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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 Nov 2011 16:00:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/25/t1322254817sb0f18gxpbicv6j.htm/, Retrieved Thu, 28 Mar 2024 13:27:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147359, Retrieved Thu, 28 Mar 2024 13:27:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- R P         [Univariate Data Series] [WS8 Time Series A...] [2010-11-30 09:10:08] [afe9379cca749d06b3d6872e02cc47ed]
- R PD          [Univariate Data Series] [] [2011-11-25 19:20:16] [f1de53e71fac758e9834be8effee591f]
- RMPD              [Exponential Smoothing] [] [2011-11-25 21:00:09] [13d85cac30d4a10947636c080219d4f4] [Current]
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Dataseries X:
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
10.943
9.867
10.203
10.837
10.573
10.647
11.502
10.656
10.866
10.835
9.945
10.331




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147359&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147359&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147359&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.415506640094717

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.415506640094717 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147359&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.415506640094717[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147359&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147359&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
beta0
gamma0.415506640094717







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139.8499.672372596153840.176627403846156
149.1729.016732881701630.155267118298372
1510.31310.15471816724940.158281832750587
169.8199.655245119463870.163754880536134
179.9559.794647071678320.160352928321682
1810.0489.91438235722610.133617642773897
1910.08210.5306176427739-0.44861764277389
2010.54110.3129362616550.228063738344993
2110.20810.08496321386950.123036786130541
2210.2339.924198499417240.308801500582756
239.4399.48251711829836-0.0435171182983627
249.96310.1670440705128-0.204044070512817
2510.1589.987085881848040.170914118151963
269.2259.3225708269164-0.0975708269163977
2710.47410.46180874633710.0121912536629321
289.7579.96460978624797-0.207609786247971
2910.4910.1025982047280.387401795271968
3010.28110.21122480160590.0697751983941153
3110.44410.5855374599111-0.141537459911122
3210.6410.6490216858756-0.00902168587559871
3310.69510.3774092420560.317590757943965
3410.78610.2938309999540.492169000045983
359.8329.705758893261030.126241106738972
369.74710.3235858309162-0.57658583091621
3710.41110.29942525939950.111574740600465
389.5119.52335292702653-0.0123529270265266
3910.40210.7081977197585-0.306197719758519
409.70110.1196699680867-0.418669968086716
4110.5410.50488964962160.0351103503784262
4210.11210.481540286426-0.369540286425989
4310.91510.76805113206930.146948867930664
4411.18310.88659654206290.296403457937137
4510.38410.7506937373879-0.366693737387891
4610.83410.73965391409530.094346085904677
479.8869.9995363379374-0.113536337937402
4810.21610.3253340161594-0.109334016159419
4910.94310.58710873155930.355891268440704
509.8679.759543630395820.107456369604179
5110.20310.8222939605904-0.619293960590417
5210.83710.18703324291190.649966757088134
5310.57310.7608016599133-0.187801659913283
5410.64710.56931727020690.0776827297930893
5511.50211.07043278902240.431567210977649
5610.65611.2510775735562-0.595077573556202
5710.86610.83965348119550.0263465188045036
5810.83511.0201787658291-0.185178765829084
599.94510.1936846622058-0.248684662205795
6010.33110.5212284330304-0.190228433030381

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9.849 & 9.67237259615384 & 0.176627403846156 \tabularnewline
14 & 9.172 & 9.01673288170163 & 0.155267118298372 \tabularnewline
15 & 10.313 & 10.1547181672494 & 0.158281832750587 \tabularnewline
16 & 9.819 & 9.65524511946387 & 0.163754880536134 \tabularnewline
17 & 9.955 & 9.79464707167832 & 0.160352928321682 \tabularnewline
18 & 10.048 & 9.9143823572261 & 0.133617642773897 \tabularnewline
19 & 10.082 & 10.5306176427739 & -0.44861764277389 \tabularnewline
20 & 10.541 & 10.312936261655 & 0.228063738344993 \tabularnewline
21 & 10.208 & 10.0849632138695 & 0.123036786130541 \tabularnewline
22 & 10.233 & 9.92419849941724 & 0.308801500582756 \tabularnewline
23 & 9.439 & 9.48251711829836 & -0.0435171182983627 \tabularnewline
24 & 9.963 & 10.1670440705128 & -0.204044070512817 \tabularnewline
25 & 10.158 & 9.98708588184804 & 0.170914118151963 \tabularnewline
26 & 9.225 & 9.3225708269164 & -0.0975708269163977 \tabularnewline
27 & 10.474 & 10.4618087463371 & 0.0121912536629321 \tabularnewline
28 & 9.757 & 9.96460978624797 & -0.207609786247971 \tabularnewline
29 & 10.49 & 10.102598204728 & 0.387401795271968 \tabularnewline
30 & 10.281 & 10.2112248016059 & 0.0697751983941153 \tabularnewline
31 & 10.444 & 10.5855374599111 & -0.141537459911122 \tabularnewline
32 & 10.64 & 10.6490216858756 & -0.00902168587559871 \tabularnewline
33 & 10.695 & 10.377409242056 & 0.317590757943965 \tabularnewline
34 & 10.786 & 10.293830999954 & 0.492169000045983 \tabularnewline
35 & 9.832 & 9.70575889326103 & 0.126241106738972 \tabularnewline
36 & 9.747 & 10.3235858309162 & -0.57658583091621 \tabularnewline
37 & 10.411 & 10.2994252593995 & 0.111574740600465 \tabularnewline
38 & 9.511 & 9.52335292702653 & -0.0123529270265266 \tabularnewline
39 & 10.402 & 10.7081977197585 & -0.306197719758519 \tabularnewline
40 & 9.701 & 10.1196699680867 & -0.418669968086716 \tabularnewline
41 & 10.54 & 10.5048896496216 & 0.0351103503784262 \tabularnewline
42 & 10.112 & 10.481540286426 & -0.369540286425989 \tabularnewline
43 & 10.915 & 10.7680511320693 & 0.146948867930664 \tabularnewline
44 & 11.183 & 10.8865965420629 & 0.296403457937137 \tabularnewline
45 & 10.384 & 10.7506937373879 & -0.366693737387891 \tabularnewline
46 & 10.834 & 10.7396539140953 & 0.094346085904677 \tabularnewline
47 & 9.886 & 9.9995363379374 & -0.113536337937402 \tabularnewline
48 & 10.216 & 10.3253340161594 & -0.109334016159419 \tabularnewline
49 & 10.943 & 10.5871087315593 & 0.355891268440704 \tabularnewline
50 & 9.867 & 9.75954363039582 & 0.107456369604179 \tabularnewline
51 & 10.203 & 10.8222939605904 & -0.619293960590417 \tabularnewline
52 & 10.837 & 10.1870332429119 & 0.649966757088134 \tabularnewline
53 & 10.573 & 10.7608016599133 & -0.187801659913283 \tabularnewline
54 & 10.647 & 10.5693172702069 & 0.0776827297930893 \tabularnewline
55 & 11.502 & 11.0704327890224 & 0.431567210977649 \tabularnewline
56 & 10.656 & 11.2510775735562 & -0.595077573556202 \tabularnewline
57 & 10.866 & 10.8396534811955 & 0.0263465188045036 \tabularnewline
58 & 10.835 & 11.0201787658291 & -0.185178765829084 \tabularnewline
59 & 9.945 & 10.1936846622058 & -0.248684662205795 \tabularnewline
60 & 10.331 & 10.5212284330304 & -0.190228433030381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147359&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]9.849[/C][C]9.67237259615384[/C][C]0.176627403846156[/C][/ROW]
[ROW][C]14[/C][C]9.172[/C][C]9.01673288170163[/C][C]0.155267118298372[/C][/ROW]
[ROW][C]15[/C][C]10.313[/C][C]10.1547181672494[/C][C]0.158281832750587[/C][/ROW]
[ROW][C]16[/C][C]9.819[/C][C]9.65524511946387[/C][C]0.163754880536134[/C][/ROW]
[ROW][C]17[/C][C]9.955[/C][C]9.79464707167832[/C][C]0.160352928321682[/C][/ROW]
[ROW][C]18[/C][C]10.048[/C][C]9.9143823572261[/C][C]0.133617642773897[/C][/ROW]
[ROW][C]19[/C][C]10.082[/C][C]10.5306176427739[/C][C]-0.44861764277389[/C][/ROW]
[ROW][C]20[/C][C]10.541[/C][C]10.312936261655[/C][C]0.228063738344993[/C][/ROW]
[ROW][C]21[/C][C]10.208[/C][C]10.0849632138695[/C][C]0.123036786130541[/C][/ROW]
[ROW][C]22[/C][C]10.233[/C][C]9.92419849941724[/C][C]0.308801500582756[/C][/ROW]
[ROW][C]23[/C][C]9.439[/C][C]9.48251711829836[/C][C]-0.0435171182983627[/C][/ROW]
[ROW][C]24[/C][C]9.963[/C][C]10.1670440705128[/C][C]-0.204044070512817[/C][/ROW]
[ROW][C]25[/C][C]10.158[/C][C]9.98708588184804[/C][C]0.170914118151963[/C][/ROW]
[ROW][C]26[/C][C]9.225[/C][C]9.3225708269164[/C][C]-0.0975708269163977[/C][/ROW]
[ROW][C]27[/C][C]10.474[/C][C]10.4618087463371[/C][C]0.0121912536629321[/C][/ROW]
[ROW][C]28[/C][C]9.757[/C][C]9.96460978624797[/C][C]-0.207609786247971[/C][/ROW]
[ROW][C]29[/C][C]10.49[/C][C]10.102598204728[/C][C]0.387401795271968[/C][/ROW]
[ROW][C]30[/C][C]10.281[/C][C]10.2112248016059[/C][C]0.0697751983941153[/C][/ROW]
[ROW][C]31[/C][C]10.444[/C][C]10.5855374599111[/C][C]-0.141537459911122[/C][/ROW]
[ROW][C]32[/C][C]10.64[/C][C]10.6490216858756[/C][C]-0.00902168587559871[/C][/ROW]
[ROW][C]33[/C][C]10.695[/C][C]10.377409242056[/C][C]0.317590757943965[/C][/ROW]
[ROW][C]34[/C][C]10.786[/C][C]10.293830999954[/C][C]0.492169000045983[/C][/ROW]
[ROW][C]35[/C][C]9.832[/C][C]9.70575889326103[/C][C]0.126241106738972[/C][/ROW]
[ROW][C]36[/C][C]9.747[/C][C]10.3235858309162[/C][C]-0.57658583091621[/C][/ROW]
[ROW][C]37[/C][C]10.411[/C][C]10.2994252593995[/C][C]0.111574740600465[/C][/ROW]
[ROW][C]38[/C][C]9.511[/C][C]9.52335292702653[/C][C]-0.0123529270265266[/C][/ROW]
[ROW][C]39[/C][C]10.402[/C][C]10.7081977197585[/C][C]-0.306197719758519[/C][/ROW]
[ROW][C]40[/C][C]9.701[/C][C]10.1196699680867[/C][C]-0.418669968086716[/C][/ROW]
[ROW][C]41[/C][C]10.54[/C][C]10.5048896496216[/C][C]0.0351103503784262[/C][/ROW]
[ROW][C]42[/C][C]10.112[/C][C]10.481540286426[/C][C]-0.369540286425989[/C][/ROW]
[ROW][C]43[/C][C]10.915[/C][C]10.7680511320693[/C][C]0.146948867930664[/C][/ROW]
[ROW][C]44[/C][C]11.183[/C][C]10.8865965420629[/C][C]0.296403457937137[/C][/ROW]
[ROW][C]45[/C][C]10.384[/C][C]10.7506937373879[/C][C]-0.366693737387891[/C][/ROW]
[ROW][C]46[/C][C]10.834[/C][C]10.7396539140953[/C][C]0.094346085904677[/C][/ROW]
[ROW][C]47[/C][C]9.886[/C][C]9.9995363379374[/C][C]-0.113536337937402[/C][/ROW]
[ROW][C]48[/C][C]10.216[/C][C]10.3253340161594[/C][C]-0.109334016159419[/C][/ROW]
[ROW][C]49[/C][C]10.943[/C][C]10.5871087315593[/C][C]0.355891268440704[/C][/ROW]
[ROW][C]50[/C][C]9.867[/C][C]9.75954363039582[/C][C]0.107456369604179[/C][/ROW]
[ROW][C]51[/C][C]10.203[/C][C]10.8222939605904[/C][C]-0.619293960590417[/C][/ROW]
[ROW][C]52[/C][C]10.837[/C][C]10.1870332429119[/C][C]0.649966757088134[/C][/ROW]
[ROW][C]53[/C][C]10.573[/C][C]10.7608016599133[/C][C]-0.187801659913283[/C][/ROW]
[ROW][C]54[/C][C]10.647[/C][C]10.5693172702069[/C][C]0.0776827297930893[/C][/ROW]
[ROW][C]55[/C][C]11.502[/C][C]11.0704327890224[/C][C]0.431567210977649[/C][/ROW]
[ROW][C]56[/C][C]10.656[/C][C]11.2510775735562[/C][C]-0.595077573556202[/C][/ROW]
[ROW][C]57[/C][C]10.866[/C][C]10.8396534811955[/C][C]0.0263465188045036[/C][/ROW]
[ROW][C]58[/C][C]10.835[/C][C]11.0201787658291[/C][C]-0.185178765829084[/C][/ROW]
[ROW][C]59[/C][C]9.945[/C][C]10.1936846622058[/C][C]-0.248684662205795[/C][/ROW]
[ROW][C]60[/C][C]10.331[/C][C]10.5212284330304[/C][C]-0.190228433030381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147359&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147359&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
139.8499.672372596153840.176627403846156
149.1729.016732881701630.155267118298372
1510.31310.15471816724940.158281832750587
169.8199.655245119463870.163754880536134
179.9559.794647071678320.160352928321682
1810.0489.91438235722610.133617642773897
1910.08210.5306176427739-0.44861764277389
2010.54110.3129362616550.228063738344993
2110.20810.08496321386950.123036786130541
2210.2339.924198499417240.308801500582756
239.4399.48251711829836-0.0435171182983627
249.96310.1670440705128-0.204044070512817
2510.1589.987085881848040.170914118151963
269.2259.3225708269164-0.0975708269163977
2710.47410.46180874633710.0121912536629321
289.7579.96460978624797-0.207609786247971
2910.4910.1025982047280.387401795271968
3010.28110.21122480160590.0697751983941153
3110.44410.5855374599111-0.141537459911122
3210.6410.6490216858756-0.00902168587559871
3310.69510.3774092420560.317590757943965
3410.78610.2938309999540.492169000045983
359.8329.705758893261030.126241106738972
369.74710.3235858309162-0.57658583091621
3710.41110.29942525939950.111574740600465
389.5119.52335292702653-0.0123529270265266
3910.40210.7081977197585-0.306197719758519
409.70110.1196699680867-0.418669968086716
4110.5410.50488964962160.0351103503784262
4210.11210.481540286426-0.369540286425989
4310.91510.76805113206930.146948867930664
4411.18310.88659654206290.296403457937137
4510.38410.7506937373879-0.366693737387891
4610.83410.73965391409530.094346085904677
479.8869.9995363379374-0.113536337937402
4810.21610.3253340161594-0.109334016159419
4910.94310.58710873155930.355891268440704
509.8679.759543630395820.107456369604179
5110.20310.8222939605904-0.619293960590417
5210.83710.18703324291190.649966757088134
5310.57310.7608016599133-0.187801659913283
5410.64710.56931727020690.0776827297930893
5511.50211.07043278902240.431567210977649
5610.65611.2510775735562-0.595077573556202
5710.86610.83965348119550.0263465188045036
5810.83511.0201787658291-0.185178765829084
599.94510.1936846622058-0.248684662205795
6010.33110.5212284330304-0.190228433030381







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6110.976307343321610.414444758863711.5381699277794
6210.04551589206039.4836533076023810.6073784765181
6310.80629663436810.244434049910111.3681592188258
6410.698422172896210.136559588438411.2602847573541
6510.924092249771910.362229665314111.4859548342298
6610.8429183868310.281055802372211.4047809712879
6711.491075257404110.929212672946312.052937841862
6811.245142316945610.683279732487711.8070049014034
6911.091924061275610.530061476817711.6537866457334
7011.18455918559610.622696601138111.7464217700539
7110.3316779603439.7698153758851310.8935405448009
7210.683510682544910.12164809808711.2453732670027

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 10.9763073433216 & 10.4144447588637 & 11.5381699277794 \tabularnewline
62 & 10.0455158920603 & 9.48365330760238 & 10.6073784765181 \tabularnewline
63 & 10.806296634368 & 10.2444340499101 & 11.3681592188258 \tabularnewline
64 & 10.6984221728962 & 10.1365595884384 & 11.2602847573541 \tabularnewline
65 & 10.9240922497719 & 10.3622296653141 & 11.4859548342298 \tabularnewline
66 & 10.84291838683 & 10.2810558023722 & 11.4047809712879 \tabularnewline
67 & 11.4910752574041 & 10.9292126729463 & 12.052937841862 \tabularnewline
68 & 11.2451423169456 & 10.6832797324877 & 11.8070049014034 \tabularnewline
69 & 11.0919240612756 & 10.5300614768177 & 11.6537866457334 \tabularnewline
70 & 11.184559185596 & 10.6226966011381 & 11.7464217700539 \tabularnewline
71 & 10.331677960343 & 9.76981537588513 & 10.8935405448009 \tabularnewline
72 & 10.6835106825449 & 10.121648098087 & 11.2453732670027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147359&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]61[/C][C]10.9763073433216[/C][C]10.4144447588637[/C][C]11.5381699277794[/C][/ROW]
[ROW][C]62[/C][C]10.0455158920603[/C][C]9.48365330760238[/C][C]10.6073784765181[/C][/ROW]
[ROW][C]63[/C][C]10.806296634368[/C][C]10.2444340499101[/C][C]11.3681592188258[/C][/ROW]
[ROW][C]64[/C][C]10.6984221728962[/C][C]10.1365595884384[/C][C]11.2602847573541[/C][/ROW]
[ROW][C]65[/C][C]10.9240922497719[/C][C]10.3622296653141[/C][C]11.4859548342298[/C][/ROW]
[ROW][C]66[/C][C]10.84291838683[/C][C]10.2810558023722[/C][C]11.4047809712879[/C][/ROW]
[ROW][C]67[/C][C]11.4910752574041[/C][C]10.9292126729463[/C][C]12.052937841862[/C][/ROW]
[ROW][C]68[/C][C]11.2451423169456[/C][C]10.6832797324877[/C][C]11.8070049014034[/C][/ROW]
[ROW][C]69[/C][C]11.0919240612756[/C][C]10.5300614768177[/C][C]11.6537866457334[/C][/ROW]
[ROW][C]70[/C][C]11.184559185596[/C][C]10.6226966011381[/C][C]11.7464217700539[/C][/ROW]
[ROW][C]71[/C][C]10.331677960343[/C][C]9.76981537588513[/C][C]10.8935405448009[/C][/ROW]
[ROW][C]72[/C][C]10.6835106825449[/C][C]10.121648098087[/C][C]11.2453732670027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147359&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147359&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
6110.976307343321610.414444758863711.5381699277794
6210.04551589206039.4836533076023810.6073784765181
6310.80629663436810.244434049910111.3681592188258
6410.698422172896210.136559588438411.2602847573541
6510.924092249771910.362229665314111.4859548342298
6610.8429183868310.281055802372211.4047809712879
6711.491075257404110.929212672946312.052937841862
6811.245142316945610.683279732487711.8070049014034
6911.091924061275610.530061476817711.6537866457334
7011.18455918559610.622696601138111.7464217700539
7110.3316779603439.7698153758851310.8935405448009
7210.683510682544910.12164809808711.2453732670027



Parameters (Session):
par1 = 12 ;
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')