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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 19:13:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461694442yiwskpb1iiz4pee.htm/, Retrieved Fri, 03 May 2024 23:38:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294951, Retrieved Fri, 03 May 2024 23:38:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 18:13:38] [66b954879edaa66f79d20403c5a86347] [Current]
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Dataseries X:
89.8
89.2
89.9
88.9
84
86.3
89.3
90.6
88.3
91.6
95.4
96.8
92.5
93.6
93.8
92.7
88.3
90.4
91.2
91.5
88.9
88.6
89.1
89.4
86.7
89.8
90.9
91.4
90.2
92.2
94
95.8
95.1
96.2
96.8
97.1
96.5
97.2
97.8
99.9
101.2
103.3
104.5
100.8
95
93.4
93.1
94.9
96.9
100.9
100.2
101.8
105.4
106.4
105.6
107.5
109.5
108.6
109.2
110.3
110.3
107.9
107.7
108.1
108
105.9
105.9
104.7




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294951&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294951&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294951&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.774437930244399
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.774437930244399 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294951&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]0.774437930244399[/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=294951&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294951&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
alpha0.774437930244399
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.590.58164684661371.91835315338633
1493.693.18628451710150.413715482898454
1593.893.78527001563980.0147299843601587
1692.792.9381573118243-0.238157311824281
1788.388.8591441957-0.559144195699986
1890.491.2348614954996-0.834861495499581
1991.290.63827187386240.561728126137623
2091.592.2369561453472-0.736956145347207
2188.989.1348382758021-0.234838275802076
2288.692.0930097382719-3.49300973827187
2389.192.8984072354697-3.79840723546975
2489.491.0763282064636-1.67632820646361
2586.786.10034697754280.599653022457161
2689.887.30314869764362.49685130235639
2790.989.42323992745471.47676007254532
2891.489.68764152049021.71235847950976
2990.287.12077990009953.07922009990052
3092.292.286235668141-0.0862356681409722
319492.58836269672461.41163730327543
3295.894.57113761447931.22886238552069
3395.192.99227669834912.10772330165092
3496.297.1502129340102-0.950212934010167
3596.8100.116267457984-3.31626745798378
3697.199.2778540608627-2.17785406086271
3796.594.12315458345292.3768454165471
3897.297.2260386232202-0.0260386232201881
3997.897.14228056922090.657719430779068
4099.996.74762642808143.15237357191859
41101.295.2671692965625.932830703438
42103.3102.1351032289571.16489677104283
43104.5103.8065700790060.693429920994049
44100.8105.266753052546-4.46675305254564
459599.311685654959-4.31168565495899
4693.497.8223506993977-4.42235069939773
4793.197.4897581994815-4.38975819948148
4894.996.0170023289586-1.11700232895856
4996.992.75297766463664.14702233536345
50100.996.68155159594494.21844840405507
51100.2100.0368372603650.163162739635382
52101.899.7922685965252.00773140347499
53105.497.94034514269687.45965485730318
54106.4104.9392317839071.4607682160935
55105.6106.746701367795-1.1467013677955
56107.5105.5782595836931.92174041630719
57109.5104.4083213476145.09167865238599
58108.6110.372189543119-1.77218954311944
59109.2112.551569113203-3.35156911320333
60110.3113.074446981741-2.77444698174099
61110.3109.4487401801860.851259819813521
62107.9110.885947092395-2.9859470923947
63107.7107.6733784121690.0266215878314995
64108.1107.724348249040.375651750960401
65108105.597346375742.40265362425954
66105.9107.317913885624-1.41791388562361
67105.9106.305796977775-0.405796977774983
68104.7106.398225343915-1.6982253439148

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.5 & 90.5816468466137 & 1.91835315338633 \tabularnewline
14 & 93.6 & 93.1862845171015 & 0.413715482898454 \tabularnewline
15 & 93.8 & 93.7852700156398 & 0.0147299843601587 \tabularnewline
16 & 92.7 & 92.9381573118243 & -0.238157311824281 \tabularnewline
17 & 88.3 & 88.8591441957 & -0.559144195699986 \tabularnewline
18 & 90.4 & 91.2348614954996 & -0.834861495499581 \tabularnewline
19 & 91.2 & 90.6382718738624 & 0.561728126137623 \tabularnewline
20 & 91.5 & 92.2369561453472 & -0.736956145347207 \tabularnewline
21 & 88.9 & 89.1348382758021 & -0.234838275802076 \tabularnewline
22 & 88.6 & 92.0930097382719 & -3.49300973827187 \tabularnewline
23 & 89.1 & 92.8984072354697 & -3.79840723546975 \tabularnewline
24 & 89.4 & 91.0763282064636 & -1.67632820646361 \tabularnewline
25 & 86.7 & 86.1003469775428 & 0.599653022457161 \tabularnewline
26 & 89.8 & 87.3031486976436 & 2.49685130235639 \tabularnewline
27 & 90.9 & 89.4232399274547 & 1.47676007254532 \tabularnewline
28 & 91.4 & 89.6876415204902 & 1.71235847950976 \tabularnewline
29 & 90.2 & 87.1207799000995 & 3.07922009990052 \tabularnewline
30 & 92.2 & 92.286235668141 & -0.0862356681409722 \tabularnewline
31 & 94 & 92.5883626967246 & 1.41163730327543 \tabularnewline
32 & 95.8 & 94.5711376144793 & 1.22886238552069 \tabularnewline
33 & 95.1 & 92.9922766983491 & 2.10772330165092 \tabularnewline
34 & 96.2 & 97.1502129340102 & -0.950212934010167 \tabularnewline
35 & 96.8 & 100.116267457984 & -3.31626745798378 \tabularnewline
36 & 97.1 & 99.2778540608627 & -2.17785406086271 \tabularnewline
37 & 96.5 & 94.1231545834529 & 2.3768454165471 \tabularnewline
38 & 97.2 & 97.2260386232202 & -0.0260386232201881 \tabularnewline
39 & 97.8 & 97.1422805692209 & 0.657719430779068 \tabularnewline
40 & 99.9 & 96.7476264280814 & 3.15237357191859 \tabularnewline
41 & 101.2 & 95.267169296562 & 5.932830703438 \tabularnewline
42 & 103.3 & 102.135103228957 & 1.16489677104283 \tabularnewline
43 & 104.5 & 103.806570079006 & 0.693429920994049 \tabularnewline
44 & 100.8 & 105.266753052546 & -4.46675305254564 \tabularnewline
45 & 95 & 99.311685654959 & -4.31168565495899 \tabularnewline
46 & 93.4 & 97.8223506993977 & -4.42235069939773 \tabularnewline
47 & 93.1 & 97.4897581994815 & -4.38975819948148 \tabularnewline
48 & 94.9 & 96.0170023289586 & -1.11700232895856 \tabularnewline
49 & 96.9 & 92.7529776646366 & 4.14702233536345 \tabularnewline
50 & 100.9 & 96.6815515959449 & 4.21844840405507 \tabularnewline
51 & 100.2 & 100.036837260365 & 0.163162739635382 \tabularnewline
52 & 101.8 & 99.792268596525 & 2.00773140347499 \tabularnewline
53 & 105.4 & 97.9403451426968 & 7.45965485730318 \tabularnewline
54 & 106.4 & 104.939231783907 & 1.4607682160935 \tabularnewline
55 & 105.6 & 106.746701367795 & -1.1467013677955 \tabularnewline
56 & 107.5 & 105.578259583693 & 1.92174041630719 \tabularnewline
57 & 109.5 & 104.408321347614 & 5.09167865238599 \tabularnewline
58 & 108.6 & 110.372189543119 & -1.77218954311944 \tabularnewline
59 & 109.2 & 112.551569113203 & -3.35156911320333 \tabularnewline
60 & 110.3 & 113.074446981741 & -2.77444698174099 \tabularnewline
61 & 110.3 & 109.448740180186 & 0.851259819813521 \tabularnewline
62 & 107.9 & 110.885947092395 & -2.9859470923947 \tabularnewline
63 & 107.7 & 107.673378412169 & 0.0266215878314995 \tabularnewline
64 & 108.1 & 107.72434824904 & 0.375651750960401 \tabularnewline
65 & 108 & 105.59734637574 & 2.40265362425954 \tabularnewline
66 & 105.9 & 107.317913885624 & -1.41791388562361 \tabularnewline
67 & 105.9 & 106.305796977775 & -0.405796977774983 \tabularnewline
68 & 104.7 & 106.398225343915 & -1.6982253439148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294951&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]92.5[/C][C]90.5816468466137[/C][C]1.91835315338633[/C][/ROW]
[ROW][C]14[/C][C]93.6[/C][C]93.1862845171015[/C][C]0.413715482898454[/C][/ROW]
[ROW][C]15[/C][C]93.8[/C][C]93.7852700156398[/C][C]0.0147299843601587[/C][/ROW]
[ROW][C]16[/C][C]92.7[/C][C]92.9381573118243[/C][C]-0.238157311824281[/C][/ROW]
[ROW][C]17[/C][C]88.3[/C][C]88.8591441957[/C][C]-0.559144195699986[/C][/ROW]
[ROW][C]18[/C][C]90.4[/C][C]91.2348614954996[/C][C]-0.834861495499581[/C][/ROW]
[ROW][C]19[/C][C]91.2[/C][C]90.6382718738624[/C][C]0.561728126137623[/C][/ROW]
[ROW][C]20[/C][C]91.5[/C][C]92.2369561453472[/C][C]-0.736956145347207[/C][/ROW]
[ROW][C]21[/C][C]88.9[/C][C]89.1348382758021[/C][C]-0.234838275802076[/C][/ROW]
[ROW][C]22[/C][C]88.6[/C][C]92.0930097382719[/C][C]-3.49300973827187[/C][/ROW]
[ROW][C]23[/C][C]89.1[/C][C]92.8984072354697[/C][C]-3.79840723546975[/C][/ROW]
[ROW][C]24[/C][C]89.4[/C][C]91.0763282064636[/C][C]-1.67632820646361[/C][/ROW]
[ROW][C]25[/C][C]86.7[/C][C]86.1003469775428[/C][C]0.599653022457161[/C][/ROW]
[ROW][C]26[/C][C]89.8[/C][C]87.3031486976436[/C][C]2.49685130235639[/C][/ROW]
[ROW][C]27[/C][C]90.9[/C][C]89.4232399274547[/C][C]1.47676007254532[/C][/ROW]
[ROW][C]28[/C][C]91.4[/C][C]89.6876415204902[/C][C]1.71235847950976[/C][/ROW]
[ROW][C]29[/C][C]90.2[/C][C]87.1207799000995[/C][C]3.07922009990052[/C][/ROW]
[ROW][C]30[/C][C]92.2[/C][C]92.286235668141[/C][C]-0.0862356681409722[/C][/ROW]
[ROW][C]31[/C][C]94[/C][C]92.5883626967246[/C][C]1.41163730327543[/C][/ROW]
[ROW][C]32[/C][C]95.8[/C][C]94.5711376144793[/C][C]1.22886238552069[/C][/ROW]
[ROW][C]33[/C][C]95.1[/C][C]92.9922766983491[/C][C]2.10772330165092[/C][/ROW]
[ROW][C]34[/C][C]96.2[/C][C]97.1502129340102[/C][C]-0.950212934010167[/C][/ROW]
[ROW][C]35[/C][C]96.8[/C][C]100.116267457984[/C][C]-3.31626745798378[/C][/ROW]
[ROW][C]36[/C][C]97.1[/C][C]99.2778540608627[/C][C]-2.17785406086271[/C][/ROW]
[ROW][C]37[/C][C]96.5[/C][C]94.1231545834529[/C][C]2.3768454165471[/C][/ROW]
[ROW][C]38[/C][C]97.2[/C][C]97.2260386232202[/C][C]-0.0260386232201881[/C][/ROW]
[ROW][C]39[/C][C]97.8[/C][C]97.1422805692209[/C][C]0.657719430779068[/C][/ROW]
[ROW][C]40[/C][C]99.9[/C][C]96.7476264280814[/C][C]3.15237357191859[/C][/ROW]
[ROW][C]41[/C][C]101.2[/C][C]95.267169296562[/C][C]5.932830703438[/C][/ROW]
[ROW][C]42[/C][C]103.3[/C][C]102.135103228957[/C][C]1.16489677104283[/C][/ROW]
[ROW][C]43[/C][C]104.5[/C][C]103.806570079006[/C][C]0.693429920994049[/C][/ROW]
[ROW][C]44[/C][C]100.8[/C][C]105.266753052546[/C][C]-4.46675305254564[/C][/ROW]
[ROW][C]45[/C][C]95[/C][C]99.311685654959[/C][C]-4.31168565495899[/C][/ROW]
[ROW][C]46[/C][C]93.4[/C][C]97.8223506993977[/C][C]-4.42235069939773[/C][/ROW]
[ROW][C]47[/C][C]93.1[/C][C]97.4897581994815[/C][C]-4.38975819948148[/C][/ROW]
[ROW][C]48[/C][C]94.9[/C][C]96.0170023289586[/C][C]-1.11700232895856[/C][/ROW]
[ROW][C]49[/C][C]96.9[/C][C]92.7529776646366[/C][C]4.14702233536345[/C][/ROW]
[ROW][C]50[/C][C]100.9[/C][C]96.6815515959449[/C][C]4.21844840405507[/C][/ROW]
[ROW][C]51[/C][C]100.2[/C][C]100.036837260365[/C][C]0.163162739635382[/C][/ROW]
[ROW][C]52[/C][C]101.8[/C][C]99.792268596525[/C][C]2.00773140347499[/C][/ROW]
[ROW][C]53[/C][C]105.4[/C][C]97.9403451426968[/C][C]7.45965485730318[/C][/ROW]
[ROW][C]54[/C][C]106.4[/C][C]104.939231783907[/C][C]1.4607682160935[/C][/ROW]
[ROW][C]55[/C][C]105.6[/C][C]106.746701367795[/C][C]-1.1467013677955[/C][/ROW]
[ROW][C]56[/C][C]107.5[/C][C]105.578259583693[/C][C]1.92174041630719[/C][/ROW]
[ROW][C]57[/C][C]109.5[/C][C]104.408321347614[/C][C]5.09167865238599[/C][/ROW]
[ROW][C]58[/C][C]108.6[/C][C]110.372189543119[/C][C]-1.77218954311944[/C][/ROW]
[ROW][C]59[/C][C]109.2[/C][C]112.551569113203[/C][C]-3.35156911320333[/C][/ROW]
[ROW][C]60[/C][C]110.3[/C][C]113.074446981741[/C][C]-2.77444698174099[/C][/ROW]
[ROW][C]61[/C][C]110.3[/C][C]109.448740180186[/C][C]0.851259819813521[/C][/ROW]
[ROW][C]62[/C][C]107.9[/C][C]110.885947092395[/C][C]-2.9859470923947[/C][/ROW]
[ROW][C]63[/C][C]107.7[/C][C]107.673378412169[/C][C]0.0266215878314995[/C][/ROW]
[ROW][C]64[/C][C]108.1[/C][C]107.72434824904[/C][C]0.375651750960401[/C][/ROW]
[ROW][C]65[/C][C]108[/C][C]105.59734637574[/C][C]2.40265362425954[/C][/ROW]
[ROW][C]66[/C][C]105.9[/C][C]107.317913885624[/C][C]-1.41791388562361[/C][/ROW]
[ROW][C]67[/C][C]105.9[/C][C]106.305796977775[/C][C]-0.405796977774983[/C][/ROW]
[ROW][C]68[/C][C]104.7[/C][C]106.398225343915[/C][C]-1.6982253439148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294951&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294951&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
1392.590.58164684661371.91835315338633
1493.693.18628451710150.413715482898454
1593.893.78527001563980.0147299843601587
1692.792.9381573118243-0.238157311824281
1788.388.8591441957-0.559144195699986
1890.491.2348614954996-0.834861495499581
1991.290.63827187386240.561728126137623
2091.592.2369561453472-0.736956145347207
2188.989.1348382758021-0.234838275802076
2288.692.0930097382719-3.49300973827187
2389.192.8984072354697-3.79840723546975
2489.491.0763282064636-1.67632820646361
2586.786.10034697754280.599653022457161
2689.887.30314869764362.49685130235639
2790.989.42323992745471.47676007254532
2891.489.68764152049021.71235847950976
2990.287.12077990009953.07922009990052
3092.292.286235668141-0.0862356681409722
319492.58836269672461.41163730327543
3295.894.57113761447931.22886238552069
3395.192.99227669834912.10772330165092
3496.297.1502129340102-0.950212934010167
3596.8100.116267457984-3.31626745798378
3697.199.2778540608627-2.17785406086271
3796.594.12315458345292.3768454165471
3897.297.2260386232202-0.0260386232201881
3997.897.14228056922090.657719430779068
4099.996.74762642808143.15237357191859
41101.295.2671692965625.932830703438
42103.3102.1351032289571.16489677104283
43104.5103.8065700790060.693429920994049
44100.8105.266753052546-4.46675305254564
459599.311685654959-4.31168565495899
4693.497.8223506993977-4.42235069939773
4793.197.4897581994815-4.38975819948148
4894.996.0170023289586-1.11700232895856
4996.992.75297766463664.14702233536345
50100.996.68155159594494.21844840405507
51100.2100.0368372603650.163162739635382
52101.899.7922685965252.00773140347499
53105.497.94034514269687.45965485730318
54106.4104.9392317839071.4607682160935
55105.6106.746701367795-1.1467013677955
56107.5105.5782595836931.92174041630719
57109.5104.4083213476145.09167865238599
58108.6110.372189543119-1.77218954311944
59109.2112.551569113203-3.35156911320333
60110.3113.074446981741-2.77444698174099
61110.3109.4487401801860.851259819813521
62107.9110.885947092395-2.9859470923947
63107.7107.6733784121690.0266215878314995
64108.1107.724348249040.375651750960401
65108105.597346375742.40265362425954
66105.9107.317913885624-1.41791388562361
67105.9106.305796977775-0.405796977774983
68104.7106.398225343915-1.6982253439148







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
69103.14577281492397.9816850399565108.30986058989
70103.59402514020197.055022678105110.133027602297
71106.63178115722498.8489715339812114.414590780467
72109.795587868715100.883148678888118.708027058542
73109.13886856235199.4215347903121118.85620233439
74109.03953902376598.5491496675607119.529928379969
75108.81507969785797.61804728957120.012112106143
76108.92357825466297.0368297948499120.810326714474
77106.93740979123294.5989077937604119.275911788704
78105.94344544249593.0885035125373118.798387372453
79106.25751040343492.7758608884921119.739159918375
80106.36778981136467.8223361628089144.913243459919

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
69 & 103.145772814923 & 97.9816850399565 & 108.30986058989 \tabularnewline
70 & 103.594025140201 & 97.055022678105 & 110.133027602297 \tabularnewline
71 & 106.631781157224 & 98.8489715339812 & 114.414590780467 \tabularnewline
72 & 109.795587868715 & 100.883148678888 & 118.708027058542 \tabularnewline
73 & 109.138868562351 & 99.4215347903121 & 118.85620233439 \tabularnewline
74 & 109.039539023765 & 98.5491496675607 & 119.529928379969 \tabularnewline
75 & 108.815079697857 & 97.61804728957 & 120.012112106143 \tabularnewline
76 & 108.923578254662 & 97.0368297948499 & 120.810326714474 \tabularnewline
77 & 106.937409791232 & 94.5989077937604 & 119.275911788704 \tabularnewline
78 & 105.943445442495 & 93.0885035125373 & 118.798387372453 \tabularnewline
79 & 106.257510403434 & 92.7758608884921 & 119.739159918375 \tabularnewline
80 & 106.367789811364 & 67.8223361628089 & 144.913243459919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294951&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]69[/C][C]103.145772814923[/C][C]97.9816850399565[/C][C]108.30986058989[/C][/ROW]
[ROW][C]70[/C][C]103.594025140201[/C][C]97.055022678105[/C][C]110.133027602297[/C][/ROW]
[ROW][C]71[/C][C]106.631781157224[/C][C]98.8489715339812[/C][C]114.414590780467[/C][/ROW]
[ROW][C]72[/C][C]109.795587868715[/C][C]100.883148678888[/C][C]118.708027058542[/C][/ROW]
[ROW][C]73[/C][C]109.138868562351[/C][C]99.4215347903121[/C][C]118.85620233439[/C][/ROW]
[ROW][C]74[/C][C]109.039539023765[/C][C]98.5491496675607[/C][C]119.529928379969[/C][/ROW]
[ROW][C]75[/C][C]108.815079697857[/C][C]97.61804728957[/C][C]120.012112106143[/C][/ROW]
[ROW][C]76[/C][C]108.923578254662[/C][C]97.0368297948499[/C][C]120.810326714474[/C][/ROW]
[ROW][C]77[/C][C]106.937409791232[/C][C]94.5989077937604[/C][C]119.275911788704[/C][/ROW]
[ROW][C]78[/C][C]105.943445442495[/C][C]93.0885035125373[/C][C]118.798387372453[/C][/ROW]
[ROW][C]79[/C][C]106.257510403434[/C][C]92.7758608884921[/C][C]119.739159918375[/C][/ROW]
[ROW][C]80[/C][C]106.367789811364[/C][C]67.8223361628089[/C][C]144.913243459919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294951&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294951&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
69103.14577281492397.9816850399565108.30986058989
70103.59402514020197.055022678105110.133027602297
71106.63178115722498.8489715339812114.414590780467
72109.795587868715100.883148678888118.708027058542
73109.13886856235199.4215347903121118.85620233439
74109.03953902376598.5491496675607119.529928379969
75108.81507969785797.61804728957120.012112106143
76108.92357825466297.0368297948499120.810326714474
77106.93740979123294.5989077937604119.275911788704
78105.94344544249593.0885035125373118.798387372453
79106.25751040343492.7758608884921119.739159918375
80106.36778981136467.8223361628089144.913243459919



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')