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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:12:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356081309pqgxlhtbbv4d0k6.htm/, Retrieved Fri, 26 Apr 2024 09:15:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203341, Retrieved Fri, 26 Apr 2024 09:15:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2012-12-21 09:02:41] [873b10c79bed0b14ae85834791a7b7d7]
-    D    [Exponential Smoothing] [] [2012-12-21 09:12:36] [e3cb5e3bac8dbaf27c4382afdd169712] [Current]
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Dataseries X:
65
65,3
62,9
63,5
62,1
59,3
61,6
61,5
60,1
59,5
62,7
65,5
63,8
63,8
62,7
62,3
62,4
64,8
66,4
65,1
67,4
68,8
68,6
71,5
75
84,3
84
79,1
78,8
82,7
85,3
84,5
80,8
70,1
68,2
68,1
72,3
73,1
71,5
74,1
80,3
80,6
81,4
87,4
89,3
93,2
92,8
96,8
100,3
95,6
89
87,4
86,7
92,8
98,6
100,8
105,5
107,8
113,7
120,3
126,5
134,8
134,5
133,1
128,8
127,1
129,1
128,4
126,5
117,1
114,2
109,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203341&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203341&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203341&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.988844701934931
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.988844701934931 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203341&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]0.988844701934931[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203341&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203341&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
alpha0.988844701934931
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1363.863.09369393575230.706306064247656
1463.863.73090441400980.0690955859902189
1562.762.53672087602850.163279123971456
1662.361.90818095840870.391819041591312
1762.462.06492016111810.335079838881875
1864.864.59156003617380.208439963826223
1966.464.86311210298091.53688789701907
2065.166.6807553996375-1.5807553996375
2167.463.98747639348713.41252360651288
2268.867.02922854657621.77077145342381
2368.672.8153876532482-4.21538765324817
2471.571.7386785787489-0.238678578748889
257569.47338214664375.52661785335627
2684.374.8070156981069.492984301894
278482.43814825560171.56185174439834
2879.182.8325520601034-3.73255206010342
2978.878.7724913886270.0275086113729941
3082.781.49477231808481.2052276819152
3185.382.70954231620042.59045768379957
3284.585.527229563598-1.02722956359804
3380.883.0306970729376-2.23069707293764
3470.180.3481222047624-10.2481222047624
3568.274.2553442992539-6.05534429925395
3668.171.3898324527334-3.28983245273341
3772.366.27373057416616.0262694258339
3873.172.1483386194660.951661380534006
3971.571.5279313138994-0.0279313138993729
4074.170.51122820204423.58877179795581
4180.373.77134697081776.52865302918228
4280.682.9790442269433-2.37904422694329
4381.480.67033955426330.729660445736741
4487.481.61070717775215.78929282224794
4589.385.78100388419183.51899611580819
4693.288.58804601571524.61195398428484
4792.898.4765899878402-5.67658998784019
4896.897.0444279054893-0.244427905489303
49100.394.1701630111326.12983698886795
5095.699.9227044669906-4.32270446699056
518993.5027507778352-4.50275077783525
5287.487.7973454822356-0.397345482235551
5386.787.0457452085662-0.345745208566242
5492.889.54419030064573.25580969935429
5598.692.81075184244965.78924815755042
56100.898.80332991185251.99667008814748
57105.598.91157825203236.58842174796773
58107.8104.5937296929383.20627030706181
59113.7113.742179554122-0.0421795541223702
60120.3118.8290276736921.47097232630811
61126.5117.024031230479.47596876952986
62134.8125.7791705679599.0208294320414
63134.5131.5533386836482.94666131635242
64133.1132.4999963810070.600003618993412
65128.8132.402311807597-3.60231180759718
66127.1132.979436686886-5.87943668688646
67129.1127.1576776720961.94232232790367
68128.4129.284678246676-0.884678246676344
69126.5126.0153145171510.48468548284869
70117.1125.394464232703-8.29446423270306
71114.2123.626528165896-9.42652816589558
72109.1119.476161149293-10.3761611492931

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 63.8 & 63.0936939357523 & 0.706306064247656 \tabularnewline
14 & 63.8 & 63.7309044140098 & 0.0690955859902189 \tabularnewline
15 & 62.7 & 62.5367208760285 & 0.163279123971456 \tabularnewline
16 & 62.3 & 61.9081809584087 & 0.391819041591312 \tabularnewline
17 & 62.4 & 62.0649201611181 & 0.335079838881875 \tabularnewline
18 & 64.8 & 64.5915600361738 & 0.208439963826223 \tabularnewline
19 & 66.4 & 64.8631121029809 & 1.53688789701907 \tabularnewline
20 & 65.1 & 66.6807553996375 & -1.5807553996375 \tabularnewline
21 & 67.4 & 63.9874763934871 & 3.41252360651288 \tabularnewline
22 & 68.8 & 67.0292285465762 & 1.77077145342381 \tabularnewline
23 & 68.6 & 72.8153876532482 & -4.21538765324817 \tabularnewline
24 & 71.5 & 71.7386785787489 & -0.238678578748889 \tabularnewline
25 & 75 & 69.4733821466437 & 5.52661785335627 \tabularnewline
26 & 84.3 & 74.807015698106 & 9.492984301894 \tabularnewline
27 & 84 & 82.4381482556017 & 1.56185174439834 \tabularnewline
28 & 79.1 & 82.8325520601034 & -3.73255206010342 \tabularnewline
29 & 78.8 & 78.772491388627 & 0.0275086113729941 \tabularnewline
30 & 82.7 & 81.4947723180848 & 1.2052276819152 \tabularnewline
31 & 85.3 & 82.7095423162004 & 2.59045768379957 \tabularnewline
32 & 84.5 & 85.527229563598 & -1.02722956359804 \tabularnewline
33 & 80.8 & 83.0306970729376 & -2.23069707293764 \tabularnewline
34 & 70.1 & 80.3481222047624 & -10.2481222047624 \tabularnewline
35 & 68.2 & 74.2553442992539 & -6.05534429925395 \tabularnewline
36 & 68.1 & 71.3898324527334 & -3.28983245273341 \tabularnewline
37 & 72.3 & 66.2737305741661 & 6.0262694258339 \tabularnewline
38 & 73.1 & 72.148338619466 & 0.951661380534006 \tabularnewline
39 & 71.5 & 71.5279313138994 & -0.0279313138993729 \tabularnewline
40 & 74.1 & 70.5112282020442 & 3.58877179795581 \tabularnewline
41 & 80.3 & 73.7713469708177 & 6.52865302918228 \tabularnewline
42 & 80.6 & 82.9790442269433 & -2.37904422694329 \tabularnewline
43 & 81.4 & 80.6703395542633 & 0.729660445736741 \tabularnewline
44 & 87.4 & 81.6107071777521 & 5.78929282224794 \tabularnewline
45 & 89.3 & 85.7810038841918 & 3.51899611580819 \tabularnewline
46 & 93.2 & 88.5880460157152 & 4.61195398428484 \tabularnewline
47 & 92.8 & 98.4765899878402 & -5.67658998784019 \tabularnewline
48 & 96.8 & 97.0444279054893 & -0.244427905489303 \tabularnewline
49 & 100.3 & 94.170163011132 & 6.12983698886795 \tabularnewline
50 & 95.6 & 99.9227044669906 & -4.32270446699056 \tabularnewline
51 & 89 & 93.5027507778352 & -4.50275077783525 \tabularnewline
52 & 87.4 & 87.7973454822356 & -0.397345482235551 \tabularnewline
53 & 86.7 & 87.0457452085662 & -0.345745208566242 \tabularnewline
54 & 92.8 & 89.5441903006457 & 3.25580969935429 \tabularnewline
55 & 98.6 & 92.8107518424496 & 5.78924815755042 \tabularnewline
56 & 100.8 & 98.8033299118525 & 1.99667008814748 \tabularnewline
57 & 105.5 & 98.9115782520323 & 6.58842174796773 \tabularnewline
58 & 107.8 & 104.593729692938 & 3.20627030706181 \tabularnewline
59 & 113.7 & 113.742179554122 & -0.0421795541223702 \tabularnewline
60 & 120.3 & 118.829027673692 & 1.47097232630811 \tabularnewline
61 & 126.5 & 117.02403123047 & 9.47596876952986 \tabularnewline
62 & 134.8 & 125.779170567959 & 9.0208294320414 \tabularnewline
63 & 134.5 & 131.553338683648 & 2.94666131635242 \tabularnewline
64 & 133.1 & 132.499996381007 & 0.600003618993412 \tabularnewline
65 & 128.8 & 132.402311807597 & -3.60231180759718 \tabularnewline
66 & 127.1 & 132.979436686886 & -5.87943668688646 \tabularnewline
67 & 129.1 & 127.157677672096 & 1.94232232790367 \tabularnewline
68 & 128.4 & 129.284678246676 & -0.884678246676344 \tabularnewline
69 & 126.5 & 126.015314517151 & 0.48468548284869 \tabularnewline
70 & 117.1 & 125.394464232703 & -8.29446423270306 \tabularnewline
71 & 114.2 & 123.626528165896 & -9.42652816589558 \tabularnewline
72 & 109.1 & 119.476161149293 & -10.3761611492931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203341&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]63.8[/C][C]63.0936939357523[/C][C]0.706306064247656[/C][/ROW]
[ROW][C]14[/C][C]63.8[/C][C]63.7309044140098[/C][C]0.0690955859902189[/C][/ROW]
[ROW][C]15[/C][C]62.7[/C][C]62.5367208760285[/C][C]0.163279123971456[/C][/ROW]
[ROW][C]16[/C][C]62.3[/C][C]61.9081809584087[/C][C]0.391819041591312[/C][/ROW]
[ROW][C]17[/C][C]62.4[/C][C]62.0649201611181[/C][C]0.335079838881875[/C][/ROW]
[ROW][C]18[/C][C]64.8[/C][C]64.5915600361738[/C][C]0.208439963826223[/C][/ROW]
[ROW][C]19[/C][C]66.4[/C][C]64.8631121029809[/C][C]1.53688789701907[/C][/ROW]
[ROW][C]20[/C][C]65.1[/C][C]66.6807553996375[/C][C]-1.5807553996375[/C][/ROW]
[ROW][C]21[/C][C]67.4[/C][C]63.9874763934871[/C][C]3.41252360651288[/C][/ROW]
[ROW][C]22[/C][C]68.8[/C][C]67.0292285465762[/C][C]1.77077145342381[/C][/ROW]
[ROW][C]23[/C][C]68.6[/C][C]72.8153876532482[/C][C]-4.21538765324817[/C][/ROW]
[ROW][C]24[/C][C]71.5[/C][C]71.7386785787489[/C][C]-0.238678578748889[/C][/ROW]
[ROW][C]25[/C][C]75[/C][C]69.4733821466437[/C][C]5.52661785335627[/C][/ROW]
[ROW][C]26[/C][C]84.3[/C][C]74.807015698106[/C][C]9.492984301894[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]82.4381482556017[/C][C]1.56185174439834[/C][/ROW]
[ROW][C]28[/C][C]79.1[/C][C]82.8325520601034[/C][C]-3.73255206010342[/C][/ROW]
[ROW][C]29[/C][C]78.8[/C][C]78.772491388627[/C][C]0.0275086113729941[/C][/ROW]
[ROW][C]30[/C][C]82.7[/C][C]81.4947723180848[/C][C]1.2052276819152[/C][/ROW]
[ROW][C]31[/C][C]85.3[/C][C]82.7095423162004[/C][C]2.59045768379957[/C][/ROW]
[ROW][C]32[/C][C]84.5[/C][C]85.527229563598[/C][C]-1.02722956359804[/C][/ROW]
[ROW][C]33[/C][C]80.8[/C][C]83.0306970729376[/C][C]-2.23069707293764[/C][/ROW]
[ROW][C]34[/C][C]70.1[/C][C]80.3481222047624[/C][C]-10.2481222047624[/C][/ROW]
[ROW][C]35[/C][C]68.2[/C][C]74.2553442992539[/C][C]-6.05534429925395[/C][/ROW]
[ROW][C]36[/C][C]68.1[/C][C]71.3898324527334[/C][C]-3.28983245273341[/C][/ROW]
[ROW][C]37[/C][C]72.3[/C][C]66.2737305741661[/C][C]6.0262694258339[/C][/ROW]
[ROW][C]38[/C][C]73.1[/C][C]72.148338619466[/C][C]0.951661380534006[/C][/ROW]
[ROW][C]39[/C][C]71.5[/C][C]71.5279313138994[/C][C]-0.0279313138993729[/C][/ROW]
[ROW][C]40[/C][C]74.1[/C][C]70.5112282020442[/C][C]3.58877179795581[/C][/ROW]
[ROW][C]41[/C][C]80.3[/C][C]73.7713469708177[/C][C]6.52865302918228[/C][/ROW]
[ROW][C]42[/C][C]80.6[/C][C]82.9790442269433[/C][C]-2.37904422694329[/C][/ROW]
[ROW][C]43[/C][C]81.4[/C][C]80.6703395542633[/C][C]0.729660445736741[/C][/ROW]
[ROW][C]44[/C][C]87.4[/C][C]81.6107071777521[/C][C]5.78929282224794[/C][/ROW]
[ROW][C]45[/C][C]89.3[/C][C]85.7810038841918[/C][C]3.51899611580819[/C][/ROW]
[ROW][C]46[/C][C]93.2[/C][C]88.5880460157152[/C][C]4.61195398428484[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]98.4765899878402[/C][C]-5.67658998784019[/C][/ROW]
[ROW][C]48[/C][C]96.8[/C][C]97.0444279054893[/C][C]-0.244427905489303[/C][/ROW]
[ROW][C]49[/C][C]100.3[/C][C]94.170163011132[/C][C]6.12983698886795[/C][/ROW]
[ROW][C]50[/C][C]95.6[/C][C]99.9227044669906[/C][C]-4.32270446699056[/C][/ROW]
[ROW][C]51[/C][C]89[/C][C]93.5027507778352[/C][C]-4.50275077783525[/C][/ROW]
[ROW][C]52[/C][C]87.4[/C][C]87.7973454822356[/C][C]-0.397345482235551[/C][/ROW]
[ROW][C]53[/C][C]86.7[/C][C]87.0457452085662[/C][C]-0.345745208566242[/C][/ROW]
[ROW][C]54[/C][C]92.8[/C][C]89.5441903006457[/C][C]3.25580969935429[/C][/ROW]
[ROW][C]55[/C][C]98.6[/C][C]92.8107518424496[/C][C]5.78924815755042[/C][/ROW]
[ROW][C]56[/C][C]100.8[/C][C]98.8033299118525[/C][C]1.99667008814748[/C][/ROW]
[ROW][C]57[/C][C]105.5[/C][C]98.9115782520323[/C][C]6.58842174796773[/C][/ROW]
[ROW][C]58[/C][C]107.8[/C][C]104.593729692938[/C][C]3.20627030706181[/C][/ROW]
[ROW][C]59[/C][C]113.7[/C][C]113.742179554122[/C][C]-0.0421795541223702[/C][/ROW]
[ROW][C]60[/C][C]120.3[/C][C]118.829027673692[/C][C]1.47097232630811[/C][/ROW]
[ROW][C]61[/C][C]126.5[/C][C]117.02403123047[/C][C]9.47596876952986[/C][/ROW]
[ROW][C]62[/C][C]134.8[/C][C]125.779170567959[/C][C]9.0208294320414[/C][/ROW]
[ROW][C]63[/C][C]134.5[/C][C]131.553338683648[/C][C]2.94666131635242[/C][/ROW]
[ROW][C]64[/C][C]133.1[/C][C]132.499996381007[/C][C]0.600003618993412[/C][/ROW]
[ROW][C]65[/C][C]128.8[/C][C]132.402311807597[/C][C]-3.60231180759718[/C][/ROW]
[ROW][C]66[/C][C]127.1[/C][C]132.979436686886[/C][C]-5.87943668688646[/C][/ROW]
[ROW][C]67[/C][C]129.1[/C][C]127.157677672096[/C][C]1.94232232790367[/C][/ROW]
[ROW][C]68[/C][C]128.4[/C][C]129.284678246676[/C][C]-0.884678246676344[/C][/ROW]
[ROW][C]69[/C][C]126.5[/C][C]126.015314517151[/C][C]0.48468548284869[/C][/ROW]
[ROW][C]70[/C][C]117.1[/C][C]125.394464232703[/C][C]-8.29446423270306[/C][/ROW]
[ROW][C]71[/C][C]114.2[/C][C]123.626528165896[/C][C]-9.42652816589558[/C][/ROW]
[ROW][C]72[/C][C]109.1[/C][C]119.476161149293[/C][C]-10.3761611492931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203341&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203341&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
1363.863.09369393575230.706306064247656
1463.863.73090441400980.0690955859902189
1562.762.53672087602850.163279123971456
1662.361.90818095840870.391819041591312
1762.462.06492016111810.335079838881875
1864.864.59156003617380.208439963826223
1966.464.86311210298091.53688789701907
2065.166.6807553996375-1.5807553996375
2167.463.98747639348713.41252360651288
2268.867.02922854657621.77077145342381
2368.672.8153876532482-4.21538765324817
2471.571.7386785787489-0.238678578748889
257569.47338214664375.52661785335627
2684.374.8070156981069.492984301894
278482.43814825560171.56185174439834
2879.182.8325520601034-3.73255206010342
2978.878.7724913886270.0275086113729941
3082.781.49477231808481.2052276819152
3185.382.70954231620042.59045768379957
3284.585.527229563598-1.02722956359804
3380.883.0306970729376-2.23069707293764
3470.180.3481222047624-10.2481222047624
3568.274.2553442992539-6.05534429925395
3668.171.3898324527334-3.28983245273341
3772.366.27373057416616.0262694258339
3873.172.1483386194660.951661380534006
3971.571.5279313138994-0.0279313138993729
4074.170.51122820204423.58877179795581
4180.373.77134697081776.52865302918228
4280.682.9790442269433-2.37904422694329
4381.480.67033955426330.729660445736741
4487.481.61070717775215.78929282224794
4589.385.78100388419183.51899611580819
4693.288.58804601571524.61195398428484
4792.898.4765899878402-5.67658998784019
4896.897.0444279054893-0.244427905489303
49100.394.1701630111326.12983698886795
5095.699.9227044669906-4.32270446699056
518993.5027507778352-4.50275077783525
5287.487.7973454822356-0.397345482235551
5386.787.0457452085662-0.345745208566242
5492.889.54419030064573.25580969935429
5598.692.81075184244965.78924815755042
56100.898.80332991185251.99667008814748
57105.598.91157825203236.58842174796773
58107.8104.5937296929383.20627030706181
59113.7113.742179554122-0.0421795541223702
60120.3118.8290276736921.47097232630811
61126.5117.024031230479.47596876952986
62134.8125.7791705679599.0208294320414
63134.5131.5533386836482.94666131635242
64133.1132.4999963810070.600003618993412
65128.8132.402311807597-3.60231180759718
66127.1132.979436686886-5.87943668688646
67129.1127.1576776720961.94232232790367
68128.4129.284678246676-0.884678246676344
69126.5126.0153145171510.48468548284869
70117.1125.394464232703-8.29446423270306
71114.2123.626528165896-9.42652816589558
72109.1119.476161149293-10.3761611492931







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73106.35767591291897.4855995376184115.229752288218
74105.8772900774993.4448422094207118.30973794556
75103.41373818561988.457116186077118.370360185161
76101.94596748804784.8221158691816119.069819106912
77101.44513613510682.320430788624120.569841481588
78104.74381501096983.1878974265932126.299732595344
79104.85929311801481.6188868600192128.099699376008
80105.05493227050380.2324414526343129.877423088371
81103.15915404410677.3146999055709129.003608182641
82102.22794654395275.2206914005785129.235201687326
83107.86329527329278.1240251292598137.602565417323
84112.74394616003967.6860278282645157.801864491814

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 106.357675912918 & 97.4855995376184 & 115.229752288218 \tabularnewline
74 & 105.87729007749 & 93.4448422094207 & 118.30973794556 \tabularnewline
75 & 103.413738185619 & 88.457116186077 & 118.370360185161 \tabularnewline
76 & 101.945967488047 & 84.8221158691816 & 119.069819106912 \tabularnewline
77 & 101.445136135106 & 82.320430788624 & 120.569841481588 \tabularnewline
78 & 104.743815010969 & 83.1878974265932 & 126.299732595344 \tabularnewline
79 & 104.859293118014 & 81.6188868600192 & 128.099699376008 \tabularnewline
80 & 105.054932270503 & 80.2324414526343 & 129.877423088371 \tabularnewline
81 & 103.159154044106 & 77.3146999055709 & 129.003608182641 \tabularnewline
82 & 102.227946543952 & 75.2206914005785 & 129.235201687326 \tabularnewline
83 & 107.863295273292 & 78.1240251292598 & 137.602565417323 \tabularnewline
84 & 112.743946160039 & 67.6860278282645 & 157.801864491814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203341&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]106.357675912918[/C][C]97.4855995376184[/C][C]115.229752288218[/C][/ROW]
[ROW][C]74[/C][C]105.87729007749[/C][C]93.4448422094207[/C][C]118.30973794556[/C][/ROW]
[ROW][C]75[/C][C]103.413738185619[/C][C]88.457116186077[/C][C]118.370360185161[/C][/ROW]
[ROW][C]76[/C][C]101.945967488047[/C][C]84.8221158691816[/C][C]119.069819106912[/C][/ROW]
[ROW][C]77[/C][C]101.445136135106[/C][C]82.320430788624[/C][C]120.569841481588[/C][/ROW]
[ROW][C]78[/C][C]104.743815010969[/C][C]83.1878974265932[/C][C]126.299732595344[/C][/ROW]
[ROW][C]79[/C][C]104.859293118014[/C][C]81.6188868600192[/C][C]128.099699376008[/C][/ROW]
[ROW][C]80[/C][C]105.054932270503[/C][C]80.2324414526343[/C][C]129.877423088371[/C][/ROW]
[ROW][C]81[/C][C]103.159154044106[/C][C]77.3146999055709[/C][C]129.003608182641[/C][/ROW]
[ROW][C]82[/C][C]102.227946543952[/C][C]75.2206914005785[/C][C]129.235201687326[/C][/ROW]
[ROW][C]83[/C][C]107.863295273292[/C][C]78.1240251292598[/C][C]137.602565417323[/C][/ROW]
[ROW][C]84[/C][C]112.743946160039[/C][C]67.6860278282645[/C][C]157.801864491814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203341&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203341&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
73106.35767591291897.4855995376184115.229752288218
74105.8772900774993.4448422094207118.30973794556
75103.41373818561988.457116186077118.370360185161
76101.94596748804784.8221158691816119.069819106912
77101.44513613510682.320430788624120.569841481588
78104.74381501096983.1878974265932126.299732595344
79104.85929311801481.6188868600192128.099699376008
80105.05493227050380.2324414526343129.877423088371
81103.15915404410677.3146999055709129.003608182641
82102.22794654395275.2206914005785129.235201687326
83107.86329527329278.1240251292598137.602565417323
84112.74394616003967.6860278282645157.801864491814



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')