2453.94675066021[/C][C]-31.5467506602072[/C][/ROW]
[ROW][C]58[/C][C]2385.96[/C][C]2085.78445130654[/C][C]300.175548693463[/C][/ROW]
[ROW][C]59[/C][C]2378.17[/C][C]2099.58623322057[/C][C]278.583766779433[/C][/ROW]
[ROW][C]60[/C][C]2457.13[/C][C]2276.87754589034[/C][C]180.252454109665[/C][/ROW]
[ROW][C]61[/C][C]2527.67[/C][C]2447.61949475958[/C][C]80.0505052404246[/C][/ROW]
[ROW][C]62[/C][C]2530.03[/C][C]2584.80283271027[/C][C]-54.7728327102745[/C][/ROW]
[ROW][C]63[/C][C]2604.92[/C][C]2526.03361196952[/C][C]78.8863880304821[/C][/ROW]
[ROW][C]64[/C][C]2596.8[/C][C]2714.46025620317[/C][C]-117.660256203167[/C][/ROW]
[ROW][C]65[/C][C]2713.2[/C][C]2732.84744575702[/C][C]-19.6474457570162[/C][/ROW]
[ROW][C]66[/C][C]2574.82[/C][C]2757.31320056299[/C][C]-182.493200562988[/C][/ROW]
[ROW][C]67[/C][C]2611.98[/C][C]2664.87467436357[/C][C]-52.8946743635688[/C][/ROW]
[ROW][C]68[/C][C]2768.46[/C][C]2725.12666259843[/C][C]43.3333374015674[/C][/ROW]
[ROW][C]69[/C][C]2785.61[/C][C]2888.41262999756[/C][C]-102.802629997556[/C][/ROW]
[ROW][C]70[/C][C]2859.27[/C][C]2529.59210146508[/C][C]329.677898534919[/C][/ROW]
[ROW][C]71[/C][C]2880.53[/C][C]2586.00650355944[/C][C]294.523496440564[/C][/ROW]
[ROW][C]72[/C][C]2824.5[/C][C]2783.49397653115[/C][C]41.0060234688544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259831&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259831&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
131905.412769.22118589744-863.811185897438
141810.991882.81795529623-71.8279552962285
151670.071600.159038554169.910961445896
161864.441731.67130997699132.768690023011
172052.021875.25567174785176.764328252153
182029.61840.65214409664188.947855903362
192070.831958.57667513376112.253324866239
202293.412125.62048920049167.789510799507
212443.272250.98009017137192.289909828627
222513.171729.470775231783.699224768998
232466.922315.73441711852151.185582881485
242502.662382.35014385793120.309856142066
252539.912458.6880992169981.2219007830063
262482.62589.46043819004-106.860438190036
272626.152392.31582494991233.834175050088
282656.322773.60990578088-117.289905780883
292446.662801.55824870019-354.898248700188
302467.382383.4988923969483.8811076030588
312462.322461.675424052070.6445759479343
322504.582598.40866068852-93.8286606885176
332579.392549.6335017730429.75649822696
342649.242016.62154712634632.618452873664
352636.872408.74844625533228.121553744673
362613.942569.3577440498644.5822559501412
372634.012605.4907223679228.5192776320791
382711.942690.6235485235921.3164514764071
392646.432687.25404900687-40.8240490068702
402717.792803.24906778063-85.4590677806341
412701.542844.58006009391-143.040060093911
422572.982704.75778069466-131.777780694663
432488.922609.56497838556-120.64497838556
442204.912645.79892809771-440.888928097715
452123.992322.30782875082-198.317828750819
462149.11677.84643820057471.253561799427
472036.711855.13010378643181.579896213569
482048.321929.69844839365118.621551606351
492159.562010.83222882145148.72777117855
502267.792186.9238506228980.866149377111
512313.552217.4182344819996.1317655180137
522247.32441.80626886602-194.506268866016
532134.432375.91329083493-241.483290834926
5421142143.84024991036-29.8402499103595
552236.942131.00254825591105.937451744091
562345.392315.3785258131230.0114741868815
572422.42453.94675066021-31.5467506602072
582385.962085.78445130654300.175548693463
592378.172099.58623322057278.583766779433
602457.132276.87754589034180.252454109665
612527.672447.6194947595880.0505052404246
622530.032584.80283271027-54.7728327102745
632604.922526.0336119695278.8863880304821
642596.82714.46025620317-117.660256203167
652713.22732.84744575702-19.6474457570162
662574.822757.31320056299-182.493200562988
672611.982664.87467436357-52.8946743635688
682768.462725.1266625984343.3333374015674
692785.612888.41262999756-102.802629997556
702859.272529.59210146508329.677898534919
712880.532586.00650355944294.523496440564
722824.52783.4939765311541.0060234688544







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732836.178004586012370.204612490913302.1513966811
742896.654399059132271.706304337973521.60249378029
752918.740617696222155.844845778623681.63638961381
763021.000640706112130.848243644053911.15303776816
773169.951885559992158.747312110744181.15645900924
783203.176217397562074.730059342114331.62237545302
793310.249470773352066.935354588714553.56358695798
803457.395282987282100.655424466664814.13514150791
813587.234969466212117.874406865535056.5955320669
823411.310352364021829.680552474294992.94015225376
833197.88218542271504.001817353584891.76255349181
843108.918392787321302.556117403264915.28066817138

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2836.17800458601 & 2370.20461249091 & 3302.1513966811 \tabularnewline
74 & 2896.65439905913 & 2271.70630433797 & 3521.60249378029 \tabularnewline
75 & 2918.74061769622 & 2155.84484577862 & 3681.63638961381 \tabularnewline
76 & 3021.00064070611 & 2130.84824364405 & 3911.15303776816 \tabularnewline
77 & 3169.95188555999 & 2158.74731211074 & 4181.15645900924 \tabularnewline
78 & 3203.17621739756 & 2074.73005934211 & 4331.62237545302 \tabularnewline
79 & 3310.24947077335 & 2066.93535458871 & 4553.56358695798 \tabularnewline
80 & 3457.39528298728 & 2100.65542446666 & 4814.13514150791 \tabularnewline
81 & 3587.23496946621 & 2117.87440686553 & 5056.5955320669 \tabularnewline
82 & 3411.31035236402 & 1829.68055247429 & 4992.94015225376 \tabularnewline
83 & 3197.8821854227 & 1504.00181735358 & 4891.76255349181 \tabularnewline
84 & 3108.91839278732 & 1302.55611740326 & 4915.28066817138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259831&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]2836.17800458601[/C][C]2370.20461249091[/C][C]3302.1513966811[/C][/ROW]
[ROW][C]74[/C][C]2896.65439905913[/C][C]2271.70630433797[/C][C]3521.60249378029[/C][/ROW]
[ROW][C]75[/C][C]2918.74061769622[/C][C]2155.84484577862[/C][C]3681.63638961381[/C][/ROW]
[ROW][C]76[/C][C]3021.00064070611[/C][C]2130.84824364405[/C][C]3911.15303776816[/C][/ROW]
[ROW][C]77[/C][C]3169.95188555999[/C][C]2158.74731211074[/C][C]4181.15645900924[/C][/ROW]
[ROW][C]78[/C][C]3203.17621739756[/C][C]2074.73005934211[/C][C]4331.62237545302[/C][/ROW]
[ROW][C]79[/C][C]3310.24947077335[/C][C]2066.93535458871[/C][C]4553.56358695798[/C][/ROW]
[ROW][C]80[/C][C]3457.39528298728[/C][C]2100.65542446666[/C][C]4814.13514150791[/C][/ROW]
[ROW][C]81[/C][C]3587.23496946621[/C][C]2117.87440686553[/C][C]5056.5955320669[/C][/ROW]
[ROW][C]82[/C][C]3411.31035236402[/C][C]1829.68055247429[/C][C]4992.94015225376[/C][/ROW]
[ROW][C]83[/C][C]3197.8821854227[/C][C]1504.00181735358[/C][C]4891.76255349181[/C][/ROW]
[ROW][C]84[/C][C]3108.91839278732[/C][C]1302.55611740326[/C][C]4915.28066817138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259831&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259831&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
732836.178004586012370.204612490913302.1513966811
742896.654399059132271.706304337973521.60249378029
752918.740617696222155.844845778623681.63638961381
763021.000640706112130.848243644053911.15303776816
773169.951885559992158.747312110744181.15645900924
783203.176217397562074.730059342114331.62237545302
793310.249470773352066.935354588714553.56358695798
803457.395282987282100.655424466664814.13514150791
813587.234969466212117.874406865535056.5955320669
823411.310352364021829.680552474294992.94015225376
833197.88218542271504.001817353584891.76255349181
843108.918392787321302.556117403264915.28066817138



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')