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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 May 2008 11:10:53 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/24/t1211649117kazyfr7t17iqj1n.htm/, Retrieved Mon, 13 May 2024 21:25:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13093, Retrieved Mon, 13 May 2024 21:25:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponentiële smoo...] [2008-05-24 17:10:53] [e1b1b3318b3a8a01c97d416cfdcee2a5] [Current]
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Dataseries X:
229,7
231,5
226,4
242,1
228,3
209,9
209,3
220,8
239,6
241,1
241,9
240,8
179,9
190,8
174,2
170
170,3
159,3
147,9
154,2
164,5
173,9
163,6
149,7
128,2
124,7
125,1
120,9
117,5
114
113,4
118,9
121,7
121,9
120,3
115,6
105,7
105,1
104,6
105
104,9
105,1
103,9
101,9
99
97
95,8
94,7
97,6
97,9
99,3
99,7
99,7
100
99,1
98,2
98,1
98,6
100,2
101,9
97,5
97,1
98,1
98,5
98,3
99,3
100,9
100,4
101,7
102
103,2
103,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13093&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13093&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.72476947564924
beta0.0542023038794262
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.72476947564924 \tabularnewline
beta & 0.0542023038794262 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13093&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]0.72476947564924[/C][/ROW]
[ROW][C]beta[/C][C]0.0542023038794262[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13093&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
alpha0.72476947564924
beta0.0542023038794262
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13179.9209.963722222222-30.0637222222223
14190.8198.354490712747-7.55449071274671
15174.2175.833324517067-1.63332451706680
16170169.9644750335110.0355249664891630
17170.3169.9398856174360.360114382564149
18159.3159.860528832139-0.560528832139084
19147.9147.5835647005910.316435299408568
20154.2152.6129616359551.58703836404527
21164.5162.5172650482991.98273495170139
22173.9171.1779140431992.72208595680084
23163.6160.9355236471302.66447635287039
24149.7146.9977179915872.70228200841314
25128.2106.56068227699221.6393177230075
26124.7139.572563048663-14.8725630486633
27125.1114.04278218265411.0572178173459
28120.9118.9951213239681.90487867603244
29117.5121.652307942916-4.152307942916
30114109.109417902184.89058209782003
31113.4102.29908409852511.1009159014746
32118.9117.1925757795931.70742422040669
33121.7128.995891871199-7.29589187119883
34121.9132.473517036474-10.5735170364740
35120.3113.3950664122446.90493358775596
36115.6103.52364576258312.0763542374170
37105.776.44358019761829.2564198023820
38105.1106.577029999478-1.47702999947767
39104.6100.0689322909614.53106770903867
4010599.69228202341825.30771797658178
41104.9105.202265868580-0.302265868580420
42105.1100.1435397187044.95646028129627
43103.997.29770535868686.60229464131319
44101.9108.376112918518-6.47611291851804
4599113.479535063656-14.4795350636563
4697112.275640310766-15.2756403107663
4795.895.842186246003-0.0421862460029701
4894.783.328474989660511.3715250103395
4997.661.407797509693536.1922024903065
5097.989.323522233318.57647776669005
5199.393.36467056555255.93532943444754
5299.795.88386806262833.81613193737174
5399.7100.374485223279-0.67448522327885
5410098.08445361443121.91554638556885
5599.194.95928755578854.1407124442115
5698.2102.028983297469-3.82898329746858
5798.1108.327113211137-10.227113211137
5898.6111.632119530416-13.0321195304159
59100.2102.751535239396-2.55153523939578
60101.993.19607130110478.70392869889528
6197.577.704160335850319.7958396641497
6297.187.022244599884310.0777554001157
6398.192.37015817324855.72984182675145
6498.595.09469395341483.40530604658520
6598.398.9730004435915-0.673000443591505
6699.398.3183573546320.98164264536797
67100.996.01352899378854.88647100621154
68100.4102.344289750442-1.94428975044234
69101.7109.235531509680-7.53553150968033
70102114.813131437624-12.8131314376242
71103.2110.078283218645-6.87828321864468
72103.1101.4172424082861.68275759171392

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 179.9 & 209.963722222222 & -30.0637222222223 \tabularnewline
14 & 190.8 & 198.354490712747 & -7.55449071274671 \tabularnewline
15 & 174.2 & 175.833324517067 & -1.63332451706680 \tabularnewline
16 & 170 & 169.964475033511 & 0.0355249664891630 \tabularnewline
17 & 170.3 & 169.939885617436 & 0.360114382564149 \tabularnewline
18 & 159.3 & 159.860528832139 & -0.560528832139084 \tabularnewline
19 & 147.9 & 147.583564700591 & 0.316435299408568 \tabularnewline
20 & 154.2 & 152.612961635955 & 1.58703836404527 \tabularnewline
21 & 164.5 & 162.517265048299 & 1.98273495170139 \tabularnewline
22 & 173.9 & 171.177914043199 & 2.72208595680084 \tabularnewline
23 & 163.6 & 160.935523647130 & 2.66447635287039 \tabularnewline
24 & 149.7 & 146.997717991587 & 2.70228200841314 \tabularnewline
25 & 128.2 & 106.560682276992 & 21.6393177230075 \tabularnewline
26 & 124.7 & 139.572563048663 & -14.8725630486633 \tabularnewline
27 & 125.1 & 114.042782182654 & 11.0572178173459 \tabularnewline
28 & 120.9 & 118.995121323968 & 1.90487867603244 \tabularnewline
29 & 117.5 & 121.652307942916 & -4.152307942916 \tabularnewline
30 & 114 & 109.10941790218 & 4.89058209782003 \tabularnewline
31 & 113.4 & 102.299084098525 & 11.1009159014746 \tabularnewline
32 & 118.9 & 117.192575779593 & 1.70742422040669 \tabularnewline
33 & 121.7 & 128.995891871199 & -7.29589187119883 \tabularnewline
34 & 121.9 & 132.473517036474 & -10.5735170364740 \tabularnewline
35 & 120.3 & 113.395066412244 & 6.90493358775596 \tabularnewline
36 & 115.6 & 103.523645762583 & 12.0763542374170 \tabularnewline
37 & 105.7 & 76.443580197618 & 29.2564198023820 \tabularnewline
38 & 105.1 & 106.577029999478 & -1.47702999947767 \tabularnewline
39 & 104.6 & 100.068932290961 & 4.53106770903867 \tabularnewline
40 & 105 & 99.6922820234182 & 5.30771797658178 \tabularnewline
41 & 104.9 & 105.202265868580 & -0.302265868580420 \tabularnewline
42 & 105.1 & 100.143539718704 & 4.95646028129627 \tabularnewline
43 & 103.9 & 97.2977053586868 & 6.60229464131319 \tabularnewline
44 & 101.9 & 108.376112918518 & -6.47611291851804 \tabularnewline
45 & 99 & 113.479535063656 & -14.4795350636563 \tabularnewline
46 & 97 & 112.275640310766 & -15.2756403107663 \tabularnewline
47 & 95.8 & 95.842186246003 & -0.0421862460029701 \tabularnewline
48 & 94.7 & 83.3284749896605 & 11.3715250103395 \tabularnewline
49 & 97.6 & 61.4077975096935 & 36.1922024903065 \tabularnewline
50 & 97.9 & 89.32352223331 & 8.57647776669005 \tabularnewline
51 & 99.3 & 93.3646705655525 & 5.93532943444754 \tabularnewline
52 & 99.7 & 95.8838680626283 & 3.81613193737174 \tabularnewline
53 & 99.7 & 100.374485223279 & -0.67448522327885 \tabularnewline
54 & 100 & 98.0844536144312 & 1.91554638556885 \tabularnewline
55 & 99.1 & 94.9592875557885 & 4.1407124442115 \tabularnewline
56 & 98.2 & 102.028983297469 & -3.82898329746858 \tabularnewline
57 & 98.1 & 108.327113211137 & -10.227113211137 \tabularnewline
58 & 98.6 & 111.632119530416 & -13.0321195304159 \tabularnewline
59 & 100.2 & 102.751535239396 & -2.55153523939578 \tabularnewline
60 & 101.9 & 93.1960713011047 & 8.70392869889528 \tabularnewline
61 & 97.5 & 77.7041603358503 & 19.7958396641497 \tabularnewline
62 & 97.1 & 87.0222445998843 & 10.0777554001157 \tabularnewline
63 & 98.1 & 92.3701581732485 & 5.72984182675145 \tabularnewline
64 & 98.5 & 95.0946939534148 & 3.40530604658520 \tabularnewline
65 & 98.3 & 98.9730004435915 & -0.673000443591505 \tabularnewline
66 & 99.3 & 98.318357354632 & 0.98164264536797 \tabularnewline
67 & 100.9 & 96.0135289937885 & 4.88647100621154 \tabularnewline
68 & 100.4 & 102.344289750442 & -1.94428975044234 \tabularnewline
69 & 101.7 & 109.235531509680 & -7.53553150968033 \tabularnewline
70 & 102 & 114.813131437624 & -12.8131314376242 \tabularnewline
71 & 103.2 & 110.078283218645 & -6.87828321864468 \tabularnewline
72 & 103.1 & 101.417242408286 & 1.68275759171392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13093&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]179.9[/C][C]209.963722222222[/C][C]-30.0637222222223[/C][/ROW]
[ROW][C]14[/C][C]190.8[/C][C]198.354490712747[/C][C]-7.55449071274671[/C][/ROW]
[ROW][C]15[/C][C]174.2[/C][C]175.833324517067[/C][C]-1.63332451706680[/C][/ROW]
[ROW][C]16[/C][C]170[/C][C]169.964475033511[/C][C]0.0355249664891630[/C][/ROW]
[ROW][C]17[/C][C]170.3[/C][C]169.939885617436[/C][C]0.360114382564149[/C][/ROW]
[ROW][C]18[/C][C]159.3[/C][C]159.860528832139[/C][C]-0.560528832139084[/C][/ROW]
[ROW][C]19[/C][C]147.9[/C][C]147.583564700591[/C][C]0.316435299408568[/C][/ROW]
[ROW][C]20[/C][C]154.2[/C][C]152.612961635955[/C][C]1.58703836404527[/C][/ROW]
[ROW][C]21[/C][C]164.5[/C][C]162.517265048299[/C][C]1.98273495170139[/C][/ROW]
[ROW][C]22[/C][C]173.9[/C][C]171.177914043199[/C][C]2.72208595680084[/C][/ROW]
[ROW][C]23[/C][C]163.6[/C][C]160.935523647130[/C][C]2.66447635287039[/C][/ROW]
[ROW][C]24[/C][C]149.7[/C][C]146.997717991587[/C][C]2.70228200841314[/C][/ROW]
[ROW][C]25[/C][C]128.2[/C][C]106.560682276992[/C][C]21.6393177230075[/C][/ROW]
[ROW][C]26[/C][C]124.7[/C][C]139.572563048663[/C][C]-14.8725630486633[/C][/ROW]
[ROW][C]27[/C][C]125.1[/C][C]114.042782182654[/C][C]11.0572178173459[/C][/ROW]
[ROW][C]28[/C][C]120.9[/C][C]118.995121323968[/C][C]1.90487867603244[/C][/ROW]
[ROW][C]29[/C][C]117.5[/C][C]121.652307942916[/C][C]-4.152307942916[/C][/ROW]
[ROW][C]30[/C][C]114[/C][C]109.10941790218[/C][C]4.89058209782003[/C][/ROW]
[ROW][C]31[/C][C]113.4[/C][C]102.299084098525[/C][C]11.1009159014746[/C][/ROW]
[ROW][C]32[/C][C]118.9[/C][C]117.192575779593[/C][C]1.70742422040669[/C][/ROW]
[ROW][C]33[/C][C]121.7[/C][C]128.995891871199[/C][C]-7.29589187119883[/C][/ROW]
[ROW][C]34[/C][C]121.9[/C][C]132.473517036474[/C][C]-10.5735170364740[/C][/ROW]
[ROW][C]35[/C][C]120.3[/C][C]113.395066412244[/C][C]6.90493358775596[/C][/ROW]
[ROW][C]36[/C][C]115.6[/C][C]103.523645762583[/C][C]12.0763542374170[/C][/ROW]
[ROW][C]37[/C][C]105.7[/C][C]76.443580197618[/C][C]29.2564198023820[/C][/ROW]
[ROW][C]38[/C][C]105.1[/C][C]106.577029999478[/C][C]-1.47702999947767[/C][/ROW]
[ROW][C]39[/C][C]104.6[/C][C]100.068932290961[/C][C]4.53106770903867[/C][/ROW]
[ROW][C]40[/C][C]105[/C][C]99.6922820234182[/C][C]5.30771797658178[/C][/ROW]
[ROW][C]41[/C][C]104.9[/C][C]105.202265868580[/C][C]-0.302265868580420[/C][/ROW]
[ROW][C]42[/C][C]105.1[/C][C]100.143539718704[/C][C]4.95646028129627[/C][/ROW]
[ROW][C]43[/C][C]103.9[/C][C]97.2977053586868[/C][C]6.60229464131319[/C][/ROW]
[ROW][C]44[/C][C]101.9[/C][C]108.376112918518[/C][C]-6.47611291851804[/C][/ROW]
[ROW][C]45[/C][C]99[/C][C]113.479535063656[/C][C]-14.4795350636563[/C][/ROW]
[ROW][C]46[/C][C]97[/C][C]112.275640310766[/C][C]-15.2756403107663[/C][/ROW]
[ROW][C]47[/C][C]95.8[/C][C]95.842186246003[/C][C]-0.0421862460029701[/C][/ROW]
[ROW][C]48[/C][C]94.7[/C][C]83.3284749896605[/C][C]11.3715250103395[/C][/ROW]
[ROW][C]49[/C][C]97.6[/C][C]61.4077975096935[/C][C]36.1922024903065[/C][/ROW]
[ROW][C]50[/C][C]97.9[/C][C]89.32352223331[/C][C]8.57647776669005[/C][/ROW]
[ROW][C]51[/C][C]99.3[/C][C]93.3646705655525[/C][C]5.93532943444754[/C][/ROW]
[ROW][C]52[/C][C]99.7[/C][C]95.8838680626283[/C][C]3.81613193737174[/C][/ROW]
[ROW][C]53[/C][C]99.7[/C][C]100.374485223279[/C][C]-0.67448522327885[/C][/ROW]
[ROW][C]54[/C][C]100[/C][C]98.0844536144312[/C][C]1.91554638556885[/C][/ROW]
[ROW][C]55[/C][C]99.1[/C][C]94.9592875557885[/C][C]4.1407124442115[/C][/ROW]
[ROW][C]56[/C][C]98.2[/C][C]102.028983297469[/C][C]-3.82898329746858[/C][/ROW]
[ROW][C]57[/C][C]98.1[/C][C]108.327113211137[/C][C]-10.227113211137[/C][/ROW]
[ROW][C]58[/C][C]98.6[/C][C]111.632119530416[/C][C]-13.0321195304159[/C][/ROW]
[ROW][C]59[/C][C]100.2[/C][C]102.751535239396[/C][C]-2.55153523939578[/C][/ROW]
[ROW][C]60[/C][C]101.9[/C][C]93.1960713011047[/C][C]8.70392869889528[/C][/ROW]
[ROW][C]61[/C][C]97.5[/C][C]77.7041603358503[/C][C]19.7958396641497[/C][/ROW]
[ROW][C]62[/C][C]97.1[/C][C]87.0222445998843[/C][C]10.0777554001157[/C][/ROW]
[ROW][C]63[/C][C]98.1[/C][C]92.3701581732485[/C][C]5.72984182675145[/C][/ROW]
[ROW][C]64[/C][C]98.5[/C][C]95.0946939534148[/C][C]3.40530604658520[/C][/ROW]
[ROW][C]65[/C][C]98.3[/C][C]98.9730004435915[/C][C]-0.673000443591505[/C][/ROW]
[ROW][C]66[/C][C]99.3[/C][C]98.318357354632[/C][C]0.98164264536797[/C][/ROW]
[ROW][C]67[/C][C]100.9[/C][C]96.0135289937885[/C][C]4.88647100621154[/C][/ROW]
[ROW][C]68[/C][C]100.4[/C][C]102.344289750442[/C][C]-1.94428975044234[/C][/ROW]
[ROW][C]69[/C][C]101.7[/C][C]109.235531509680[/C][C]-7.53553150968033[/C][/ROW]
[ROW][C]70[/C][C]102[/C][C]114.813131437624[/C][C]-12.8131314376242[/C][/ROW]
[ROW][C]71[/C][C]103.2[/C][C]110.078283218645[/C][C]-6.87828321864468[/C][/ROW]
[ROW][C]72[/C][C]103.1[/C][C]101.417242408286[/C][C]1.68275759171392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13093&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13093&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
13179.9209.963722222222-30.0637222222223
14190.8198.354490712747-7.55449071274671
15174.2175.833324517067-1.63332451706680
16170169.9644750335110.0355249664891630
17170.3169.9398856174360.360114382564149
18159.3159.860528832139-0.560528832139084
19147.9147.5835647005910.316435299408568
20154.2152.6129616359551.58703836404527
21164.5162.5172650482991.98273495170139
22173.9171.1779140431992.72208595680084
23163.6160.9355236471302.66447635287039
24149.7146.9977179915872.70228200841314
25128.2106.56068227699221.6393177230075
26124.7139.572563048663-14.8725630486633
27125.1114.04278218265411.0572178173459
28120.9118.9951213239681.90487867603244
29117.5121.652307942916-4.152307942916
30114109.109417902184.89058209782003
31113.4102.29908409852511.1009159014746
32118.9117.1925757795931.70742422040669
33121.7128.995891871199-7.29589187119883
34121.9132.473517036474-10.5735170364740
35120.3113.3950664122446.90493358775596
36115.6103.52364576258312.0763542374170
37105.776.44358019761829.2564198023820
38105.1106.577029999478-1.47702999947767
39104.6100.0689322909614.53106770903867
4010599.69228202341825.30771797658178
41104.9105.202265868580-0.302265868580420
42105.1100.1435397187044.95646028129627
43103.997.29770535868686.60229464131319
44101.9108.376112918518-6.47611291851804
4599113.479535063656-14.4795350636563
4697112.275640310766-15.2756403107663
4795.895.842186246003-0.0421862460029701
4894.783.328474989660511.3715250103395
4997.661.407797509693536.1922024903065
5097.989.323522233318.57647776669005
5199.393.36467056555255.93532943444754
5299.795.88386806262833.81613193737174
5399.7100.374485223279-0.67448522327885
5410098.08445361443121.91554638556885
5599.194.95928755578854.1407124442115
5698.2102.028983297469-3.82898329746858
5798.1108.327113211137-10.227113211137
5898.6111.632119530416-13.0321195304159
59100.2102.751535239396-2.55153523939578
60101.993.19607130110478.70392869889528
6197.577.704160335850319.7958396641497
6297.187.022244599884310.0777554001157
6398.192.37015817324855.72984182675145
6498.595.09469395341483.40530604658520
6598.398.9730004435915-0.673000443591505
6699.398.3183573546320.98164264536797
67100.996.01352899378854.88647100621154
68100.4102.344289750442-1.94428975044234
69101.7109.235531509680-7.53553150968033
70102114.813131437624-12.8131314376242
71103.2110.078283218645-6.87828321864468
72103.1101.4172424082861.68275759171392







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7384.546083245808564.034527826971105.057638664646
7476.721020345500650.9075886056059102.534452085395
7573.05129617553842.4269899708937103.675602380182
7670.241232472977735.0763766647834105.406088281172
7769.653226186945430.1084581384381109.197994235453
7869.092423364385825.2653600376298112.919486691142
7966.262957116414218.2115883028516114.314325929977
8066.092256776420413.8480711059262118.336442446915
8171.850297614007815.4262538407205128.274341387295
8280.729408925327220.1250696065826141.333748244072
8386.71047670724721.9154677690395151.505485645454
8485.456971114179716.4533987850128154.460543443347

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 84.5460832458085 & 64.034527826971 & 105.057638664646 \tabularnewline
74 & 76.7210203455006 & 50.9075886056059 & 102.534452085395 \tabularnewline
75 & 73.051296175538 & 42.4269899708937 & 103.675602380182 \tabularnewline
76 & 70.2412324729777 & 35.0763766647834 & 105.406088281172 \tabularnewline
77 & 69.6532261869454 & 30.1084581384381 & 109.197994235453 \tabularnewline
78 & 69.0924233643858 & 25.2653600376298 & 112.919486691142 \tabularnewline
79 & 66.2629571164142 & 18.2115883028516 & 114.314325929977 \tabularnewline
80 & 66.0922567764204 & 13.8480711059262 & 118.336442446915 \tabularnewline
81 & 71.8502976140078 & 15.4262538407205 & 128.274341387295 \tabularnewline
82 & 80.7294089253272 & 20.1250696065826 & 141.333748244072 \tabularnewline
83 & 86.710476707247 & 21.9154677690395 & 151.505485645454 \tabularnewline
84 & 85.4569711141797 & 16.4533987850128 & 154.460543443347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13093&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]84.5460832458085[/C][C]64.034527826971[/C][C]105.057638664646[/C][/ROW]
[ROW][C]74[/C][C]76.7210203455006[/C][C]50.9075886056059[/C][C]102.534452085395[/C][/ROW]
[ROW][C]75[/C][C]73.051296175538[/C][C]42.4269899708937[/C][C]103.675602380182[/C][/ROW]
[ROW][C]76[/C][C]70.2412324729777[/C][C]35.0763766647834[/C][C]105.406088281172[/C][/ROW]
[ROW][C]77[/C][C]69.6532261869454[/C][C]30.1084581384381[/C][C]109.197994235453[/C][/ROW]
[ROW][C]78[/C][C]69.0924233643858[/C][C]25.2653600376298[/C][C]112.919486691142[/C][/ROW]
[ROW][C]79[/C][C]66.2629571164142[/C][C]18.2115883028516[/C][C]114.314325929977[/C][/ROW]
[ROW][C]80[/C][C]66.0922567764204[/C][C]13.8480711059262[/C][C]118.336442446915[/C][/ROW]
[ROW][C]81[/C][C]71.8502976140078[/C][C]15.4262538407205[/C][C]128.274341387295[/C][/ROW]
[ROW][C]82[/C][C]80.7294089253272[/C][C]20.1250696065826[/C][C]141.333748244072[/C][/ROW]
[ROW][C]83[/C][C]86.710476707247[/C][C]21.9154677690395[/C][C]151.505485645454[/C][/ROW]
[ROW][C]84[/C][C]85.4569711141797[/C][C]16.4533987850128[/C][C]154.460543443347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13093&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13093&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
7384.546083245808564.034527826971105.057638664646
7476.721020345500650.9075886056059102.534452085395
7573.05129617553842.4269899708937103.675602380182
7670.241232472977735.0763766647834105.406088281172
7769.653226186945430.1084581384381109.197994235453
7869.092423364385825.2653600376298112.919486691142
7966.262957116414218.2115883028516114.314325929977
8066.092256776420413.8480711059262118.336442446915
8171.850297614007815.4262538407205128.274341387295
8280.729408925327220.1250696065826141.333748244072
8386.71047670724721.9154677690395151.505485645454
8485.456971114179716.4533987850128154.460543443347



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')