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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 19:56:30 +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/Jun/06/t1275854414ezahivfj1emsdgq.htm/, Retrieved Sun, 28 Apr 2024 02:46:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77788, Retrieved Sun, 28 Apr 2024 02:46:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2010-06-05 08:52:21] [74be16979710d4c4e7c6647856088456]
-   P     [Exponential Smoothing] [] [2010-06-06 19:56:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2
2.4
1.5
1.2
1.5
0.6
2.7
3.7
4.9
6.6
7.4
7.2
5.3
4.7
6.1
6.6
7
7.5
6.6
7.8
4.7
5.4
4.3
4.5
5.8
4.6
5.2
3.6
4.8
6.7
6.3
4.8
8.7
6.8
7.4
9
7.9
9.1
8.7
9.8
6.4
6.1
4.7
4.8
4.2
2.8
6.1
5.8
4.9
4.6
4.1
3.6
5.9
4.5
4.8
5.7
5
7
4.6
2.6
5
4.1
3.2
0
2.3
3.8
4.5
5.9
5
4.2
4.5
6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77788&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77788&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77788&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.52534352356398
beta0
gamma0.582031924980555

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.52534352356398 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.582031924980555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77788&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]0.52534352356398[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.582031924980555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77788&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77788&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
alpha0.52534352356398
beta0
gamma0.582031924980555







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135.32.433207070707072.86679292929293
144.73.005924836176791.69407516382321
156.15.13339625192190.966603748078098
166.66.199528604160730.400471395839267
1776.989080325004180.0109196749958151
187.57.73648357220933-0.236483572209326
196.65.187248459119881.41275154088012
207.86.696094998192951.10390500180705
214.78.18852434152217-3.48852434152217
225.47.63918400524153-2.23918400524153
234.36.80867652335317-2.50867652335317
244.54.77409289242592-0.274092892425916
255.83.072095153536632.72790484646337
264.63.247867829568011.35213217043199
275.24.99472665563950.205273344360502
283.65.50449633063275-1.90449633063275
294.84.97552859144418-0.175528591444176
306.75.556633536213331.14336646378667
316.34.187920008800732.11207999119927
324.85.97883066220063-1.17883066220063
338.75.003311093237013.69668890676299
346.88.57382528858044-1.77382528858044
357.47.9133395840961-0.513339584096101
3697.544331035940881.45566896405912
377.97.580400059496760.319599940503242
389.16.11090720570752.98909279429250
398.78.400895484880990.299104515119012
409.88.377102768665541.42289723133446
416.410.0738133450862-3.67381334508625
426.19.18148188707782-3.08148188707782
434.75.86089349886677-1.16089349886677
444.85.02320456196742-0.223204561967418
454.25.8966534751326-1.69665347513261
462.85.12249735740854-2.32249735740854
476.14.521998698844961.57800130115504
485.85.795631125344860.00436887465514246
494.94.755412684406850.144587315593146
504.63.931466119286040.668533880713963
514.14.2592135911977-0.159213591197697
523.64.30511127109319-0.70511127109319
535.93.475842480320912.42415751967909
544.55.95068110514855-1.45068110514855
554.84.017415124701590.782584875298406
565.74.45977080781791.24022919218210
5755.69496247378058-0.69496247378058
5875.27413933672641.7258606632736
594.67.8779914758853-3.27799147588531
602.66.16581963376298-3.56581963376298
6153.288763260835191.71123673916481
624.13.432594038570890.667405961429107
633.23.53107112573691-0.331071125736907
6403.33587201878725-3.33587201878725
652.31.989058246490060.310941753509940
663.82.283249499112761.51675050088724
674.52.525878217917761.97412178208224
685.93.72063130721462.17936869278540
6954.914567671007880.0854323289921188
704.25.5725091324515-1.3725091324515
714.55.16626244031471-0.666262440314706
7264.746628622202441.25337137779756

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.3 & 2.43320707070707 & 2.86679292929293 \tabularnewline
14 & 4.7 & 3.00592483617679 & 1.69407516382321 \tabularnewline
15 & 6.1 & 5.1333962519219 & 0.966603748078098 \tabularnewline
16 & 6.6 & 6.19952860416073 & 0.400471395839267 \tabularnewline
17 & 7 & 6.98908032500418 & 0.0109196749958151 \tabularnewline
18 & 7.5 & 7.73648357220933 & -0.236483572209326 \tabularnewline
19 & 6.6 & 5.18724845911988 & 1.41275154088012 \tabularnewline
20 & 7.8 & 6.69609499819295 & 1.10390500180705 \tabularnewline
21 & 4.7 & 8.18852434152217 & -3.48852434152217 \tabularnewline
22 & 5.4 & 7.63918400524153 & -2.23918400524153 \tabularnewline
23 & 4.3 & 6.80867652335317 & -2.50867652335317 \tabularnewline
24 & 4.5 & 4.77409289242592 & -0.274092892425916 \tabularnewline
25 & 5.8 & 3.07209515353663 & 2.72790484646337 \tabularnewline
26 & 4.6 & 3.24786782956801 & 1.35213217043199 \tabularnewline
27 & 5.2 & 4.9947266556395 & 0.205273344360502 \tabularnewline
28 & 3.6 & 5.50449633063275 & -1.90449633063275 \tabularnewline
29 & 4.8 & 4.97552859144418 & -0.175528591444176 \tabularnewline
30 & 6.7 & 5.55663353621333 & 1.14336646378667 \tabularnewline
31 & 6.3 & 4.18792000880073 & 2.11207999119927 \tabularnewline
32 & 4.8 & 5.97883066220063 & -1.17883066220063 \tabularnewline
33 & 8.7 & 5.00331109323701 & 3.69668890676299 \tabularnewline
34 & 6.8 & 8.57382528858044 & -1.77382528858044 \tabularnewline
35 & 7.4 & 7.9133395840961 & -0.513339584096101 \tabularnewline
36 & 9 & 7.54433103594088 & 1.45566896405912 \tabularnewline
37 & 7.9 & 7.58040005949676 & 0.319599940503242 \tabularnewline
38 & 9.1 & 6.1109072057075 & 2.98909279429250 \tabularnewline
39 & 8.7 & 8.40089548488099 & 0.299104515119012 \tabularnewline
40 & 9.8 & 8.37710276866554 & 1.42289723133446 \tabularnewline
41 & 6.4 & 10.0738133450862 & -3.67381334508625 \tabularnewline
42 & 6.1 & 9.18148188707782 & -3.08148188707782 \tabularnewline
43 & 4.7 & 5.86089349886677 & -1.16089349886677 \tabularnewline
44 & 4.8 & 5.02320456196742 & -0.223204561967418 \tabularnewline
45 & 4.2 & 5.8966534751326 & -1.69665347513261 \tabularnewline
46 & 2.8 & 5.12249735740854 & -2.32249735740854 \tabularnewline
47 & 6.1 & 4.52199869884496 & 1.57800130115504 \tabularnewline
48 & 5.8 & 5.79563112534486 & 0.00436887465514246 \tabularnewline
49 & 4.9 & 4.75541268440685 & 0.144587315593146 \tabularnewline
50 & 4.6 & 3.93146611928604 & 0.668533880713963 \tabularnewline
51 & 4.1 & 4.2592135911977 & -0.159213591197697 \tabularnewline
52 & 3.6 & 4.30511127109319 & -0.70511127109319 \tabularnewline
53 & 5.9 & 3.47584248032091 & 2.42415751967909 \tabularnewline
54 & 4.5 & 5.95068110514855 & -1.45068110514855 \tabularnewline
55 & 4.8 & 4.01741512470159 & 0.782584875298406 \tabularnewline
56 & 5.7 & 4.4597708078179 & 1.24022919218210 \tabularnewline
57 & 5 & 5.69496247378058 & -0.69496247378058 \tabularnewline
58 & 7 & 5.2741393367264 & 1.7258606632736 \tabularnewline
59 & 4.6 & 7.8779914758853 & -3.27799147588531 \tabularnewline
60 & 2.6 & 6.16581963376298 & -3.56581963376298 \tabularnewline
61 & 5 & 3.28876326083519 & 1.71123673916481 \tabularnewline
62 & 4.1 & 3.43259403857089 & 0.667405961429107 \tabularnewline
63 & 3.2 & 3.53107112573691 & -0.331071125736907 \tabularnewline
64 & 0 & 3.33587201878725 & -3.33587201878725 \tabularnewline
65 & 2.3 & 1.98905824649006 & 0.310941753509940 \tabularnewline
66 & 3.8 & 2.28324949911276 & 1.51675050088724 \tabularnewline
67 & 4.5 & 2.52587821791776 & 1.97412178208224 \tabularnewline
68 & 5.9 & 3.7206313072146 & 2.17936869278540 \tabularnewline
69 & 5 & 4.91456767100788 & 0.0854323289921188 \tabularnewline
70 & 4.2 & 5.5725091324515 & -1.3725091324515 \tabularnewline
71 & 4.5 & 5.16626244031471 & -0.666262440314706 \tabularnewline
72 & 6 & 4.74662862220244 & 1.25337137779756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77788&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]5.3[/C][C]2.43320707070707[/C][C]2.86679292929293[/C][/ROW]
[ROW][C]14[/C][C]4.7[/C][C]3.00592483617679[/C][C]1.69407516382321[/C][/ROW]
[ROW][C]15[/C][C]6.1[/C][C]5.1333962519219[/C][C]0.966603748078098[/C][/ROW]
[ROW][C]16[/C][C]6.6[/C][C]6.19952860416073[/C][C]0.400471395839267[/C][/ROW]
[ROW][C]17[/C][C]7[/C][C]6.98908032500418[/C][C]0.0109196749958151[/C][/ROW]
[ROW][C]18[/C][C]7.5[/C][C]7.73648357220933[/C][C]-0.236483572209326[/C][/ROW]
[ROW][C]19[/C][C]6.6[/C][C]5.18724845911988[/C][C]1.41275154088012[/C][/ROW]
[ROW][C]20[/C][C]7.8[/C][C]6.69609499819295[/C][C]1.10390500180705[/C][/ROW]
[ROW][C]21[/C][C]4.7[/C][C]8.18852434152217[/C][C]-3.48852434152217[/C][/ROW]
[ROW][C]22[/C][C]5.4[/C][C]7.63918400524153[/C][C]-2.23918400524153[/C][/ROW]
[ROW][C]23[/C][C]4.3[/C][C]6.80867652335317[/C][C]-2.50867652335317[/C][/ROW]
[ROW][C]24[/C][C]4.5[/C][C]4.77409289242592[/C][C]-0.274092892425916[/C][/ROW]
[ROW][C]25[/C][C]5.8[/C][C]3.07209515353663[/C][C]2.72790484646337[/C][/ROW]
[ROW][C]26[/C][C]4.6[/C][C]3.24786782956801[/C][C]1.35213217043199[/C][/ROW]
[ROW][C]27[/C][C]5.2[/C][C]4.9947266556395[/C][C]0.205273344360502[/C][/ROW]
[ROW][C]28[/C][C]3.6[/C][C]5.50449633063275[/C][C]-1.90449633063275[/C][/ROW]
[ROW][C]29[/C][C]4.8[/C][C]4.97552859144418[/C][C]-0.175528591444176[/C][/ROW]
[ROW][C]30[/C][C]6.7[/C][C]5.55663353621333[/C][C]1.14336646378667[/C][/ROW]
[ROW][C]31[/C][C]6.3[/C][C]4.18792000880073[/C][C]2.11207999119927[/C][/ROW]
[ROW][C]32[/C][C]4.8[/C][C]5.97883066220063[/C][C]-1.17883066220063[/C][/ROW]
[ROW][C]33[/C][C]8.7[/C][C]5.00331109323701[/C][C]3.69668890676299[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]8.57382528858044[/C][C]-1.77382528858044[/C][/ROW]
[ROW][C]35[/C][C]7.4[/C][C]7.9133395840961[/C][C]-0.513339584096101[/C][/ROW]
[ROW][C]36[/C][C]9[/C][C]7.54433103594088[/C][C]1.45566896405912[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]7.58040005949676[/C][C]0.319599940503242[/C][/ROW]
[ROW][C]38[/C][C]9.1[/C][C]6.1109072057075[/C][C]2.98909279429250[/C][/ROW]
[ROW][C]39[/C][C]8.7[/C][C]8.40089548488099[/C][C]0.299104515119012[/C][/ROW]
[ROW][C]40[/C][C]9.8[/C][C]8.37710276866554[/C][C]1.42289723133446[/C][/ROW]
[ROW][C]41[/C][C]6.4[/C][C]10.0738133450862[/C][C]-3.67381334508625[/C][/ROW]
[ROW][C]42[/C][C]6.1[/C][C]9.18148188707782[/C][C]-3.08148188707782[/C][/ROW]
[ROW][C]43[/C][C]4.7[/C][C]5.86089349886677[/C][C]-1.16089349886677[/C][/ROW]
[ROW][C]44[/C][C]4.8[/C][C]5.02320456196742[/C][C]-0.223204561967418[/C][/ROW]
[ROW][C]45[/C][C]4.2[/C][C]5.8966534751326[/C][C]-1.69665347513261[/C][/ROW]
[ROW][C]46[/C][C]2.8[/C][C]5.12249735740854[/C][C]-2.32249735740854[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]4.52199869884496[/C][C]1.57800130115504[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.79563112534486[/C][C]0.00436887465514246[/C][/ROW]
[ROW][C]49[/C][C]4.9[/C][C]4.75541268440685[/C][C]0.144587315593146[/C][/ROW]
[ROW][C]50[/C][C]4.6[/C][C]3.93146611928604[/C][C]0.668533880713963[/C][/ROW]
[ROW][C]51[/C][C]4.1[/C][C]4.2592135911977[/C][C]-0.159213591197697[/C][/ROW]
[ROW][C]52[/C][C]3.6[/C][C]4.30511127109319[/C][C]-0.70511127109319[/C][/ROW]
[ROW][C]53[/C][C]5.9[/C][C]3.47584248032091[/C][C]2.42415751967909[/C][/ROW]
[ROW][C]54[/C][C]4.5[/C][C]5.95068110514855[/C][C]-1.45068110514855[/C][/ROW]
[ROW][C]55[/C][C]4.8[/C][C]4.01741512470159[/C][C]0.782584875298406[/C][/ROW]
[ROW][C]56[/C][C]5.7[/C][C]4.4597708078179[/C][C]1.24022919218210[/C][/ROW]
[ROW][C]57[/C][C]5[/C][C]5.69496247378058[/C][C]-0.69496247378058[/C][/ROW]
[ROW][C]58[/C][C]7[/C][C]5.2741393367264[/C][C]1.7258606632736[/C][/ROW]
[ROW][C]59[/C][C]4.6[/C][C]7.8779914758853[/C][C]-3.27799147588531[/C][/ROW]
[ROW][C]60[/C][C]2.6[/C][C]6.16581963376298[/C][C]-3.56581963376298[/C][/ROW]
[ROW][C]61[/C][C]5[/C][C]3.28876326083519[/C][C]1.71123673916481[/C][/ROW]
[ROW][C]62[/C][C]4.1[/C][C]3.43259403857089[/C][C]0.667405961429107[/C][/ROW]
[ROW][C]63[/C][C]3.2[/C][C]3.53107112573691[/C][C]-0.331071125736907[/C][/ROW]
[ROW][C]64[/C][C]0[/C][C]3.33587201878725[/C][C]-3.33587201878725[/C][/ROW]
[ROW][C]65[/C][C]2.3[/C][C]1.98905824649006[/C][C]0.310941753509940[/C][/ROW]
[ROW][C]66[/C][C]3.8[/C][C]2.28324949911276[/C][C]1.51675050088724[/C][/ROW]
[ROW][C]67[/C][C]4.5[/C][C]2.52587821791776[/C][C]1.97412178208224[/C][/ROW]
[ROW][C]68[/C][C]5.9[/C][C]3.7206313072146[/C][C]2.17936869278540[/C][/ROW]
[ROW][C]69[/C][C]5[/C][C]4.91456767100788[/C][C]0.0854323289921188[/C][/ROW]
[ROW][C]70[/C][C]4.2[/C][C]5.5725091324515[/C][C]-1.3725091324515[/C][/ROW]
[ROW][C]71[/C][C]4.5[/C][C]5.16626244031471[/C][C]-0.666262440314706[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]4.74662862220244[/C][C]1.25337137779756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77788&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77788&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
135.32.433207070707072.86679292929293
144.73.005924836176791.69407516382321
156.15.13339625192190.966603748078098
166.66.199528604160730.400471395839267
1776.989080325004180.0109196749958151
187.57.73648357220933-0.236483572209326
196.65.187248459119881.41275154088012
207.86.696094998192951.10390500180705
214.78.18852434152217-3.48852434152217
225.47.63918400524153-2.23918400524153
234.36.80867652335317-2.50867652335317
244.54.77409289242592-0.274092892425916
255.83.072095153536632.72790484646337
264.63.247867829568011.35213217043199
275.24.99472665563950.205273344360502
283.65.50449633063275-1.90449633063275
294.84.97552859144418-0.175528591444176
306.75.556633536213331.14336646378667
316.34.187920008800732.11207999119927
324.85.97883066220063-1.17883066220063
338.75.003311093237013.69668890676299
346.88.57382528858044-1.77382528858044
357.47.9133395840961-0.513339584096101
3697.544331035940881.45566896405912
377.97.580400059496760.319599940503242
389.16.11090720570752.98909279429250
398.78.400895484880990.299104515119012
409.88.377102768665541.42289723133446
416.410.0738133450862-3.67381334508625
426.19.18148188707782-3.08148188707782
434.75.86089349886677-1.16089349886677
444.85.02320456196742-0.223204561967418
454.25.8966534751326-1.69665347513261
462.85.12249735740854-2.32249735740854
476.14.521998698844961.57800130115504
485.85.795631125344860.00436887465514246
494.94.755412684406850.144587315593146
504.63.931466119286040.668533880713963
514.14.2592135911977-0.159213591197697
523.64.30511127109319-0.70511127109319
535.93.475842480320912.42415751967909
544.55.95068110514855-1.45068110514855
554.84.017415124701590.782584875298406
565.74.45977080781791.24022919218210
5755.69496247378058-0.69496247378058
5875.27413933672641.7258606632736
594.67.8779914758853-3.27799147588531
602.66.16581963376298-3.56581963376298
6153.288763260835191.71123673916481
624.13.432594038570890.667405961429107
633.23.53107112573691-0.331071125736907
6403.33587201878725-3.33587201878725
652.31.989058246490060.310941753509940
663.82.283249499112761.51675050088724
674.52.525878217917761.97412178208224
685.93.72063130721462.17936869278540
6954.914567671007880.0854323289921188
704.25.5725091324515-1.3725091324515
714.55.16626244031471-0.666262440314706
7264.746628622202441.25337137779756







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.859170190001512.322222302425319.3961180775777
744.81563968727610.8203195450737968.8109598294784
754.28765488018601-0.1186094920396488.69391925241167
763.43625985714-1.345763605496188.21828331977618
774.84941266424374-0.2809217377675619.97974706625504
785.31337570256353-0.14308045099606810.7698318561231
794.88554514771385-0.87861102947081610.6497013248985
805.09990872755792-0.95633425916526711.1561517142811
814.57044606730768-1.7644305529187610.9053226875341
824.78072768550555-1.8210330245436511.3824883955548
835.29063117680796-1.5676358894418612.1488982430578
845.75134208094253-1.354177592611612.8568617544967

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.85917019000151 & 2.32222230242531 & 9.3961180775777 \tabularnewline
74 & 4.8156396872761 & 0.820319545073796 & 8.8109598294784 \tabularnewline
75 & 4.28765488018601 & -0.118609492039648 & 8.69391925241167 \tabularnewline
76 & 3.43625985714 & -1.34576360549618 & 8.21828331977618 \tabularnewline
77 & 4.84941266424374 & -0.280921737767561 & 9.97974706625504 \tabularnewline
78 & 5.31337570256353 & -0.143080450996068 & 10.7698318561231 \tabularnewline
79 & 4.88554514771385 & -0.878611029470816 & 10.6497013248985 \tabularnewline
80 & 5.09990872755792 & -0.956334259165267 & 11.1561517142811 \tabularnewline
81 & 4.57044606730768 & -1.76443055291876 & 10.9053226875341 \tabularnewline
82 & 4.78072768550555 & -1.82103302454365 & 11.3824883955548 \tabularnewline
83 & 5.29063117680796 & -1.56763588944186 & 12.1488982430578 \tabularnewline
84 & 5.75134208094253 & -1.3541775926116 & 12.8568617544967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77788&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]5.85917019000151[/C][C]2.32222230242531[/C][C]9.3961180775777[/C][/ROW]
[ROW][C]74[/C][C]4.8156396872761[/C][C]0.820319545073796[/C][C]8.8109598294784[/C][/ROW]
[ROW][C]75[/C][C]4.28765488018601[/C][C]-0.118609492039648[/C][C]8.69391925241167[/C][/ROW]
[ROW][C]76[/C][C]3.43625985714[/C][C]-1.34576360549618[/C][C]8.21828331977618[/C][/ROW]
[ROW][C]77[/C][C]4.84941266424374[/C][C]-0.280921737767561[/C][C]9.97974706625504[/C][/ROW]
[ROW][C]78[/C][C]5.31337570256353[/C][C]-0.143080450996068[/C][C]10.7698318561231[/C][/ROW]
[ROW][C]79[/C][C]4.88554514771385[/C][C]-0.878611029470816[/C][C]10.6497013248985[/C][/ROW]
[ROW][C]80[/C][C]5.09990872755792[/C][C]-0.956334259165267[/C][C]11.1561517142811[/C][/ROW]
[ROW][C]81[/C][C]4.57044606730768[/C][C]-1.76443055291876[/C][C]10.9053226875341[/C][/ROW]
[ROW][C]82[/C][C]4.78072768550555[/C][C]-1.82103302454365[/C][C]11.3824883955548[/C][/ROW]
[ROW][C]83[/C][C]5.29063117680796[/C][C]-1.56763588944186[/C][C]12.1488982430578[/C][/ROW]
[ROW][C]84[/C][C]5.75134208094253[/C][C]-1.3541775926116[/C][C]12.8568617544967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77788&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77788&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
735.859170190001512.322222302425319.3961180775777
744.81563968727610.8203195450737968.8109598294784
754.28765488018601-0.1186094920396488.69391925241167
763.43625985714-1.345763605496188.21828331977618
774.84941266424374-0.2809217377675619.97974706625504
785.31337570256353-0.14308045099606810.7698318561231
794.88554514771385-0.87861102947081610.6497013248985
805.09990872755792-0.95633425916526711.1561517142811
814.57044606730768-1.7644305529187610.9053226875341
824.78072768550555-1.8210330245436511.3824883955548
835.29063117680796-1.5676358894418612.1488982430578
845.75134208094253-1.354177592611612.8568617544967



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')