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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 10 Dec 2010 15:44:28 +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/Dec/10/t12919958055rinm9jwcybe3sm.htm/, Retrieved Mon, 29 Apr 2024 13:24:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107780, Retrieved Mon, 29 Apr 2024 13:24:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [Workshop 8 (Smoot...] [2010-12-10 15:44:28] [6427096bd21c899f2c90594929aeeec2] [Current]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107780&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107780&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107780&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.365156398722266
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.365156398722266 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107780&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]0.365156398722266[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107780&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107780&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
alpha0.365156398722266
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23037-7
34734.443905208944112.5560947910559
43539.0288435648615-4.0288435648615
53037.5576855577013-7.5576855577013
64334.79794831677588.20205168322419
78237.792979971555944.2070200284441
84053.9354562033856-13.9354562033856
94748.8468352016055-1.84683520160546
101948.1724515103537-29.1724515103537
115237.51994417493314.480055825067
1213642.807429213311893.1925707866882
138076.83729274944883.16270725055122
144277.9921755392729-35.9921755392729
155464.8494023371723-10.8494023371723
166660.88767365144155.11232634855845
178162.754472329974118.2455276700259
186369.4169435067482-6.41694350674823
1913767.073755525019869.9262444749802
207292.6077711336764-20.6077711336764
2110785.082711640810421.9172883591896
225893.0859497278095-35.0859497278095
233680.2740906794521-44.2740906794521
245264.1071231702403-12.1071231702403
257959.686129674508519.3138703254915
267766.738713007953810.2612869920462
275470.485687612225-16.4856876122250
288464.465833293284719.5341667067153
294871.5988592599492-23.5988592599492
309662.981584798632633.0184152013674
318375.03847038508047.96152961491958
326677.9456738675851-11.9456738675851
336173.583634617787-12.5836346177871
345368.9886399179191-15.9886399179191
353063.1502857450247-33.1502857450247
367451.045246785757422.9547532142426
376959.42732180302869.5726781969714
385962.9228464995618-3.92284649956183
394261.4903939990416-19.4903939990416
406554.373351916673510.6266480833265
417058.253740461269911.7462595387301
4210062.542962292889637.4570377071104
436376.2206392888222-13.2206392888222
4410571.393038257309833.6069617426902
458283.6648353792675-1.66483537926752
468183.0569100877088-2.05691008770877
477582.3058162075855-7.30581620758554
4810279.638050671496822.3619493285032
4912187.803659556702933.1963404432971
509899.9255156837356-1.92551568373557
517699.2224013109794-23.2224013109794
527790.742592878579-13.7425928785790
536385.7243971539308-22.7243971539308
543777.4264381260669-40.4264381260669
553562.6644655667838-27.6644655667838
562352.5626089478409-29.5626089478409
574041.7676331276127-1.76763312761265
582941.1221705804714-12.1221705804714
593736.69568242660950.30431757339052
605136.806805935776714.1931940642233
612041.9895415666347-21.9895415666347
622833.9599197586088-5.95991975860879
631331.7836169228815-18.7836169228815
642224.9246590123435-2.92465901234348
652523.85670105990551.14329894009448
661324.2741839835334-11.2741839835334
671620.1573435615741-4.15734356157409
681318.6392629583785-5.6392629583785
691616.5800500050491-0.580050005049131
701716.36824103412660.631758965873445
71916.5989318629654-7.5989318629654
721713.82413326974913.17586673025092
732514.983821327789410.0161786722106
741418.6412930606926-4.64129306069257
75816.9464952012354-8.94649520123542
76713.6796252323663-6.67962523236626
771011.240517337701-1.24051733770101
78710.7875344941136-3.78753449411358
79109.40449203820670.595507961793299
8039.62194558094558-6.62194558094558

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 30 & 37 & -7 \tabularnewline
3 & 47 & 34.4439052089441 & 12.5560947910559 \tabularnewline
4 & 35 & 39.0288435648615 & -4.0288435648615 \tabularnewline
5 & 30 & 37.5576855577013 & -7.5576855577013 \tabularnewline
6 & 43 & 34.7979483167758 & 8.20205168322419 \tabularnewline
7 & 82 & 37.7929799715559 & 44.2070200284441 \tabularnewline
8 & 40 & 53.9354562033856 & -13.9354562033856 \tabularnewline
9 & 47 & 48.8468352016055 & -1.84683520160546 \tabularnewline
10 & 19 & 48.1724515103537 & -29.1724515103537 \tabularnewline
11 & 52 & 37.519944174933 & 14.480055825067 \tabularnewline
12 & 136 & 42.8074292133118 & 93.1925707866882 \tabularnewline
13 & 80 & 76.8372927494488 & 3.16270725055122 \tabularnewline
14 & 42 & 77.9921755392729 & -35.9921755392729 \tabularnewline
15 & 54 & 64.8494023371723 & -10.8494023371723 \tabularnewline
16 & 66 & 60.8876736514415 & 5.11232634855845 \tabularnewline
17 & 81 & 62.7544723299741 & 18.2455276700259 \tabularnewline
18 & 63 & 69.4169435067482 & -6.41694350674823 \tabularnewline
19 & 137 & 67.0737555250198 & 69.9262444749802 \tabularnewline
20 & 72 & 92.6077711336764 & -20.6077711336764 \tabularnewline
21 & 107 & 85.0827116408104 & 21.9172883591896 \tabularnewline
22 & 58 & 93.0859497278095 & -35.0859497278095 \tabularnewline
23 & 36 & 80.2740906794521 & -44.2740906794521 \tabularnewline
24 & 52 & 64.1071231702403 & -12.1071231702403 \tabularnewline
25 & 79 & 59.6861296745085 & 19.3138703254915 \tabularnewline
26 & 77 & 66.7387130079538 & 10.2612869920462 \tabularnewline
27 & 54 & 70.485687612225 & -16.4856876122250 \tabularnewline
28 & 84 & 64.4658332932847 & 19.5341667067153 \tabularnewline
29 & 48 & 71.5988592599492 & -23.5988592599492 \tabularnewline
30 & 96 & 62.9815847986326 & 33.0184152013674 \tabularnewline
31 & 83 & 75.0384703850804 & 7.96152961491958 \tabularnewline
32 & 66 & 77.9456738675851 & -11.9456738675851 \tabularnewline
33 & 61 & 73.583634617787 & -12.5836346177871 \tabularnewline
34 & 53 & 68.9886399179191 & -15.9886399179191 \tabularnewline
35 & 30 & 63.1502857450247 & -33.1502857450247 \tabularnewline
36 & 74 & 51.0452467857574 & 22.9547532142426 \tabularnewline
37 & 69 & 59.4273218030286 & 9.5726781969714 \tabularnewline
38 & 59 & 62.9228464995618 & -3.92284649956183 \tabularnewline
39 & 42 & 61.4903939990416 & -19.4903939990416 \tabularnewline
40 & 65 & 54.3733519166735 & 10.6266480833265 \tabularnewline
41 & 70 & 58.2537404612699 & 11.7462595387301 \tabularnewline
42 & 100 & 62.5429622928896 & 37.4570377071104 \tabularnewline
43 & 63 & 76.2206392888222 & -13.2206392888222 \tabularnewline
44 & 105 & 71.3930382573098 & 33.6069617426902 \tabularnewline
45 & 82 & 83.6648353792675 & -1.66483537926752 \tabularnewline
46 & 81 & 83.0569100877088 & -2.05691008770877 \tabularnewline
47 & 75 & 82.3058162075855 & -7.30581620758554 \tabularnewline
48 & 102 & 79.6380506714968 & 22.3619493285032 \tabularnewline
49 & 121 & 87.8036595567029 & 33.1963404432971 \tabularnewline
50 & 98 & 99.9255156837356 & -1.92551568373557 \tabularnewline
51 & 76 & 99.2224013109794 & -23.2224013109794 \tabularnewline
52 & 77 & 90.742592878579 & -13.7425928785790 \tabularnewline
53 & 63 & 85.7243971539308 & -22.7243971539308 \tabularnewline
54 & 37 & 77.4264381260669 & -40.4264381260669 \tabularnewline
55 & 35 & 62.6644655667838 & -27.6644655667838 \tabularnewline
56 & 23 & 52.5626089478409 & -29.5626089478409 \tabularnewline
57 & 40 & 41.7676331276127 & -1.76763312761265 \tabularnewline
58 & 29 & 41.1221705804714 & -12.1221705804714 \tabularnewline
59 & 37 & 36.6956824266095 & 0.30431757339052 \tabularnewline
60 & 51 & 36.8068059357767 & 14.1931940642233 \tabularnewline
61 & 20 & 41.9895415666347 & -21.9895415666347 \tabularnewline
62 & 28 & 33.9599197586088 & -5.95991975860879 \tabularnewline
63 & 13 & 31.7836169228815 & -18.7836169228815 \tabularnewline
64 & 22 & 24.9246590123435 & -2.92465901234348 \tabularnewline
65 & 25 & 23.8567010599055 & 1.14329894009448 \tabularnewline
66 & 13 & 24.2741839835334 & -11.2741839835334 \tabularnewline
67 & 16 & 20.1573435615741 & -4.15734356157409 \tabularnewline
68 & 13 & 18.6392629583785 & -5.6392629583785 \tabularnewline
69 & 16 & 16.5800500050491 & -0.580050005049131 \tabularnewline
70 & 17 & 16.3682410341266 & 0.631758965873445 \tabularnewline
71 & 9 & 16.5989318629654 & -7.5989318629654 \tabularnewline
72 & 17 & 13.8241332697491 & 3.17586673025092 \tabularnewline
73 & 25 & 14.9838213277894 & 10.0161786722106 \tabularnewline
74 & 14 & 18.6412930606926 & -4.64129306069257 \tabularnewline
75 & 8 & 16.9464952012354 & -8.94649520123542 \tabularnewline
76 & 7 & 13.6796252323663 & -6.67962523236626 \tabularnewline
77 & 10 & 11.240517337701 & -1.24051733770101 \tabularnewline
78 & 7 & 10.7875344941136 & -3.78753449411358 \tabularnewline
79 & 10 & 9.4044920382067 & 0.595507961793299 \tabularnewline
80 & 3 & 9.62194558094558 & -6.62194558094558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107780&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]2[/C][C]30[/C][C]37[/C][C]-7[/C][/ROW]
[ROW][C]3[/C][C]47[/C][C]34.4439052089441[/C][C]12.5560947910559[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]39.0288435648615[/C][C]-4.0288435648615[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]37.5576855577013[/C][C]-7.5576855577013[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]34.7979483167758[/C][C]8.20205168322419[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]37.7929799715559[/C][C]44.2070200284441[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]53.9354562033856[/C][C]-13.9354562033856[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]48.8468352016055[/C][C]-1.84683520160546[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]48.1724515103537[/C][C]-29.1724515103537[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]37.519944174933[/C][C]14.480055825067[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]42.8074292133118[/C][C]93.1925707866882[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]76.8372927494488[/C][C]3.16270725055122[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]77.9921755392729[/C][C]-35.9921755392729[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]64.8494023371723[/C][C]-10.8494023371723[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]60.8876736514415[/C][C]5.11232634855845[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]62.7544723299741[/C][C]18.2455276700259[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]69.4169435067482[/C][C]-6.41694350674823[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]67.0737555250198[/C][C]69.9262444749802[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]92.6077711336764[/C][C]-20.6077711336764[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]85.0827116408104[/C][C]21.9172883591896[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]93.0859497278095[/C][C]-35.0859497278095[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]80.2740906794521[/C][C]-44.2740906794521[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]64.1071231702403[/C][C]-12.1071231702403[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]59.6861296745085[/C][C]19.3138703254915[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]66.7387130079538[/C][C]10.2612869920462[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]70.485687612225[/C][C]-16.4856876122250[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]64.4658332932847[/C][C]19.5341667067153[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]71.5988592599492[/C][C]-23.5988592599492[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]62.9815847986326[/C][C]33.0184152013674[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]75.0384703850804[/C][C]7.96152961491958[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]77.9456738675851[/C][C]-11.9456738675851[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]73.583634617787[/C][C]-12.5836346177871[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]68.9886399179191[/C][C]-15.9886399179191[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]63.1502857450247[/C][C]-33.1502857450247[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]51.0452467857574[/C][C]22.9547532142426[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]59.4273218030286[/C][C]9.5726781969714[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]62.9228464995618[/C][C]-3.92284649956183[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]61.4903939990416[/C][C]-19.4903939990416[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]54.3733519166735[/C][C]10.6266480833265[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]58.2537404612699[/C][C]11.7462595387301[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]62.5429622928896[/C][C]37.4570377071104[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]76.2206392888222[/C][C]-13.2206392888222[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]71.3930382573098[/C][C]33.6069617426902[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]83.6648353792675[/C][C]-1.66483537926752[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]83.0569100877088[/C][C]-2.05691008770877[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]82.3058162075855[/C][C]-7.30581620758554[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]79.6380506714968[/C][C]22.3619493285032[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]87.8036595567029[/C][C]33.1963404432971[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]99.9255156837356[/C][C]-1.92551568373557[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]99.2224013109794[/C][C]-23.2224013109794[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]90.742592878579[/C][C]-13.7425928785790[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]85.7243971539308[/C][C]-22.7243971539308[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]77.4264381260669[/C][C]-40.4264381260669[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]62.6644655667838[/C][C]-27.6644655667838[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]52.5626089478409[/C][C]-29.5626089478409[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]41.7676331276127[/C][C]-1.76763312761265[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]41.1221705804714[/C][C]-12.1221705804714[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]36.6956824266095[/C][C]0.30431757339052[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]36.8068059357767[/C][C]14.1931940642233[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]41.9895415666347[/C][C]-21.9895415666347[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]33.9599197586088[/C][C]-5.95991975860879[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]31.7836169228815[/C][C]-18.7836169228815[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]24.9246590123435[/C][C]-2.92465901234348[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]23.8567010599055[/C][C]1.14329894009448[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]24.2741839835334[/C][C]-11.2741839835334[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]20.1573435615741[/C][C]-4.15734356157409[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]18.6392629583785[/C][C]-5.6392629583785[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]16.5800500050491[/C][C]-0.580050005049131[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]16.3682410341266[/C][C]0.631758965873445[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]16.5989318629654[/C][C]-7.5989318629654[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]13.8241332697491[/C][C]3.17586673025092[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]14.9838213277894[/C][C]10.0161786722106[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]18.6412930606926[/C][C]-4.64129306069257[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]16.9464952012354[/C][C]-8.94649520123542[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]13.6796252323663[/C][C]-6.67962523236626[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]11.240517337701[/C][C]-1.24051733770101[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]10.7875344941136[/C][C]-3.78753449411358[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]9.4044920382067[/C][C]0.595507961793299[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]9.62194558094558[/C][C]-6.62194558094558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107780&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107780&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
23037-7
34734.443905208944112.5560947910559
43539.0288435648615-4.0288435648615
53037.5576855577013-7.5576855577013
64334.79794831677588.20205168322419
78237.792979971555944.2070200284441
84053.9354562033856-13.9354562033856
94748.8468352016055-1.84683520160546
101948.1724515103537-29.1724515103537
115237.51994417493314.480055825067
1213642.807429213311893.1925707866882
138076.83729274944883.16270725055122
144277.9921755392729-35.9921755392729
155464.8494023371723-10.8494023371723
166660.88767365144155.11232634855845
178162.754472329974118.2455276700259
186369.4169435067482-6.41694350674823
1913767.073755525019869.9262444749802
207292.6077711336764-20.6077711336764
2110785.082711640810421.9172883591896
225893.0859497278095-35.0859497278095
233680.2740906794521-44.2740906794521
245264.1071231702403-12.1071231702403
257959.686129674508519.3138703254915
267766.738713007953810.2612869920462
275470.485687612225-16.4856876122250
288464.465833293284719.5341667067153
294871.5988592599492-23.5988592599492
309662.981584798632633.0184152013674
318375.03847038508047.96152961491958
326677.9456738675851-11.9456738675851
336173.583634617787-12.5836346177871
345368.9886399179191-15.9886399179191
353063.1502857450247-33.1502857450247
367451.045246785757422.9547532142426
376959.42732180302869.5726781969714
385962.9228464995618-3.92284649956183
394261.4903939990416-19.4903939990416
406554.373351916673510.6266480833265
417058.253740461269911.7462595387301
4210062.542962292889637.4570377071104
436376.2206392888222-13.2206392888222
4410571.393038257309833.6069617426902
458283.6648353792675-1.66483537926752
468183.0569100877088-2.05691008770877
477582.3058162075855-7.30581620758554
4810279.638050671496822.3619493285032
4912187.803659556702933.1963404432971
509899.9255156837356-1.92551568373557
517699.2224013109794-23.2224013109794
527790.742592878579-13.7425928785790
536385.7243971539308-22.7243971539308
543777.4264381260669-40.4264381260669
553562.6644655667838-27.6644655667838
562352.5626089478409-29.5626089478409
574041.7676331276127-1.76763312761265
582941.1221705804714-12.1221705804714
593736.69568242660950.30431757339052
605136.806805935776714.1931940642233
612041.9895415666347-21.9895415666347
622833.9599197586088-5.95991975860879
631331.7836169228815-18.7836169228815
642224.9246590123435-2.92465901234348
652523.85670105990551.14329894009448
661324.2741839835334-11.2741839835334
671620.1573435615741-4.15734356157409
681318.6392629583785-5.6392629583785
691616.5800500050491-0.580050005049131
701716.36824103412660.631758965873445
71916.5989318629654-7.5989318629654
721713.82413326974913.17586673025092
732514.983821327789410.0161786722106
741418.6412930606926-4.64129306069257
75816.9464952012354-8.94649520123542
76713.6796252323663-6.67962523236626
771011.240517337701-1.24051733770101
78710.7875344941136-3.78753449411358
79109.40449203820670.595507961793299
8039.62194558094558-6.62194558094558







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
817.20389978007267-36.933000232124351.3407997922696
827.20389978007267-39.783539906716554.1913394668618
837.20389978007267-42.470772176092556.8785717362378
847.20389978007267-45.01991260073359.4277121608784
857.20389978007267-47.450286932553261.8580864926985
867.20389978007267-49.777094163974664.1848937241199
877.20389978007267-52.012544021328766.420343581474
887.20389978007267-54.166620521758768.574420081904
897.20389978007267-56.2476116893270.6554112494653
907.20389978007267-58.262487422700772.670286982846
917.20389978007267-60.217175552618574.6249751127638
927.20389978007267-62.116767734380776.524567294526

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 7.20389978007267 & -36.9330002321243 & 51.3407997922696 \tabularnewline
82 & 7.20389978007267 & -39.7835399067165 & 54.1913394668618 \tabularnewline
83 & 7.20389978007267 & -42.4707721760925 & 56.8785717362378 \tabularnewline
84 & 7.20389978007267 & -45.019912600733 & 59.4277121608784 \tabularnewline
85 & 7.20389978007267 & -47.4502869325532 & 61.8580864926985 \tabularnewline
86 & 7.20389978007267 & -49.7770941639746 & 64.1848937241199 \tabularnewline
87 & 7.20389978007267 & -52.0125440213287 & 66.420343581474 \tabularnewline
88 & 7.20389978007267 & -54.1666205217587 & 68.574420081904 \tabularnewline
89 & 7.20389978007267 & -56.24761168932 & 70.6554112494653 \tabularnewline
90 & 7.20389978007267 & -58.2624874227007 & 72.670286982846 \tabularnewline
91 & 7.20389978007267 & -60.2171755526185 & 74.6249751127638 \tabularnewline
92 & 7.20389978007267 & -62.1167677343807 & 76.524567294526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107780&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]81[/C][C]7.20389978007267[/C][C]-36.9330002321243[/C][C]51.3407997922696[/C][/ROW]
[ROW][C]82[/C][C]7.20389978007267[/C][C]-39.7835399067165[/C][C]54.1913394668618[/C][/ROW]
[ROW][C]83[/C][C]7.20389978007267[/C][C]-42.4707721760925[/C][C]56.8785717362378[/C][/ROW]
[ROW][C]84[/C][C]7.20389978007267[/C][C]-45.019912600733[/C][C]59.4277121608784[/C][/ROW]
[ROW][C]85[/C][C]7.20389978007267[/C][C]-47.4502869325532[/C][C]61.8580864926985[/C][/ROW]
[ROW][C]86[/C][C]7.20389978007267[/C][C]-49.7770941639746[/C][C]64.1848937241199[/C][/ROW]
[ROW][C]87[/C][C]7.20389978007267[/C][C]-52.0125440213287[/C][C]66.420343581474[/C][/ROW]
[ROW][C]88[/C][C]7.20389978007267[/C][C]-54.1666205217587[/C][C]68.574420081904[/C][/ROW]
[ROW][C]89[/C][C]7.20389978007267[/C][C]-56.24761168932[/C][C]70.6554112494653[/C][/ROW]
[ROW][C]90[/C][C]7.20389978007267[/C][C]-58.2624874227007[/C][C]72.670286982846[/C][/ROW]
[ROW][C]91[/C][C]7.20389978007267[/C][C]-60.2171755526185[/C][C]74.6249751127638[/C][/ROW]
[ROW][C]92[/C][C]7.20389978007267[/C][C]-62.1167677343807[/C][C]76.524567294526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107780&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107780&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
817.20389978007267-36.933000232124351.3407997922696
827.20389978007267-39.783539906716554.1913394668618
837.20389978007267-42.470772176092556.8785717362378
847.20389978007267-45.01991260073359.4277121608784
857.20389978007267-47.450286932553261.8580864926985
867.20389978007267-49.777094163974664.1848937241199
877.20389978007267-52.012544021328766.420343581474
887.20389978007267-54.166620521758768.574420081904
897.20389978007267-56.2476116893270.6554112494653
907.20389978007267-58.262487422700772.670286982846
917.20389978007267-60.217175552618574.6249751127638
927.20389978007267-62.116767734380776.524567294526



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')