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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 02 Jan 2015 17:43:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jan/02/t1420220801x9bd91c1fnliaco.htm/, Retrieved Tue, 14 May 2024 11:51:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271867, Retrieved Tue, 14 May 2024 11:51:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2014-11-29 17:54:24] [3d50c3f1d1505d45371c80c331b9aa00]
- R PD    [Exponential Smoothing] [] [2015-01-02 17:43:50] [3b96c46cffecdf3c11148678d326f85c] [Current]
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Dataseries X:
111.4
117
141.7
120
132.1
146.7
122.5
99.6
122.7
139
117.8
125.5
134.5
121.3
126.7
117.7
123
132.1
113.1
89.2
121.7
105.3
85.3
105.3
72.2
92.1
97.2
78.6
78.1
93
81
65.9
88.6
85.7
76.3
96.8
76.8
85.6
119.2
91.4
95.7
112.3
95.2
82.8
111.3
108.2
97
124.4
99.3
117.6
131.5
114.2
116.8
116.5
105.4
89.2
115.8
111.4
106.4
128.4
107.7
111
129.8
130.5
142.9
159.9
84.1
75
100.7
106.8
97.4
113
76.9
87.3
103.7
92.1
92.9
112.2
88.7
74.6
101.5
119.7
120.7
153.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271867&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271867&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.510905998109683
beta0.0107479053757706
gamma0.663061333464774

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.510905998109683 \tabularnewline
beta & 0.0107479053757706 \tabularnewline
gamma & 0.663061333464774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271867&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]0.510905998109683[/C][/ROW]
[ROW][C]beta[/C][C]0.0107479053757706[/C][/ROW]
[ROW][C]gamma[/C][C]0.663061333464774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271867&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
alpha0.510905998109683
beta0.0107479053757706
gamma0.663061333464774







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13134.5138.63141025641-4.13141025641028
14121.3123.19982650436-1.89982650436002
15126.7127.147940007495-0.447940007495447
16117.7118.406204649359-0.706204649358796
17123125.141142447288-2.14114244728778
18132.1134.368704541617-2.26870454161653
19113.1112.4353032227050.664696777295219
2089.287.75007752837421.44992247162584
21121.7111.06149012094510.6385098790553
22105.3132.600824993223-27.3008249932227
2385.396.860979328917-11.560979328917
24105.398.51173192878416.78826807121592
2572.2109.547187074301-37.3471870743013
2692.177.51700836568714.582991634313
2797.290.0954918280137.10450817198696
2878.684.9084177701004-6.30841777010042
2978.188.0648645003861-9.9648645003861
309392.95997295921990.0400270407800747
318172.87619533557148.12380466442862
3265.952.016258810908513.8837411890915
3388.684.48805087751424.11194912248581
3485.790.1814019745297-4.48140197452969
3576.371.12203878614175.17796121385825
3696.887.2848624617599.51513753824101
3776.885.4247646128246-8.62476461282463
3885.685.09205638222650.507943617773492
39119.288.159048671045431.0409513289546
4091.491.08768567245040.312314327549586
4195.796.7135179658564-1.01351796585641
42112.3109.7482529689062.55174703109402
4395.293.90483440303321.29516559696683
4482.871.722094164955311.0779058350447
45111.399.874020710130311.4259792898697
46108.2106.8401364651391.35986353486103
479794.25251186582632.74748813417372
48124.4110.92166554467413.4783344553259
4999.3105.566923346071-6.26692334607057
50117.6109.7768212715197.8231787284809
51131.5126.8994537534144.60054624658648
52114.2106.6254733732077.57452662679293
53116.8115.8427452994020.957254700597787
54116.5131.362493065237-14.8624930652371
55105.4106.440821903234-1.040821903234
5689.286.45061598201352.74938401798654
57115.8110.6280657617195.17193423828085
58111.4111.2679108629610.132089137038875
59106.498.62966573867187.77033426132823
60128.4121.4992601703526.90073982964779
61107.7106.4987254012141.20127459878631
62111119.252703804445-8.25270380444476
63129.8127.1878213722852.61217862771487
64130.5106.92236082699523.5776391730047
65142.9122.31754690871320.5824530912866
66159.9142.98916283397716.9108371660229
6784.1139.213078025087-55.1130780250875
687592.9593161968043-17.9593161968043
69100.7107.361606105997-6.6616061059967
70106.8100.2756340385986.52436596140234
7197.493.36984818475134.03015181524869
72113114.015543103007-1.01554310300659
7376.993.0477205620533-16.1477205620533
7487.393.702329594828-6.40232959482802
75103.7105.946704255696-2.24670425569606
7692.189.81163078774392.28836921225613
7792.993.055496217745-0.155496217745011
78112.2101.52422318903410.6757768109665
7988.770.754020364143617.9459796358564
8074.673.82540722010060.774592779899393
81101.5101.515572544488-0.0155725444877532
82119.7102.1905644109117.5094355890901
83120.7100.23782917695620.4621708230435
84153.5127.88224134135325.6177586586473

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 134.5 & 138.63141025641 & -4.13141025641028 \tabularnewline
14 & 121.3 & 123.19982650436 & -1.89982650436002 \tabularnewline
15 & 126.7 & 127.147940007495 & -0.447940007495447 \tabularnewline
16 & 117.7 & 118.406204649359 & -0.706204649358796 \tabularnewline
17 & 123 & 125.141142447288 & -2.14114244728778 \tabularnewline
18 & 132.1 & 134.368704541617 & -2.26870454161653 \tabularnewline
19 & 113.1 & 112.435303222705 & 0.664696777295219 \tabularnewline
20 & 89.2 & 87.7500775283742 & 1.44992247162584 \tabularnewline
21 & 121.7 & 111.061490120945 & 10.6385098790553 \tabularnewline
22 & 105.3 & 132.600824993223 & -27.3008249932227 \tabularnewline
23 & 85.3 & 96.860979328917 & -11.560979328917 \tabularnewline
24 & 105.3 & 98.5117319287841 & 6.78826807121592 \tabularnewline
25 & 72.2 & 109.547187074301 & -37.3471870743013 \tabularnewline
26 & 92.1 & 77.517008365687 & 14.582991634313 \tabularnewline
27 & 97.2 & 90.095491828013 & 7.10450817198696 \tabularnewline
28 & 78.6 & 84.9084177701004 & -6.30841777010042 \tabularnewline
29 & 78.1 & 88.0648645003861 & -9.9648645003861 \tabularnewline
30 & 93 & 92.9599729592199 & 0.0400270407800747 \tabularnewline
31 & 81 & 72.8761953355714 & 8.12380466442862 \tabularnewline
32 & 65.9 & 52.0162588109085 & 13.8837411890915 \tabularnewline
33 & 88.6 & 84.4880508775142 & 4.11194912248581 \tabularnewline
34 & 85.7 & 90.1814019745297 & -4.48140197452969 \tabularnewline
35 & 76.3 & 71.1220387861417 & 5.17796121385825 \tabularnewline
36 & 96.8 & 87.284862461759 & 9.51513753824101 \tabularnewline
37 & 76.8 & 85.4247646128246 & -8.62476461282463 \tabularnewline
38 & 85.6 & 85.0920563822265 & 0.507943617773492 \tabularnewline
39 & 119.2 & 88.1590486710454 & 31.0409513289546 \tabularnewline
40 & 91.4 & 91.0876856724504 & 0.312314327549586 \tabularnewline
41 & 95.7 & 96.7135179658564 & -1.01351796585641 \tabularnewline
42 & 112.3 & 109.748252968906 & 2.55174703109402 \tabularnewline
43 & 95.2 & 93.9048344030332 & 1.29516559696683 \tabularnewline
44 & 82.8 & 71.7220941649553 & 11.0779058350447 \tabularnewline
45 & 111.3 & 99.8740207101303 & 11.4259792898697 \tabularnewline
46 & 108.2 & 106.840136465139 & 1.35986353486103 \tabularnewline
47 & 97 & 94.2525118658263 & 2.74748813417372 \tabularnewline
48 & 124.4 & 110.921665544674 & 13.4783344553259 \tabularnewline
49 & 99.3 & 105.566923346071 & -6.26692334607057 \tabularnewline
50 & 117.6 & 109.776821271519 & 7.8231787284809 \tabularnewline
51 & 131.5 & 126.899453753414 & 4.60054624658648 \tabularnewline
52 & 114.2 & 106.625473373207 & 7.57452662679293 \tabularnewline
53 & 116.8 & 115.842745299402 & 0.957254700597787 \tabularnewline
54 & 116.5 & 131.362493065237 & -14.8624930652371 \tabularnewline
55 & 105.4 & 106.440821903234 & -1.040821903234 \tabularnewline
56 & 89.2 & 86.4506159820135 & 2.74938401798654 \tabularnewline
57 & 115.8 & 110.628065761719 & 5.17193423828085 \tabularnewline
58 & 111.4 & 111.267910862961 & 0.132089137038875 \tabularnewline
59 & 106.4 & 98.6296657386718 & 7.77033426132823 \tabularnewline
60 & 128.4 & 121.499260170352 & 6.90073982964779 \tabularnewline
61 & 107.7 & 106.498725401214 & 1.20127459878631 \tabularnewline
62 & 111 & 119.252703804445 & -8.25270380444476 \tabularnewline
63 & 129.8 & 127.187821372285 & 2.61217862771487 \tabularnewline
64 & 130.5 & 106.922360826995 & 23.5776391730047 \tabularnewline
65 & 142.9 & 122.317546908713 & 20.5824530912866 \tabularnewline
66 & 159.9 & 142.989162833977 & 16.9108371660229 \tabularnewline
67 & 84.1 & 139.213078025087 & -55.1130780250875 \tabularnewline
68 & 75 & 92.9593161968043 & -17.9593161968043 \tabularnewline
69 & 100.7 & 107.361606105997 & -6.6616061059967 \tabularnewline
70 & 106.8 & 100.275634038598 & 6.52436596140234 \tabularnewline
71 & 97.4 & 93.3698481847513 & 4.03015181524869 \tabularnewline
72 & 113 & 114.015543103007 & -1.01554310300659 \tabularnewline
73 & 76.9 & 93.0477205620533 & -16.1477205620533 \tabularnewline
74 & 87.3 & 93.702329594828 & -6.40232959482802 \tabularnewline
75 & 103.7 & 105.946704255696 & -2.24670425569606 \tabularnewline
76 & 92.1 & 89.8116307877439 & 2.28836921225613 \tabularnewline
77 & 92.9 & 93.055496217745 & -0.155496217745011 \tabularnewline
78 & 112.2 & 101.524223189034 & 10.6757768109665 \tabularnewline
79 & 88.7 & 70.7540203641436 & 17.9459796358564 \tabularnewline
80 & 74.6 & 73.8254072201006 & 0.774592779899393 \tabularnewline
81 & 101.5 & 101.515572544488 & -0.0155725444877532 \tabularnewline
82 & 119.7 & 102.19056441091 & 17.5094355890901 \tabularnewline
83 & 120.7 & 100.237829176956 & 20.4621708230435 \tabularnewline
84 & 153.5 & 127.882241341353 & 25.6177586586473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271867&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]134.5[/C][C]138.63141025641[/C][C]-4.13141025641028[/C][/ROW]
[ROW][C]14[/C][C]121.3[/C][C]123.19982650436[/C][C]-1.89982650436002[/C][/ROW]
[ROW][C]15[/C][C]126.7[/C][C]127.147940007495[/C][C]-0.447940007495447[/C][/ROW]
[ROW][C]16[/C][C]117.7[/C][C]118.406204649359[/C][C]-0.706204649358796[/C][/ROW]
[ROW][C]17[/C][C]123[/C][C]125.141142447288[/C][C]-2.14114244728778[/C][/ROW]
[ROW][C]18[/C][C]132.1[/C][C]134.368704541617[/C][C]-2.26870454161653[/C][/ROW]
[ROW][C]19[/C][C]113.1[/C][C]112.435303222705[/C][C]0.664696777295219[/C][/ROW]
[ROW][C]20[/C][C]89.2[/C][C]87.7500775283742[/C][C]1.44992247162584[/C][/ROW]
[ROW][C]21[/C][C]121.7[/C][C]111.061490120945[/C][C]10.6385098790553[/C][/ROW]
[ROW][C]22[/C][C]105.3[/C][C]132.600824993223[/C][C]-27.3008249932227[/C][/ROW]
[ROW][C]23[/C][C]85.3[/C][C]96.860979328917[/C][C]-11.560979328917[/C][/ROW]
[ROW][C]24[/C][C]105.3[/C][C]98.5117319287841[/C][C]6.78826807121592[/C][/ROW]
[ROW][C]25[/C][C]72.2[/C][C]109.547187074301[/C][C]-37.3471870743013[/C][/ROW]
[ROW][C]26[/C][C]92.1[/C][C]77.517008365687[/C][C]14.582991634313[/C][/ROW]
[ROW][C]27[/C][C]97.2[/C][C]90.095491828013[/C][C]7.10450817198696[/C][/ROW]
[ROW][C]28[/C][C]78.6[/C][C]84.9084177701004[/C][C]-6.30841777010042[/C][/ROW]
[ROW][C]29[/C][C]78.1[/C][C]88.0648645003861[/C][C]-9.9648645003861[/C][/ROW]
[ROW][C]30[/C][C]93[/C][C]92.9599729592199[/C][C]0.0400270407800747[/C][/ROW]
[ROW][C]31[/C][C]81[/C][C]72.8761953355714[/C][C]8.12380466442862[/C][/ROW]
[ROW][C]32[/C][C]65.9[/C][C]52.0162588109085[/C][C]13.8837411890915[/C][/ROW]
[ROW][C]33[/C][C]88.6[/C][C]84.4880508775142[/C][C]4.11194912248581[/C][/ROW]
[ROW][C]34[/C][C]85.7[/C][C]90.1814019745297[/C][C]-4.48140197452969[/C][/ROW]
[ROW][C]35[/C][C]76.3[/C][C]71.1220387861417[/C][C]5.17796121385825[/C][/ROW]
[ROW][C]36[/C][C]96.8[/C][C]87.284862461759[/C][C]9.51513753824101[/C][/ROW]
[ROW][C]37[/C][C]76.8[/C][C]85.4247646128246[/C][C]-8.62476461282463[/C][/ROW]
[ROW][C]38[/C][C]85.6[/C][C]85.0920563822265[/C][C]0.507943617773492[/C][/ROW]
[ROW][C]39[/C][C]119.2[/C][C]88.1590486710454[/C][C]31.0409513289546[/C][/ROW]
[ROW][C]40[/C][C]91.4[/C][C]91.0876856724504[/C][C]0.312314327549586[/C][/ROW]
[ROW][C]41[/C][C]95.7[/C][C]96.7135179658564[/C][C]-1.01351796585641[/C][/ROW]
[ROW][C]42[/C][C]112.3[/C][C]109.748252968906[/C][C]2.55174703109402[/C][/ROW]
[ROW][C]43[/C][C]95.2[/C][C]93.9048344030332[/C][C]1.29516559696683[/C][/ROW]
[ROW][C]44[/C][C]82.8[/C][C]71.7220941649553[/C][C]11.0779058350447[/C][/ROW]
[ROW][C]45[/C][C]111.3[/C][C]99.8740207101303[/C][C]11.4259792898697[/C][/ROW]
[ROW][C]46[/C][C]108.2[/C][C]106.840136465139[/C][C]1.35986353486103[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]94.2525118658263[/C][C]2.74748813417372[/C][/ROW]
[ROW][C]48[/C][C]124.4[/C][C]110.921665544674[/C][C]13.4783344553259[/C][/ROW]
[ROW][C]49[/C][C]99.3[/C][C]105.566923346071[/C][C]-6.26692334607057[/C][/ROW]
[ROW][C]50[/C][C]117.6[/C][C]109.776821271519[/C][C]7.8231787284809[/C][/ROW]
[ROW][C]51[/C][C]131.5[/C][C]126.899453753414[/C][C]4.60054624658648[/C][/ROW]
[ROW][C]52[/C][C]114.2[/C][C]106.625473373207[/C][C]7.57452662679293[/C][/ROW]
[ROW][C]53[/C][C]116.8[/C][C]115.842745299402[/C][C]0.957254700597787[/C][/ROW]
[ROW][C]54[/C][C]116.5[/C][C]131.362493065237[/C][C]-14.8624930652371[/C][/ROW]
[ROW][C]55[/C][C]105.4[/C][C]106.440821903234[/C][C]-1.040821903234[/C][/ROW]
[ROW][C]56[/C][C]89.2[/C][C]86.4506159820135[/C][C]2.74938401798654[/C][/ROW]
[ROW][C]57[/C][C]115.8[/C][C]110.628065761719[/C][C]5.17193423828085[/C][/ROW]
[ROW][C]58[/C][C]111.4[/C][C]111.267910862961[/C][C]0.132089137038875[/C][/ROW]
[ROW][C]59[/C][C]106.4[/C][C]98.6296657386718[/C][C]7.77033426132823[/C][/ROW]
[ROW][C]60[/C][C]128.4[/C][C]121.499260170352[/C][C]6.90073982964779[/C][/ROW]
[ROW][C]61[/C][C]107.7[/C][C]106.498725401214[/C][C]1.20127459878631[/C][/ROW]
[ROW][C]62[/C][C]111[/C][C]119.252703804445[/C][C]-8.25270380444476[/C][/ROW]
[ROW][C]63[/C][C]129.8[/C][C]127.187821372285[/C][C]2.61217862771487[/C][/ROW]
[ROW][C]64[/C][C]130.5[/C][C]106.922360826995[/C][C]23.5776391730047[/C][/ROW]
[ROW][C]65[/C][C]142.9[/C][C]122.317546908713[/C][C]20.5824530912866[/C][/ROW]
[ROW][C]66[/C][C]159.9[/C][C]142.989162833977[/C][C]16.9108371660229[/C][/ROW]
[ROW][C]67[/C][C]84.1[/C][C]139.213078025087[/C][C]-55.1130780250875[/C][/ROW]
[ROW][C]68[/C][C]75[/C][C]92.9593161968043[/C][C]-17.9593161968043[/C][/ROW]
[ROW][C]69[/C][C]100.7[/C][C]107.361606105997[/C][C]-6.6616061059967[/C][/ROW]
[ROW][C]70[/C][C]106.8[/C][C]100.275634038598[/C][C]6.52436596140234[/C][/ROW]
[ROW][C]71[/C][C]97.4[/C][C]93.3698481847513[/C][C]4.03015181524869[/C][/ROW]
[ROW][C]72[/C][C]113[/C][C]114.015543103007[/C][C]-1.01554310300659[/C][/ROW]
[ROW][C]73[/C][C]76.9[/C][C]93.0477205620533[/C][C]-16.1477205620533[/C][/ROW]
[ROW][C]74[/C][C]87.3[/C][C]93.702329594828[/C][C]-6.40232959482802[/C][/ROW]
[ROW][C]75[/C][C]103.7[/C][C]105.946704255696[/C][C]-2.24670425569606[/C][/ROW]
[ROW][C]76[/C][C]92.1[/C][C]89.8116307877439[/C][C]2.28836921225613[/C][/ROW]
[ROW][C]77[/C][C]92.9[/C][C]93.055496217745[/C][C]-0.155496217745011[/C][/ROW]
[ROW][C]78[/C][C]112.2[/C][C]101.524223189034[/C][C]10.6757768109665[/C][/ROW]
[ROW][C]79[/C][C]88.7[/C][C]70.7540203641436[/C][C]17.9459796358564[/C][/ROW]
[ROW][C]80[/C][C]74.6[/C][C]73.8254072201006[/C][C]0.774592779899393[/C][/ROW]
[ROW][C]81[/C][C]101.5[/C][C]101.515572544488[/C][C]-0.0155725444877532[/C][/ROW]
[ROW][C]82[/C][C]119.7[/C][C]102.19056441091[/C][C]17.5094355890901[/C][/ROW]
[ROW][C]83[/C][C]120.7[/C][C]100.237829176956[/C][C]20.4621708230435[/C][/ROW]
[ROW][C]84[/C][C]153.5[/C][C]127.882241341353[/C][C]25.6177586586473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271867&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271867&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
13134.5138.63141025641-4.13141025641028
14121.3123.19982650436-1.89982650436002
15126.7127.147940007495-0.447940007495447
16117.7118.406204649359-0.706204649358796
17123125.141142447288-2.14114244728778
18132.1134.368704541617-2.26870454161653
19113.1112.4353032227050.664696777295219
2089.287.75007752837421.44992247162584
21121.7111.06149012094510.6385098790553
22105.3132.600824993223-27.3008249932227
2385.396.860979328917-11.560979328917
24105.398.51173192878416.78826807121592
2572.2109.547187074301-37.3471870743013
2692.177.51700836568714.582991634313
2797.290.0954918280137.10450817198696
2878.684.9084177701004-6.30841777010042
2978.188.0648645003861-9.9648645003861
309392.95997295921990.0400270407800747
318172.87619533557148.12380466442862
3265.952.016258810908513.8837411890915
3388.684.48805087751424.11194912248581
3485.790.1814019745297-4.48140197452969
3576.371.12203878614175.17796121385825
3696.887.2848624617599.51513753824101
3776.885.4247646128246-8.62476461282463
3885.685.09205638222650.507943617773492
39119.288.159048671045431.0409513289546
4091.491.08768567245040.312314327549586
4195.796.7135179658564-1.01351796585641
42112.3109.7482529689062.55174703109402
4395.293.90483440303321.29516559696683
4482.871.722094164955311.0779058350447
45111.399.874020710130311.4259792898697
46108.2106.8401364651391.35986353486103
479794.25251186582632.74748813417372
48124.4110.92166554467413.4783344553259
4999.3105.566923346071-6.26692334607057
50117.6109.7768212715197.8231787284809
51131.5126.8994537534144.60054624658648
52114.2106.6254733732077.57452662679293
53116.8115.8427452994020.957254700597787
54116.5131.362493065237-14.8624930652371
55105.4106.440821903234-1.040821903234
5689.286.45061598201352.74938401798654
57115.8110.6280657617195.17193423828085
58111.4111.2679108629610.132089137038875
59106.498.62966573867187.77033426132823
60128.4121.4992601703526.90073982964779
61107.7106.4987254012141.20127459878631
62111119.252703804445-8.25270380444476
63129.8127.1878213722852.61217862771487
64130.5106.92236082699523.5776391730047
65142.9122.31754690871320.5824530912866
66159.9142.98916283397716.9108371660229
6784.1139.213078025087-55.1130780250875
687592.9593161968043-17.9593161968043
69100.7107.361606105997-6.6616061059967
70106.8100.2756340385986.52436596140234
7197.493.36984818475134.03015181524869
72113114.015543103007-1.01554310300659
7376.993.0477205620533-16.1477205620533
7487.393.702329594828-6.40232959482802
75103.7105.946704255696-2.24670425569606
7692.189.81163078774392.28836921225613
7792.993.055496217745-0.155496217745011
78112.2101.52422318903410.6757768109665
7988.770.754020364143617.9459796358564
8074.673.82540722010060.774592779899393
81101.5101.515572544488-0.0155725444877532
82119.7102.1905644109117.5094355890901
83120.7100.23782917695620.4621708230435
84153.5127.88224134135325.6177586586473







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85116.00024112342590.4546880291033141.545794217747
86128.53997456931699.7894102997456157.290538838886
87145.912894021888114.221645980107177.604142063669
88132.91862323803198.4826622829011167.354584193161
89134.71046414617797.6816252051748171.739303087179
90147.281724347875107.781432249975186.782016445776
91113.86681724830571.9945203381396155.73911415847
92102.55417424632458.3928474366967146.715501055951
93129.94143985443183.5613466989839176.321533009878
94136.65691603771588.1182781373356185.195553938095
95126.96910786469376.3240575234921177.614158205893
96145.97189930660793.2659446169221198.677853996292

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 116.000241123425 & 90.4546880291033 & 141.545794217747 \tabularnewline
86 & 128.539974569316 & 99.7894102997456 & 157.290538838886 \tabularnewline
87 & 145.912894021888 & 114.221645980107 & 177.604142063669 \tabularnewline
88 & 132.918623238031 & 98.4826622829011 & 167.354584193161 \tabularnewline
89 & 134.710464146177 & 97.6816252051748 & 171.739303087179 \tabularnewline
90 & 147.281724347875 & 107.781432249975 & 186.782016445776 \tabularnewline
91 & 113.866817248305 & 71.9945203381396 & 155.73911415847 \tabularnewline
92 & 102.554174246324 & 58.3928474366967 & 146.715501055951 \tabularnewline
93 & 129.941439854431 & 83.5613466989839 & 176.321533009878 \tabularnewline
94 & 136.656916037715 & 88.1182781373356 & 185.195553938095 \tabularnewline
95 & 126.969107864693 & 76.3240575234921 & 177.614158205893 \tabularnewline
96 & 145.971899306607 & 93.2659446169221 & 198.677853996292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271867&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]85[/C][C]116.000241123425[/C][C]90.4546880291033[/C][C]141.545794217747[/C][/ROW]
[ROW][C]86[/C][C]128.539974569316[/C][C]99.7894102997456[/C][C]157.290538838886[/C][/ROW]
[ROW][C]87[/C][C]145.912894021888[/C][C]114.221645980107[/C][C]177.604142063669[/C][/ROW]
[ROW][C]88[/C][C]132.918623238031[/C][C]98.4826622829011[/C][C]167.354584193161[/C][/ROW]
[ROW][C]89[/C][C]134.710464146177[/C][C]97.6816252051748[/C][C]171.739303087179[/C][/ROW]
[ROW][C]90[/C][C]147.281724347875[/C][C]107.781432249975[/C][C]186.782016445776[/C][/ROW]
[ROW][C]91[/C][C]113.866817248305[/C][C]71.9945203381396[/C][C]155.73911415847[/C][/ROW]
[ROW][C]92[/C][C]102.554174246324[/C][C]58.3928474366967[/C][C]146.715501055951[/C][/ROW]
[ROW][C]93[/C][C]129.941439854431[/C][C]83.5613466989839[/C][C]176.321533009878[/C][/ROW]
[ROW][C]94[/C][C]136.656916037715[/C][C]88.1182781373356[/C][C]185.195553938095[/C][/ROW]
[ROW][C]95[/C][C]126.969107864693[/C][C]76.3240575234921[/C][C]177.614158205893[/C][/ROW]
[ROW][C]96[/C][C]145.971899306607[/C][C]93.2659446169221[/C][C]198.677853996292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271867&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271867&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
85116.00024112342590.4546880291033141.545794217747
86128.53997456931699.7894102997456157.290538838886
87145.912894021888114.221645980107177.604142063669
88132.91862323803198.4826622829011167.354584193161
89134.71046414617797.6816252051748171.739303087179
90147.281724347875107.781432249975186.782016445776
91113.86681724830571.9945203381396155.73911415847
92102.55417424632458.3928474366967146.715501055951
93129.94143985443183.5613466989839176.321533009878
94136.65691603771588.1182781373356185.195553938095
95126.96910786469376.3240575234921177.614158205893
96145.97189930660793.2659446169221198.677853996292



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=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')