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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 16 Jan 2010 16:22:37 -0700
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/Jan/17/t1263684218ba3wy94ozpew4dz.htm/, Retrieved Sun, 28 Apr 2024 07:05:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72259, Retrieved Sun, 28 Apr 2024 07:05:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opdracht 10 b] [2010-01-16 23:22:37] [dd4c09afc8b527b51f4c8ef6a655ef42] [Current]
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Dataseries X:
84.9
81.9
95.9
81
89.2
102.5
89.8
88.8
83.2
90.2
100.4
187.1
87.6
85.4
86.1
86.7
89.1
103.7
86.9
85.2
80.8
91.2
102.8
182.5
80.9
83.1
88.3
86.6
93
105.3
93.8
86.4
87
96.7
100.5
196.7
86.8
88.2
93.8
85
90.4
115.9
94.9
87.7
91.7
95.9
106.8
204.5
90.2
90.5
93.2
97.8
99.4
120
108.2
98.5
104.3
102.9
111.1
188.1
93.8
94.5
112.4
102.5
115.8
136.5
122.1
110.6
116.4
112.6
121.5
199.3
102.1
100.6
119
106.8
121.3
145.5
129.7
117.7
121.3
124.3
135.2
210.1
106.8
110.5
111.5
122.1
126.3
143.2
137.3
121.5
121.9
123.9
131.6
220.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72259&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72259&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0536868572060943
beta0.0982858832672798
gamma0.910497809224067

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0536868572060943 \tabularnewline
beta & 0.0982858832672798 \tabularnewline
gamma & 0.910497809224067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72259&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]0.0536868572060943[/C][/ROW]
[ROW][C]beta[/C][C]0.0982858832672798[/C][/ROW]
[ROW][C]gamma[/C][C]0.910497809224067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72259&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
alpha0.0536868572060943
beta0.0982858832672798
gamma0.910497809224067







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1387.687.47244697004080.127553029959202
1485.485.4652147636646-0.0652147636646419
1586.186.3288295614751-0.228829561475138
1686.786.914198608956-0.214198608956039
1789.189.120207340686-0.0202073406860137
18103.7103.751481005857-0.0514810058570134
1986.989.3286739359633-2.42867393596329
2085.287.9022547215732-2.70225472157323
2180.882.3631625078487-1.5631625078487
2291.289.26169356400181.93830643599817
23102.899.1397255843363.66027441566408
24182.5184.890092969064-2.39009296906366
2580.986.6044003132953-5.70440031329531
2683.184.1028982193727-1.00289821937268
2788.384.7109345002493.58906549975099
2886.685.4725083006011.12749169939896
299387.85873629321875.14126370678134
30105.3102.5828637094582.71713629054153
3193.886.42575365901257.37424634098748
3286.485.35508984104941.0449101589506
338781.07755976643415.92244023356587
3496.791.58429678606735.1157032139327
35100.5103.381845750047-2.88184575004691
36196.7184.38406061385912.3159393861415
3786.882.8616000280943.93839997190599
3888.285.16391602261023.03608397738985
3993.890.28861769121113.51138230878888
408589.1070000115617-4.10700001156169
4190.495.0274568479773-4.62745684797727
42115.9107.6099461110738.29005388892676
4394.995.5695471684893-0.669547168489245
4487.788.5650001443302-0.865000144330168
4591.788.48037920087953.21962079912046
4695.998.4804238591472-2.58042385914717
47106.8103.1413750011513.65862499884895
48204.5200.1812696512424.31873034875846
4990.288.41197432134721.78802567865283
5090.589.90447172613150.595528273868482
5193.295.469114356397-2.26911435639711
5297.887.261250470640310.5387495293597
5399.493.7695053634645.63049463653603
54120119.0551608579170.94483914208287
55108.298.33394361563519.86605638436485
5698.591.59296333249956.90703666750055
57104.395.81397159186198.48602840813813
58102.9101.5979923852771.30200761472348
59111.1112.718341323270-1.61834132327026
60188.1216.162802775936-28.0628027759363
6193.894.7348742910747-0.934874291074749
6294.595.2053216060283-0.705321606028292
63112.498.518784407651213.8812155923488
64102.5102.556522899516-0.0565228995160396
65115.8104.50793914713211.2920608528676
66136.5127.5921382898708.90786171012984
67122.1114.2791536419277.82084635807337
68110.6104.3750226585686.22497734143208
69116.4110.4372129058935.96278709410657
70112.6110.0060254988682.59397450113164
71121.5119.4788678414942.02113215850621
72199.3206.569975262126-7.2699752621262
73102.1101.8963504886850.203649511315049
74100.6102.917299765070-2.31729976507039
75119120.258732181516-1.25873218151563
76106.8110.923395793423-4.12339579342331
77121.3123.456787301719-2.15678730171933
78145.5145.3222845633830.177715436617405
79129.7129.5612817976950.138718202305370
80117.7117.0500446797310.649955320269257
81121.3122.869961720829-1.56996172082857
82124.3118.8225352079395.47746479206111
83135.2128.4042054512016.7957945487993
84210.1212.482950264386-2.38295026438641
85106.8108.388470443026-1.58847044302576
86110.5107.0251548452713.47484515472908
87111.5126.743431486855-15.2434314868553
88122.1113.4337247519078.66627524809331
89126.3129.244089618442-2.94408961844211
90143.2154.561506283968-11.3615062839677
91137.3137.1595777124520.140422287548063
92121.5124.331045370537-2.83104537053738
93121.9128.184714245078-6.2847142450776
94123.9129.950505473243-6.05050547324274
95131.6140.341352628503-8.74135262850268
96220.9218.2302912367172.66970876328344

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 87.6 & 87.4724469700408 & 0.127553029959202 \tabularnewline
14 & 85.4 & 85.4652147636646 & -0.0652147636646419 \tabularnewline
15 & 86.1 & 86.3288295614751 & -0.228829561475138 \tabularnewline
16 & 86.7 & 86.914198608956 & -0.214198608956039 \tabularnewline
17 & 89.1 & 89.120207340686 & -0.0202073406860137 \tabularnewline
18 & 103.7 & 103.751481005857 & -0.0514810058570134 \tabularnewline
19 & 86.9 & 89.3286739359633 & -2.42867393596329 \tabularnewline
20 & 85.2 & 87.9022547215732 & -2.70225472157323 \tabularnewline
21 & 80.8 & 82.3631625078487 & -1.5631625078487 \tabularnewline
22 & 91.2 & 89.2616935640018 & 1.93830643599817 \tabularnewline
23 & 102.8 & 99.139725584336 & 3.66027441566408 \tabularnewline
24 & 182.5 & 184.890092969064 & -2.39009296906366 \tabularnewline
25 & 80.9 & 86.6044003132953 & -5.70440031329531 \tabularnewline
26 & 83.1 & 84.1028982193727 & -1.00289821937268 \tabularnewline
27 & 88.3 & 84.710934500249 & 3.58906549975099 \tabularnewline
28 & 86.6 & 85.472508300601 & 1.12749169939896 \tabularnewline
29 & 93 & 87.8587362932187 & 5.14126370678134 \tabularnewline
30 & 105.3 & 102.582863709458 & 2.71713629054153 \tabularnewline
31 & 93.8 & 86.4257536590125 & 7.37424634098748 \tabularnewline
32 & 86.4 & 85.3550898410494 & 1.0449101589506 \tabularnewline
33 & 87 & 81.0775597664341 & 5.92244023356587 \tabularnewline
34 & 96.7 & 91.5842967860673 & 5.1157032139327 \tabularnewline
35 & 100.5 & 103.381845750047 & -2.88184575004691 \tabularnewline
36 & 196.7 & 184.384060613859 & 12.3159393861415 \tabularnewline
37 & 86.8 & 82.861600028094 & 3.93839997190599 \tabularnewline
38 & 88.2 & 85.1639160226102 & 3.03608397738985 \tabularnewline
39 & 93.8 & 90.2886176912111 & 3.51138230878888 \tabularnewline
40 & 85 & 89.1070000115617 & -4.10700001156169 \tabularnewline
41 & 90.4 & 95.0274568479773 & -4.62745684797727 \tabularnewline
42 & 115.9 & 107.609946111073 & 8.29005388892676 \tabularnewline
43 & 94.9 & 95.5695471684893 & -0.669547168489245 \tabularnewline
44 & 87.7 & 88.5650001443302 & -0.865000144330168 \tabularnewline
45 & 91.7 & 88.4803792008795 & 3.21962079912046 \tabularnewline
46 & 95.9 & 98.4804238591472 & -2.58042385914717 \tabularnewline
47 & 106.8 & 103.141375001151 & 3.65862499884895 \tabularnewline
48 & 204.5 & 200.181269651242 & 4.31873034875846 \tabularnewline
49 & 90.2 & 88.4119743213472 & 1.78802567865283 \tabularnewline
50 & 90.5 & 89.9044717261315 & 0.595528273868482 \tabularnewline
51 & 93.2 & 95.469114356397 & -2.26911435639711 \tabularnewline
52 & 97.8 & 87.2612504706403 & 10.5387495293597 \tabularnewline
53 & 99.4 & 93.769505363464 & 5.63049463653603 \tabularnewline
54 & 120 & 119.055160857917 & 0.94483914208287 \tabularnewline
55 & 108.2 & 98.3339436156351 & 9.86605638436485 \tabularnewline
56 & 98.5 & 91.5929633324995 & 6.90703666750055 \tabularnewline
57 & 104.3 & 95.8139715918619 & 8.48602840813813 \tabularnewline
58 & 102.9 & 101.597992385277 & 1.30200761472348 \tabularnewline
59 & 111.1 & 112.718341323270 & -1.61834132327026 \tabularnewline
60 & 188.1 & 216.162802775936 & -28.0628027759363 \tabularnewline
61 & 93.8 & 94.7348742910747 & -0.934874291074749 \tabularnewline
62 & 94.5 & 95.2053216060283 & -0.705321606028292 \tabularnewline
63 & 112.4 & 98.5187844076512 & 13.8812155923488 \tabularnewline
64 & 102.5 & 102.556522899516 & -0.0565228995160396 \tabularnewline
65 & 115.8 & 104.507939147132 & 11.2920608528676 \tabularnewline
66 & 136.5 & 127.592138289870 & 8.90786171012984 \tabularnewline
67 & 122.1 & 114.279153641927 & 7.82084635807337 \tabularnewline
68 & 110.6 & 104.375022658568 & 6.22497734143208 \tabularnewline
69 & 116.4 & 110.437212905893 & 5.96278709410657 \tabularnewline
70 & 112.6 & 110.006025498868 & 2.59397450113164 \tabularnewline
71 & 121.5 & 119.478867841494 & 2.02113215850621 \tabularnewline
72 & 199.3 & 206.569975262126 & -7.2699752621262 \tabularnewline
73 & 102.1 & 101.896350488685 & 0.203649511315049 \tabularnewline
74 & 100.6 & 102.917299765070 & -2.31729976507039 \tabularnewline
75 & 119 & 120.258732181516 & -1.25873218151563 \tabularnewline
76 & 106.8 & 110.923395793423 & -4.12339579342331 \tabularnewline
77 & 121.3 & 123.456787301719 & -2.15678730171933 \tabularnewline
78 & 145.5 & 145.322284563383 & 0.177715436617405 \tabularnewline
79 & 129.7 & 129.561281797695 & 0.138718202305370 \tabularnewline
80 & 117.7 & 117.050044679731 & 0.649955320269257 \tabularnewline
81 & 121.3 & 122.869961720829 & -1.56996172082857 \tabularnewline
82 & 124.3 & 118.822535207939 & 5.47746479206111 \tabularnewline
83 & 135.2 & 128.404205451201 & 6.7957945487993 \tabularnewline
84 & 210.1 & 212.482950264386 & -2.38295026438641 \tabularnewline
85 & 106.8 & 108.388470443026 & -1.58847044302576 \tabularnewline
86 & 110.5 & 107.025154845271 & 3.47484515472908 \tabularnewline
87 & 111.5 & 126.743431486855 & -15.2434314868553 \tabularnewline
88 & 122.1 & 113.433724751907 & 8.66627524809331 \tabularnewline
89 & 126.3 & 129.244089618442 & -2.94408961844211 \tabularnewline
90 & 143.2 & 154.561506283968 & -11.3615062839677 \tabularnewline
91 & 137.3 & 137.159577712452 & 0.140422287548063 \tabularnewline
92 & 121.5 & 124.331045370537 & -2.83104537053738 \tabularnewline
93 & 121.9 & 128.184714245078 & -6.2847142450776 \tabularnewline
94 & 123.9 & 129.950505473243 & -6.05050547324274 \tabularnewline
95 & 131.6 & 140.341352628503 & -8.74135262850268 \tabularnewline
96 & 220.9 & 218.230291236717 & 2.66970876328344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72259&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]87.6[/C][C]87.4724469700408[/C][C]0.127553029959202[/C][/ROW]
[ROW][C]14[/C][C]85.4[/C][C]85.4652147636646[/C][C]-0.0652147636646419[/C][/ROW]
[ROW][C]15[/C][C]86.1[/C][C]86.3288295614751[/C][C]-0.228829561475138[/C][/ROW]
[ROW][C]16[/C][C]86.7[/C][C]86.914198608956[/C][C]-0.214198608956039[/C][/ROW]
[ROW][C]17[/C][C]89.1[/C][C]89.120207340686[/C][C]-0.0202073406860137[/C][/ROW]
[ROW][C]18[/C][C]103.7[/C][C]103.751481005857[/C][C]-0.0514810058570134[/C][/ROW]
[ROW][C]19[/C][C]86.9[/C][C]89.3286739359633[/C][C]-2.42867393596329[/C][/ROW]
[ROW][C]20[/C][C]85.2[/C][C]87.9022547215732[/C][C]-2.70225472157323[/C][/ROW]
[ROW][C]21[/C][C]80.8[/C][C]82.3631625078487[/C][C]-1.5631625078487[/C][/ROW]
[ROW][C]22[/C][C]91.2[/C][C]89.2616935640018[/C][C]1.93830643599817[/C][/ROW]
[ROW][C]23[/C][C]102.8[/C][C]99.139725584336[/C][C]3.66027441566408[/C][/ROW]
[ROW][C]24[/C][C]182.5[/C][C]184.890092969064[/C][C]-2.39009296906366[/C][/ROW]
[ROW][C]25[/C][C]80.9[/C][C]86.6044003132953[/C][C]-5.70440031329531[/C][/ROW]
[ROW][C]26[/C][C]83.1[/C][C]84.1028982193727[/C][C]-1.00289821937268[/C][/ROW]
[ROW][C]27[/C][C]88.3[/C][C]84.710934500249[/C][C]3.58906549975099[/C][/ROW]
[ROW][C]28[/C][C]86.6[/C][C]85.472508300601[/C][C]1.12749169939896[/C][/ROW]
[ROW][C]29[/C][C]93[/C][C]87.8587362932187[/C][C]5.14126370678134[/C][/ROW]
[ROW][C]30[/C][C]105.3[/C][C]102.582863709458[/C][C]2.71713629054153[/C][/ROW]
[ROW][C]31[/C][C]93.8[/C][C]86.4257536590125[/C][C]7.37424634098748[/C][/ROW]
[ROW][C]32[/C][C]86.4[/C][C]85.3550898410494[/C][C]1.0449101589506[/C][/ROW]
[ROW][C]33[/C][C]87[/C][C]81.0775597664341[/C][C]5.92244023356587[/C][/ROW]
[ROW][C]34[/C][C]96.7[/C][C]91.5842967860673[/C][C]5.1157032139327[/C][/ROW]
[ROW][C]35[/C][C]100.5[/C][C]103.381845750047[/C][C]-2.88184575004691[/C][/ROW]
[ROW][C]36[/C][C]196.7[/C][C]184.384060613859[/C][C]12.3159393861415[/C][/ROW]
[ROW][C]37[/C][C]86.8[/C][C]82.861600028094[/C][C]3.93839997190599[/C][/ROW]
[ROW][C]38[/C][C]88.2[/C][C]85.1639160226102[/C][C]3.03608397738985[/C][/ROW]
[ROW][C]39[/C][C]93.8[/C][C]90.2886176912111[/C][C]3.51138230878888[/C][/ROW]
[ROW][C]40[/C][C]85[/C][C]89.1070000115617[/C][C]-4.10700001156169[/C][/ROW]
[ROW][C]41[/C][C]90.4[/C][C]95.0274568479773[/C][C]-4.62745684797727[/C][/ROW]
[ROW][C]42[/C][C]115.9[/C][C]107.609946111073[/C][C]8.29005388892676[/C][/ROW]
[ROW][C]43[/C][C]94.9[/C][C]95.5695471684893[/C][C]-0.669547168489245[/C][/ROW]
[ROW][C]44[/C][C]87.7[/C][C]88.5650001443302[/C][C]-0.865000144330168[/C][/ROW]
[ROW][C]45[/C][C]91.7[/C][C]88.4803792008795[/C][C]3.21962079912046[/C][/ROW]
[ROW][C]46[/C][C]95.9[/C][C]98.4804238591472[/C][C]-2.58042385914717[/C][/ROW]
[ROW][C]47[/C][C]106.8[/C][C]103.141375001151[/C][C]3.65862499884895[/C][/ROW]
[ROW][C]48[/C][C]204.5[/C][C]200.181269651242[/C][C]4.31873034875846[/C][/ROW]
[ROW][C]49[/C][C]90.2[/C][C]88.4119743213472[/C][C]1.78802567865283[/C][/ROW]
[ROW][C]50[/C][C]90.5[/C][C]89.9044717261315[/C][C]0.595528273868482[/C][/ROW]
[ROW][C]51[/C][C]93.2[/C][C]95.469114356397[/C][C]-2.26911435639711[/C][/ROW]
[ROW][C]52[/C][C]97.8[/C][C]87.2612504706403[/C][C]10.5387495293597[/C][/ROW]
[ROW][C]53[/C][C]99.4[/C][C]93.769505363464[/C][C]5.63049463653603[/C][/ROW]
[ROW][C]54[/C][C]120[/C][C]119.055160857917[/C][C]0.94483914208287[/C][/ROW]
[ROW][C]55[/C][C]108.2[/C][C]98.3339436156351[/C][C]9.86605638436485[/C][/ROW]
[ROW][C]56[/C][C]98.5[/C][C]91.5929633324995[/C][C]6.90703666750055[/C][/ROW]
[ROW][C]57[/C][C]104.3[/C][C]95.8139715918619[/C][C]8.48602840813813[/C][/ROW]
[ROW][C]58[/C][C]102.9[/C][C]101.597992385277[/C][C]1.30200761472348[/C][/ROW]
[ROW][C]59[/C][C]111.1[/C][C]112.718341323270[/C][C]-1.61834132327026[/C][/ROW]
[ROW][C]60[/C][C]188.1[/C][C]216.162802775936[/C][C]-28.0628027759363[/C][/ROW]
[ROW][C]61[/C][C]93.8[/C][C]94.7348742910747[/C][C]-0.934874291074749[/C][/ROW]
[ROW][C]62[/C][C]94.5[/C][C]95.2053216060283[/C][C]-0.705321606028292[/C][/ROW]
[ROW][C]63[/C][C]112.4[/C][C]98.5187844076512[/C][C]13.8812155923488[/C][/ROW]
[ROW][C]64[/C][C]102.5[/C][C]102.556522899516[/C][C]-0.0565228995160396[/C][/ROW]
[ROW][C]65[/C][C]115.8[/C][C]104.507939147132[/C][C]11.2920608528676[/C][/ROW]
[ROW][C]66[/C][C]136.5[/C][C]127.592138289870[/C][C]8.90786171012984[/C][/ROW]
[ROW][C]67[/C][C]122.1[/C][C]114.279153641927[/C][C]7.82084635807337[/C][/ROW]
[ROW][C]68[/C][C]110.6[/C][C]104.375022658568[/C][C]6.22497734143208[/C][/ROW]
[ROW][C]69[/C][C]116.4[/C][C]110.437212905893[/C][C]5.96278709410657[/C][/ROW]
[ROW][C]70[/C][C]112.6[/C][C]110.006025498868[/C][C]2.59397450113164[/C][/ROW]
[ROW][C]71[/C][C]121.5[/C][C]119.478867841494[/C][C]2.02113215850621[/C][/ROW]
[ROW][C]72[/C][C]199.3[/C][C]206.569975262126[/C][C]-7.2699752621262[/C][/ROW]
[ROW][C]73[/C][C]102.1[/C][C]101.896350488685[/C][C]0.203649511315049[/C][/ROW]
[ROW][C]74[/C][C]100.6[/C][C]102.917299765070[/C][C]-2.31729976507039[/C][/ROW]
[ROW][C]75[/C][C]119[/C][C]120.258732181516[/C][C]-1.25873218151563[/C][/ROW]
[ROW][C]76[/C][C]106.8[/C][C]110.923395793423[/C][C]-4.12339579342331[/C][/ROW]
[ROW][C]77[/C][C]121.3[/C][C]123.456787301719[/C][C]-2.15678730171933[/C][/ROW]
[ROW][C]78[/C][C]145.5[/C][C]145.322284563383[/C][C]0.177715436617405[/C][/ROW]
[ROW][C]79[/C][C]129.7[/C][C]129.561281797695[/C][C]0.138718202305370[/C][/ROW]
[ROW][C]80[/C][C]117.7[/C][C]117.050044679731[/C][C]0.649955320269257[/C][/ROW]
[ROW][C]81[/C][C]121.3[/C][C]122.869961720829[/C][C]-1.56996172082857[/C][/ROW]
[ROW][C]82[/C][C]124.3[/C][C]118.822535207939[/C][C]5.47746479206111[/C][/ROW]
[ROW][C]83[/C][C]135.2[/C][C]128.404205451201[/C][C]6.7957945487993[/C][/ROW]
[ROW][C]84[/C][C]210.1[/C][C]212.482950264386[/C][C]-2.38295026438641[/C][/ROW]
[ROW][C]85[/C][C]106.8[/C][C]108.388470443026[/C][C]-1.58847044302576[/C][/ROW]
[ROW][C]86[/C][C]110.5[/C][C]107.025154845271[/C][C]3.47484515472908[/C][/ROW]
[ROW][C]87[/C][C]111.5[/C][C]126.743431486855[/C][C]-15.2434314868553[/C][/ROW]
[ROW][C]88[/C][C]122.1[/C][C]113.433724751907[/C][C]8.66627524809331[/C][/ROW]
[ROW][C]89[/C][C]126.3[/C][C]129.244089618442[/C][C]-2.94408961844211[/C][/ROW]
[ROW][C]90[/C][C]143.2[/C][C]154.561506283968[/C][C]-11.3615062839677[/C][/ROW]
[ROW][C]91[/C][C]137.3[/C][C]137.159577712452[/C][C]0.140422287548063[/C][/ROW]
[ROW][C]92[/C][C]121.5[/C][C]124.331045370537[/C][C]-2.83104537053738[/C][/ROW]
[ROW][C]93[/C][C]121.9[/C][C]128.184714245078[/C][C]-6.2847142450776[/C][/ROW]
[ROW][C]94[/C][C]123.9[/C][C]129.950505473243[/C][C]-6.05050547324274[/C][/ROW]
[ROW][C]95[/C][C]131.6[/C][C]140.341352628503[/C][C]-8.74135262850268[/C][/ROW]
[ROW][C]96[/C][C]220.9[/C][C]218.230291236717[/C][C]2.66970876328344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72259&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72259&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
1387.687.47244697004080.127553029959202
1485.485.4652147636646-0.0652147636646419
1586.186.3288295614751-0.228829561475138
1686.786.914198608956-0.214198608956039
1789.189.120207340686-0.0202073406860137
18103.7103.751481005857-0.0514810058570134
1986.989.3286739359633-2.42867393596329
2085.287.9022547215732-2.70225472157323
2180.882.3631625078487-1.5631625078487
2291.289.26169356400181.93830643599817
23102.899.1397255843363.66027441566408
24182.5184.890092969064-2.39009296906366
2580.986.6044003132953-5.70440031329531
2683.184.1028982193727-1.00289821937268
2788.384.7109345002493.58906549975099
2886.685.4725083006011.12749169939896
299387.85873629321875.14126370678134
30105.3102.5828637094582.71713629054153
3193.886.42575365901257.37424634098748
3286.485.35508984104941.0449101589506
338781.07755976643415.92244023356587
3496.791.58429678606735.1157032139327
35100.5103.381845750047-2.88184575004691
36196.7184.38406061385912.3159393861415
3786.882.8616000280943.93839997190599
3888.285.16391602261023.03608397738985
3993.890.28861769121113.51138230878888
408589.1070000115617-4.10700001156169
4190.495.0274568479773-4.62745684797727
42115.9107.6099461110738.29005388892676
4394.995.5695471684893-0.669547168489245
4487.788.5650001443302-0.865000144330168
4591.788.48037920087953.21962079912046
4695.998.4804238591472-2.58042385914717
47106.8103.1413750011513.65862499884895
48204.5200.1812696512424.31873034875846
4990.288.41197432134721.78802567865283
5090.589.90447172613150.595528273868482
5193.295.469114356397-2.26911435639711
5297.887.261250470640310.5387495293597
5399.493.7695053634645.63049463653603
54120119.0551608579170.94483914208287
55108.298.33394361563519.86605638436485
5698.591.59296333249956.90703666750055
57104.395.81397159186198.48602840813813
58102.9101.5979923852771.30200761472348
59111.1112.718341323270-1.61834132327026
60188.1216.162802775936-28.0628027759363
6193.894.7348742910747-0.934874291074749
6294.595.2053216060283-0.705321606028292
63112.498.518784407651213.8812155923488
64102.5102.556522899516-0.0565228995160396
65115.8104.50793914713211.2920608528676
66136.5127.5921382898708.90786171012984
67122.1114.2791536419277.82084635807337
68110.6104.3750226585686.22497734143208
69116.4110.4372129058935.96278709410657
70112.6110.0060254988682.59397450113164
71121.5119.4788678414942.02113215850621
72199.3206.569975262126-7.2699752621262
73102.1101.8963504886850.203649511315049
74100.6102.917299765070-2.31729976507039
75119120.258732181516-1.25873218151563
76106.8110.923395793423-4.12339579342331
77121.3123.456787301719-2.15678730171933
78145.5145.3222845633830.177715436617405
79129.7129.5612817976950.138718202305370
80117.7117.0500446797310.649955320269257
81121.3122.869961720829-1.56996172082857
82124.3118.8225352079395.47746479206111
83135.2128.4042054512016.7957945487993
84210.1212.482950264386-2.38295026438641
85106.8108.388470443026-1.58847044302576
86110.5107.0251548452713.47484515472908
87111.5126.743431486855-15.2434314868553
88122.1113.4337247519078.66627524809331
89126.3129.244089618442-2.94408961844211
90143.2154.561506283968-11.3615062839677
91137.3137.1595777124520.140422287548063
92121.5124.331045370537-2.83104537053738
93121.9128.184714245078-6.2847142450776
94123.9129.950505473243-6.05050547324274
95131.6140.341352628503-8.74135262850268
96220.9218.2302912367172.66970876328344







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97110.937461598575100.093192696182121.781730500967
98113.948107193902103.080285419281124.815928968524
99117.172597960547106.275431725216128.069764195877
100125.422001563343114.481454771639136.362548355047
101130.740301880711119.750622152608141.729981608815
102149.318877821006138.227934500818160.409821141194
103142.047444371941130.927641558720153.167247185163
104125.987281168629114.878706054167137.095856283091
105126.925928324180115.756420840829138.095435807532
106129.220367716602117.974692796636140.466042636567
107137.861879301625126.483067256692149.240691346559
108229.713370985837185.529030909053273.897711062621

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 110.937461598575 & 100.093192696182 & 121.781730500967 \tabularnewline
98 & 113.948107193902 & 103.080285419281 & 124.815928968524 \tabularnewline
99 & 117.172597960547 & 106.275431725216 & 128.069764195877 \tabularnewline
100 & 125.422001563343 & 114.481454771639 & 136.362548355047 \tabularnewline
101 & 130.740301880711 & 119.750622152608 & 141.729981608815 \tabularnewline
102 & 149.318877821006 & 138.227934500818 & 160.409821141194 \tabularnewline
103 & 142.047444371941 & 130.927641558720 & 153.167247185163 \tabularnewline
104 & 125.987281168629 & 114.878706054167 & 137.095856283091 \tabularnewline
105 & 126.925928324180 & 115.756420840829 & 138.095435807532 \tabularnewline
106 & 129.220367716602 & 117.974692796636 & 140.466042636567 \tabularnewline
107 & 137.861879301625 & 126.483067256692 & 149.240691346559 \tabularnewline
108 & 229.713370985837 & 185.529030909053 & 273.897711062621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72259&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]97[/C][C]110.937461598575[/C][C]100.093192696182[/C][C]121.781730500967[/C][/ROW]
[ROW][C]98[/C][C]113.948107193902[/C][C]103.080285419281[/C][C]124.815928968524[/C][/ROW]
[ROW][C]99[/C][C]117.172597960547[/C][C]106.275431725216[/C][C]128.069764195877[/C][/ROW]
[ROW][C]100[/C][C]125.422001563343[/C][C]114.481454771639[/C][C]136.362548355047[/C][/ROW]
[ROW][C]101[/C][C]130.740301880711[/C][C]119.750622152608[/C][C]141.729981608815[/C][/ROW]
[ROW][C]102[/C][C]149.318877821006[/C][C]138.227934500818[/C][C]160.409821141194[/C][/ROW]
[ROW][C]103[/C][C]142.047444371941[/C][C]130.927641558720[/C][C]153.167247185163[/C][/ROW]
[ROW][C]104[/C][C]125.987281168629[/C][C]114.878706054167[/C][C]137.095856283091[/C][/ROW]
[ROW][C]105[/C][C]126.925928324180[/C][C]115.756420840829[/C][C]138.095435807532[/C][/ROW]
[ROW][C]106[/C][C]129.220367716602[/C][C]117.974692796636[/C][C]140.466042636567[/C][/ROW]
[ROW][C]107[/C][C]137.861879301625[/C][C]126.483067256692[/C][C]149.240691346559[/C][/ROW]
[ROW][C]108[/C][C]229.713370985837[/C][C]185.529030909053[/C][C]273.897711062621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72259&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72259&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
97110.937461598575100.093192696182121.781730500967
98113.948107193902103.080285419281124.815928968524
99117.172597960547106.275431725216128.069764195877
100125.422001563343114.481454771639136.362548355047
101130.740301880711119.750622152608141.729981608815
102149.318877821006138.227934500818160.409821141194
103142.047444371941130.927641558720153.167247185163
104125.987281168629114.878706054167137.095856283091
105126.925928324180115.756420840829138.095435807532
106129.220367716602117.974692796636140.466042636567
107137.861879301625126.483067256692149.240691346559
108229.713370985837185.529030909053273.897711062621



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')