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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 17:28:29 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t14616881510jj138jzi73tis1.htm/, Retrieved Fri, 03 May 2024 15:31:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294916, Retrieved Fri, 03 May 2024 15:31:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 16:28:29] [3d038f408b3fdbe799ace9817e748893] [Current]
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Dataseries X:
90,4
89,5
88,9
88,4
87,6
87,1
86,5
85,7
85,3
84,9
84,5
84,4
84,3
84,2
84,1
83,8
83,5
83,2
82,8
82,2
81,5
80,8
80,3
79,8
79,2
78,8
78,1
77,8
77,3
76,7
76,2
76,1
76,3
76,2
76,2
76,6
75,5
75,4
75,5
75,5
75,2
74,9
74,6
74,4
74
73,3
72,7
72
71,2
70,9
70,4
70
69,7
69,2
68,7
68,6
68,4
67,9
67,4
66,5
65,6
64,6
63,8
63
62,1
61,7
61,4
61,1
61,1
61
60,5
60,2
59,9
59,4
59,6
59,5
59,3
59,3
59,1
58,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294916&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294916&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294916&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.982203501720176
beta0.0023726461264415
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.982203501720176 \tabularnewline
beta & 0.0023726461264415 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294916&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]0.982203501720176[/C][/ROW]
[ROW][C]beta[/C][C]0.0023726461264415[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294916&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294916&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
alpha0.982203501720176
beta0.0023726461264415
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1384.386.5014880266812-2.20148802668122
1484.284.18778219163040.0122178083695843
1584.184.05237809814130.0476219018587045
1683.883.77694815010870.023051849891317
1783.583.49417354344820.00582645655184422
1883.283.2154402193831-0.0154402193830947
1982.882.21207580813920.587924191860765
2082.282.12799272172120.0720072782788463
2181.581.8686929182221-0.368692918222109
2280.881.1478943869928-0.347894386992792
2380.380.4191557114383-0.119155711438268
2479.880.1723211441787-0.372321144178656
2579.279.6220124630764-0.422012463076371
2678.879.0789109312305-0.278910931230499
2778.178.6422000084893-0.542200008489345
2877.877.78069471796970.0193052820302881
2977.377.4863766518298-0.186376651829775
3076.777.008779844968-0.308779844968043
3176.275.77162845659860.428371543401383
3276.175.54179413281690.558205867183133
3376.375.74694851330710.553051486692908
3476.275.93011858986450.269881410135483
3576.275.81325185795080.386748142049157
3676.676.04800854509770.551991454902321
3775.576.4003796981365-0.900379698136533
3875.475.38067651125750.0193234887425149
3975.575.22605420055720.273945799442828
4075.575.17882504551940.321174954480611
4175.275.18078149003850.0192185099615045
4274.974.9063796646957-0.00637966469571438
4374.673.99835962804520.601640371954829
4474.473.95334121721750.446658782782478
457474.0544705815275-0.0544705815275393
4673.373.6407854112654-0.340785411265387
4772.772.9303547663755-0.230354766375541
487272.5539473518111-0.553947351811075
4971.271.7850630151026-0.585063015102577
5070.971.0779339982546-0.177933998254616
5170.470.7223986776876-0.32239867768763
527070.0856480723814-0.0856480723814457
5369.769.67718094446560.0228190555343559
5469.269.3985327602012-0.198532760201175
5568.768.35021208357940.349787916420553
5668.668.07407699265770.525923007342271
5768.468.24032795373550.159672046264546
5867.968.0299589801887-0.129958980188704
5967.467.5276890666719-0.127689066671905
6066.567.2296570974365-0.729657097436544
6165.666.2750128766186-0.675012876618624
6264.665.4656700367169-0.865670036716949
6363.864.412052087957-0.612052087957025
646363.4858146662715-0.485814666271452
6562.162.676467021974-0.576467021973976
6661.761.7918653752693-0.0918653752692791
6761.460.90356992509380.496430074906222
6861.160.79555051449860.304449485501429
6961.160.73076344404180.369236555958203
706160.71627288922130.283727110778713
7160.560.6166242500802-0.11662425008015
7260.260.2952155539349-0.0952155539349064
7359.959.9487921654929-0.0487921654929124
7459.459.7297003246345-0.32970032463448
7559.659.19197925816990.40802074183015
7659.559.2676534021450.232346597854956
7759.359.16239347587660.137606524123356
7859.358.98899089825690.311009101743139
7959.158.52797023240690.57202976759315
8058.858.50450933802950.29549066197049

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 84.3 & 86.5014880266812 & -2.20148802668122 \tabularnewline
14 & 84.2 & 84.1877821916304 & 0.0122178083695843 \tabularnewline
15 & 84.1 & 84.0523780981413 & 0.0476219018587045 \tabularnewline
16 & 83.8 & 83.7769481501087 & 0.023051849891317 \tabularnewline
17 & 83.5 & 83.4941735434482 & 0.00582645655184422 \tabularnewline
18 & 83.2 & 83.2154402193831 & -0.0154402193830947 \tabularnewline
19 & 82.8 & 82.2120758081392 & 0.587924191860765 \tabularnewline
20 & 82.2 & 82.1279927217212 & 0.0720072782788463 \tabularnewline
21 & 81.5 & 81.8686929182221 & -0.368692918222109 \tabularnewline
22 & 80.8 & 81.1478943869928 & -0.347894386992792 \tabularnewline
23 & 80.3 & 80.4191557114383 & -0.119155711438268 \tabularnewline
24 & 79.8 & 80.1723211441787 & -0.372321144178656 \tabularnewline
25 & 79.2 & 79.6220124630764 & -0.422012463076371 \tabularnewline
26 & 78.8 & 79.0789109312305 & -0.278910931230499 \tabularnewline
27 & 78.1 & 78.6422000084893 & -0.542200008489345 \tabularnewline
28 & 77.8 & 77.7806947179697 & 0.0193052820302881 \tabularnewline
29 & 77.3 & 77.4863766518298 & -0.186376651829775 \tabularnewline
30 & 76.7 & 77.008779844968 & -0.308779844968043 \tabularnewline
31 & 76.2 & 75.7716284565986 & 0.428371543401383 \tabularnewline
32 & 76.1 & 75.5417941328169 & 0.558205867183133 \tabularnewline
33 & 76.3 & 75.7469485133071 & 0.553051486692908 \tabularnewline
34 & 76.2 & 75.9301185898645 & 0.269881410135483 \tabularnewline
35 & 76.2 & 75.8132518579508 & 0.386748142049157 \tabularnewline
36 & 76.6 & 76.0480085450977 & 0.551991454902321 \tabularnewline
37 & 75.5 & 76.4003796981365 & -0.900379698136533 \tabularnewline
38 & 75.4 & 75.3806765112575 & 0.0193234887425149 \tabularnewline
39 & 75.5 & 75.2260542005572 & 0.273945799442828 \tabularnewline
40 & 75.5 & 75.1788250455194 & 0.321174954480611 \tabularnewline
41 & 75.2 & 75.1807814900385 & 0.0192185099615045 \tabularnewline
42 & 74.9 & 74.9063796646957 & -0.00637966469571438 \tabularnewline
43 & 74.6 & 73.9983596280452 & 0.601640371954829 \tabularnewline
44 & 74.4 & 73.9533412172175 & 0.446658782782478 \tabularnewline
45 & 74 & 74.0544705815275 & -0.0544705815275393 \tabularnewline
46 & 73.3 & 73.6407854112654 & -0.340785411265387 \tabularnewline
47 & 72.7 & 72.9303547663755 & -0.230354766375541 \tabularnewline
48 & 72 & 72.5539473518111 & -0.553947351811075 \tabularnewline
49 & 71.2 & 71.7850630151026 & -0.585063015102577 \tabularnewline
50 & 70.9 & 71.0779339982546 & -0.177933998254616 \tabularnewline
51 & 70.4 & 70.7223986776876 & -0.32239867768763 \tabularnewline
52 & 70 & 70.0856480723814 & -0.0856480723814457 \tabularnewline
53 & 69.7 & 69.6771809444656 & 0.0228190555343559 \tabularnewline
54 & 69.2 & 69.3985327602012 & -0.198532760201175 \tabularnewline
55 & 68.7 & 68.3502120835794 & 0.349787916420553 \tabularnewline
56 & 68.6 & 68.0740769926577 & 0.525923007342271 \tabularnewline
57 & 68.4 & 68.2403279537355 & 0.159672046264546 \tabularnewline
58 & 67.9 & 68.0299589801887 & -0.129958980188704 \tabularnewline
59 & 67.4 & 67.5276890666719 & -0.127689066671905 \tabularnewline
60 & 66.5 & 67.2296570974365 & -0.729657097436544 \tabularnewline
61 & 65.6 & 66.2750128766186 & -0.675012876618624 \tabularnewline
62 & 64.6 & 65.4656700367169 & -0.865670036716949 \tabularnewline
63 & 63.8 & 64.412052087957 & -0.612052087957025 \tabularnewline
64 & 63 & 63.4858146662715 & -0.485814666271452 \tabularnewline
65 & 62.1 & 62.676467021974 & -0.576467021973976 \tabularnewline
66 & 61.7 & 61.7918653752693 & -0.0918653752692791 \tabularnewline
67 & 61.4 & 60.9035699250938 & 0.496430074906222 \tabularnewline
68 & 61.1 & 60.7955505144986 & 0.304449485501429 \tabularnewline
69 & 61.1 & 60.7307634440418 & 0.369236555958203 \tabularnewline
70 & 61 & 60.7162728892213 & 0.283727110778713 \tabularnewline
71 & 60.5 & 60.6166242500802 & -0.11662425008015 \tabularnewline
72 & 60.2 & 60.2952155539349 & -0.0952155539349064 \tabularnewline
73 & 59.9 & 59.9487921654929 & -0.0487921654929124 \tabularnewline
74 & 59.4 & 59.7297003246345 & -0.32970032463448 \tabularnewline
75 & 59.6 & 59.1919792581699 & 0.40802074183015 \tabularnewline
76 & 59.5 & 59.267653402145 & 0.232346597854956 \tabularnewline
77 & 59.3 & 59.1623934758766 & 0.137606524123356 \tabularnewline
78 & 59.3 & 58.9889908982569 & 0.311009101743139 \tabularnewline
79 & 59.1 & 58.5279702324069 & 0.57202976759315 \tabularnewline
80 & 58.8 & 58.5045093380295 & 0.29549066197049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294916&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]84.3[/C][C]86.5014880266812[/C][C]-2.20148802668122[/C][/ROW]
[ROW][C]14[/C][C]84.2[/C][C]84.1877821916304[/C][C]0.0122178083695843[/C][/ROW]
[ROW][C]15[/C][C]84.1[/C][C]84.0523780981413[/C][C]0.0476219018587045[/C][/ROW]
[ROW][C]16[/C][C]83.8[/C][C]83.7769481501087[/C][C]0.023051849891317[/C][/ROW]
[ROW][C]17[/C][C]83.5[/C][C]83.4941735434482[/C][C]0.00582645655184422[/C][/ROW]
[ROW][C]18[/C][C]83.2[/C][C]83.2154402193831[/C][C]-0.0154402193830947[/C][/ROW]
[ROW][C]19[/C][C]82.8[/C][C]82.2120758081392[/C][C]0.587924191860765[/C][/ROW]
[ROW][C]20[/C][C]82.2[/C][C]82.1279927217212[/C][C]0.0720072782788463[/C][/ROW]
[ROW][C]21[/C][C]81.5[/C][C]81.8686929182221[/C][C]-0.368692918222109[/C][/ROW]
[ROW][C]22[/C][C]80.8[/C][C]81.1478943869928[/C][C]-0.347894386992792[/C][/ROW]
[ROW][C]23[/C][C]80.3[/C][C]80.4191557114383[/C][C]-0.119155711438268[/C][/ROW]
[ROW][C]24[/C][C]79.8[/C][C]80.1723211441787[/C][C]-0.372321144178656[/C][/ROW]
[ROW][C]25[/C][C]79.2[/C][C]79.6220124630764[/C][C]-0.422012463076371[/C][/ROW]
[ROW][C]26[/C][C]78.8[/C][C]79.0789109312305[/C][C]-0.278910931230499[/C][/ROW]
[ROW][C]27[/C][C]78.1[/C][C]78.6422000084893[/C][C]-0.542200008489345[/C][/ROW]
[ROW][C]28[/C][C]77.8[/C][C]77.7806947179697[/C][C]0.0193052820302881[/C][/ROW]
[ROW][C]29[/C][C]77.3[/C][C]77.4863766518298[/C][C]-0.186376651829775[/C][/ROW]
[ROW][C]30[/C][C]76.7[/C][C]77.008779844968[/C][C]-0.308779844968043[/C][/ROW]
[ROW][C]31[/C][C]76.2[/C][C]75.7716284565986[/C][C]0.428371543401383[/C][/ROW]
[ROW][C]32[/C][C]76.1[/C][C]75.5417941328169[/C][C]0.558205867183133[/C][/ROW]
[ROW][C]33[/C][C]76.3[/C][C]75.7469485133071[/C][C]0.553051486692908[/C][/ROW]
[ROW][C]34[/C][C]76.2[/C][C]75.9301185898645[/C][C]0.269881410135483[/C][/ROW]
[ROW][C]35[/C][C]76.2[/C][C]75.8132518579508[/C][C]0.386748142049157[/C][/ROW]
[ROW][C]36[/C][C]76.6[/C][C]76.0480085450977[/C][C]0.551991454902321[/C][/ROW]
[ROW][C]37[/C][C]75.5[/C][C]76.4003796981365[/C][C]-0.900379698136533[/C][/ROW]
[ROW][C]38[/C][C]75.4[/C][C]75.3806765112575[/C][C]0.0193234887425149[/C][/ROW]
[ROW][C]39[/C][C]75.5[/C][C]75.2260542005572[/C][C]0.273945799442828[/C][/ROW]
[ROW][C]40[/C][C]75.5[/C][C]75.1788250455194[/C][C]0.321174954480611[/C][/ROW]
[ROW][C]41[/C][C]75.2[/C][C]75.1807814900385[/C][C]0.0192185099615045[/C][/ROW]
[ROW][C]42[/C][C]74.9[/C][C]74.9063796646957[/C][C]-0.00637966469571438[/C][/ROW]
[ROW][C]43[/C][C]74.6[/C][C]73.9983596280452[/C][C]0.601640371954829[/C][/ROW]
[ROW][C]44[/C][C]74.4[/C][C]73.9533412172175[/C][C]0.446658782782478[/C][/ROW]
[ROW][C]45[/C][C]74[/C][C]74.0544705815275[/C][C]-0.0544705815275393[/C][/ROW]
[ROW][C]46[/C][C]73.3[/C][C]73.6407854112654[/C][C]-0.340785411265387[/C][/ROW]
[ROW][C]47[/C][C]72.7[/C][C]72.9303547663755[/C][C]-0.230354766375541[/C][/ROW]
[ROW][C]48[/C][C]72[/C][C]72.5539473518111[/C][C]-0.553947351811075[/C][/ROW]
[ROW][C]49[/C][C]71.2[/C][C]71.7850630151026[/C][C]-0.585063015102577[/C][/ROW]
[ROW][C]50[/C][C]70.9[/C][C]71.0779339982546[/C][C]-0.177933998254616[/C][/ROW]
[ROW][C]51[/C][C]70.4[/C][C]70.7223986776876[/C][C]-0.32239867768763[/C][/ROW]
[ROW][C]52[/C][C]70[/C][C]70.0856480723814[/C][C]-0.0856480723814457[/C][/ROW]
[ROW][C]53[/C][C]69.7[/C][C]69.6771809444656[/C][C]0.0228190555343559[/C][/ROW]
[ROW][C]54[/C][C]69.2[/C][C]69.3985327602012[/C][C]-0.198532760201175[/C][/ROW]
[ROW][C]55[/C][C]68.7[/C][C]68.3502120835794[/C][C]0.349787916420553[/C][/ROW]
[ROW][C]56[/C][C]68.6[/C][C]68.0740769926577[/C][C]0.525923007342271[/C][/ROW]
[ROW][C]57[/C][C]68.4[/C][C]68.2403279537355[/C][C]0.159672046264546[/C][/ROW]
[ROW][C]58[/C][C]67.9[/C][C]68.0299589801887[/C][C]-0.129958980188704[/C][/ROW]
[ROW][C]59[/C][C]67.4[/C][C]67.5276890666719[/C][C]-0.127689066671905[/C][/ROW]
[ROW][C]60[/C][C]66.5[/C][C]67.2296570974365[/C][C]-0.729657097436544[/C][/ROW]
[ROW][C]61[/C][C]65.6[/C][C]66.2750128766186[/C][C]-0.675012876618624[/C][/ROW]
[ROW][C]62[/C][C]64.6[/C][C]65.4656700367169[/C][C]-0.865670036716949[/C][/ROW]
[ROW][C]63[/C][C]63.8[/C][C]64.412052087957[/C][C]-0.612052087957025[/C][/ROW]
[ROW][C]64[/C][C]63[/C][C]63.4858146662715[/C][C]-0.485814666271452[/C][/ROW]
[ROW][C]65[/C][C]62.1[/C][C]62.676467021974[/C][C]-0.576467021973976[/C][/ROW]
[ROW][C]66[/C][C]61.7[/C][C]61.7918653752693[/C][C]-0.0918653752692791[/C][/ROW]
[ROW][C]67[/C][C]61.4[/C][C]60.9035699250938[/C][C]0.496430074906222[/C][/ROW]
[ROW][C]68[/C][C]61.1[/C][C]60.7955505144986[/C][C]0.304449485501429[/C][/ROW]
[ROW][C]69[/C][C]61.1[/C][C]60.7307634440418[/C][C]0.369236555958203[/C][/ROW]
[ROW][C]70[/C][C]61[/C][C]60.7162728892213[/C][C]0.283727110778713[/C][/ROW]
[ROW][C]71[/C][C]60.5[/C][C]60.6166242500802[/C][C]-0.11662425008015[/C][/ROW]
[ROW][C]72[/C][C]60.2[/C][C]60.2952155539349[/C][C]-0.0952155539349064[/C][/ROW]
[ROW][C]73[/C][C]59.9[/C][C]59.9487921654929[/C][C]-0.0487921654929124[/C][/ROW]
[ROW][C]74[/C][C]59.4[/C][C]59.7297003246345[/C][C]-0.32970032463448[/C][/ROW]
[ROW][C]75[/C][C]59.6[/C][C]59.1919792581699[/C][C]0.40802074183015[/C][/ROW]
[ROW][C]76[/C][C]59.5[/C][C]59.267653402145[/C][C]0.232346597854956[/C][/ROW]
[ROW][C]77[/C][C]59.3[/C][C]59.1623934758766[/C][C]0.137606524123356[/C][/ROW]
[ROW][C]78[/C][C]59.3[/C][C]58.9889908982569[/C][C]0.311009101743139[/C][/ROW]
[ROW][C]79[/C][C]59.1[/C][C]58.5279702324069[/C][C]0.57202976759315[/C][/ROW]
[ROW][C]80[/C][C]58.8[/C][C]58.5045093380295[/C][C]0.29549066197049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294916&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294916&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
1384.386.5014880266812-2.20148802668122
1484.284.18778219163040.0122178083695843
1584.184.05237809814130.0476219018587045
1683.883.77694815010870.023051849891317
1783.583.49417354344820.00582645655184422
1883.283.2154402193831-0.0154402193830947
1982.882.21207580813920.587924191860765
2082.282.12799272172120.0720072782788463
2181.581.8686929182221-0.368692918222109
2280.881.1478943869928-0.347894386992792
2380.380.4191557114383-0.119155711438268
2479.880.1723211441787-0.372321144178656
2579.279.6220124630764-0.422012463076371
2678.879.0789109312305-0.278910931230499
2778.178.6422000084893-0.542200008489345
2877.877.78069471796970.0193052820302881
2977.377.4863766518298-0.186376651829775
3076.777.008779844968-0.308779844968043
3176.275.77162845659860.428371543401383
3276.175.54179413281690.558205867183133
3376.375.74694851330710.553051486692908
3476.275.93011858986450.269881410135483
3576.275.81325185795080.386748142049157
3676.676.04800854509770.551991454902321
3775.576.4003796981365-0.900379698136533
3875.475.38067651125750.0193234887425149
3975.575.22605420055720.273945799442828
4075.575.17882504551940.321174954480611
4175.275.18078149003850.0192185099615045
4274.974.9063796646957-0.00637966469571438
4374.673.99835962804520.601640371954829
4474.473.95334121721750.446658782782478
457474.0544705815275-0.0544705815275393
4673.373.6407854112654-0.340785411265387
4772.772.9303547663755-0.230354766375541
487272.5539473518111-0.553947351811075
4971.271.7850630151026-0.585063015102577
5070.971.0779339982546-0.177933998254616
5170.470.7223986776876-0.32239867768763
527070.0856480723814-0.0856480723814457
5369.769.67718094446560.0228190555343559
5469.269.3985327602012-0.198532760201175
5568.768.35021208357940.349787916420553
5668.668.07407699265770.525923007342271
5768.468.24032795373550.159672046264546
5867.968.0299589801887-0.129958980188704
5967.467.5276890666719-0.127689066671905
6066.567.2296570974365-0.729657097436544
6165.666.2750128766186-0.675012876618624
6264.665.4656700367169-0.865670036716949
6363.864.412052087957-0.612052087957025
646363.4858146662715-0.485814666271452
6562.162.676467021974-0.576467021973976
6661.761.7918653752693-0.0918653752692791
6761.460.90356992509380.496430074906222
6861.160.79555051449860.304449485501429
6961.160.73076344404180.369236555958203
706160.71627288922130.283727110778713
7160.560.6166242500802-0.11662425008015
7260.260.2952155539349-0.0952155539349064
7359.959.9487921654929-0.0487921654929124
7459.459.7297003246345-0.32970032463448
7559.659.19197925816990.40802074183015
7659.559.2676534021450.232346597854956
7759.359.16239347587660.137606524123356
7859.358.98899089825690.311009101743139
7959.158.52797023240690.57202976759315
8058.858.50450933802950.29549066197049







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8158.436898314101357.523712608838859.3500840193638
8258.062965267158956.781698139245459.3442323950724
8357.682079676655756.11612039327359.2480389600385
8457.472011783133555.660837633055459.2831859332116
8557.218794777947955.191049754279259.2465398016166
8657.038188970590554.810934820901359.2654431202796
8756.835579649224254.42410479742659.2470545010224
8856.509486035992853.930095878937459.0888761930482
8956.176160392948553.438553643683358.9137671422138
9055.870554225706152.98128374097858.7598247104343
9155.134066089473352.121152518810258.1469796601364
9254.560351537147150.613137792070358.507565282224

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 58.4368983141013 & 57.5237126088388 & 59.3500840193638 \tabularnewline
82 & 58.0629652671589 & 56.7816981392454 & 59.3442323950724 \tabularnewline
83 & 57.6820796766557 & 56.116120393273 & 59.2480389600385 \tabularnewline
84 & 57.4720117831335 & 55.6608376330554 & 59.2831859332116 \tabularnewline
85 & 57.2187947779479 & 55.1910497542792 & 59.2465398016166 \tabularnewline
86 & 57.0381889705905 & 54.8109348209013 & 59.2654431202796 \tabularnewline
87 & 56.8355796492242 & 54.424104797426 & 59.2470545010224 \tabularnewline
88 & 56.5094860359928 & 53.9300958789374 & 59.0888761930482 \tabularnewline
89 & 56.1761603929485 & 53.4385536436833 & 58.9137671422138 \tabularnewline
90 & 55.8705542257061 & 52.981283740978 & 58.7598247104343 \tabularnewline
91 & 55.1340660894733 & 52.1211525188102 & 58.1469796601364 \tabularnewline
92 & 54.5603515371471 & 50.6131377920703 & 58.507565282224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294916&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]58.4368983141013[/C][C]57.5237126088388[/C][C]59.3500840193638[/C][/ROW]
[ROW][C]82[/C][C]58.0629652671589[/C][C]56.7816981392454[/C][C]59.3442323950724[/C][/ROW]
[ROW][C]83[/C][C]57.6820796766557[/C][C]56.116120393273[/C][C]59.2480389600385[/C][/ROW]
[ROW][C]84[/C][C]57.4720117831335[/C][C]55.6608376330554[/C][C]59.2831859332116[/C][/ROW]
[ROW][C]85[/C][C]57.2187947779479[/C][C]55.1910497542792[/C][C]59.2465398016166[/C][/ROW]
[ROW][C]86[/C][C]57.0381889705905[/C][C]54.8109348209013[/C][C]59.2654431202796[/C][/ROW]
[ROW][C]87[/C][C]56.8355796492242[/C][C]54.424104797426[/C][C]59.2470545010224[/C][/ROW]
[ROW][C]88[/C][C]56.5094860359928[/C][C]53.9300958789374[/C][C]59.0888761930482[/C][/ROW]
[ROW][C]89[/C][C]56.1761603929485[/C][C]53.4385536436833[/C][C]58.9137671422138[/C][/ROW]
[ROW][C]90[/C][C]55.8705542257061[/C][C]52.981283740978[/C][C]58.7598247104343[/C][/ROW]
[ROW][C]91[/C][C]55.1340660894733[/C][C]52.1211525188102[/C][C]58.1469796601364[/C][/ROW]
[ROW][C]92[/C][C]54.5603515371471[/C][C]50.6131377920703[/C][C]58.507565282224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294916&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294916&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
8158.436898314101357.523712608838859.3500840193638
8258.062965267158956.781698139245459.3442323950724
8357.682079676655756.11612039327359.2480389600385
8457.472011783133555.660837633055459.2831859332116
8557.218794777947955.191049754279259.2465398016166
8657.038188970590554.810934820901359.2654431202796
8756.835579649224254.42410479742659.2470545010224
8856.509486035992853.930095878937459.0888761930482
8956.176160392948553.438553643683358.9137671422138
9055.870554225706152.98128374097858.7598247104343
9155.134066089473352.121152518810258.1469796601364
9254.560351537147150.613137792070358.507565282224



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')