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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 11 Jan 2014 13:54:06 -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/2014/Jan/11/t13894664633l31nkh5rycun80.htm/, Retrieved Fri, 03 May 2024 09:56:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232934, Retrieved Fri, 03 May 2024 09:56:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2013-12-11 23:28:36] [bbad914f60bdb4cc08661b92002a4d31]
- R P     [Exponential Smoothing] [] [2014-01-11 18:54:06] [c37684f2e387cbe6dfbcb0e59307bb9b] [Current]
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Dataseries X:
3.875
3.863
3.876
3.878
3.881
3.883
3.884
3.885
3.895
3.903
3.911
3.929
3.946
3.965
3.992
4.010
4.015
4.020
4.037
4.059
4.083
4.102
4.126
4.145
4.162
4.169
4.178
4.174
4.168
4.170
4.159
4.159
4.143
4.159
4.167
4.176
4.185
4.195
4.210
4.226
4.250
4.259
4.270
4.277
4.286
4.303
4.320
4.336
4.352
4.371
4.392
4.415
4.442
4.457
4.472
4.474
4.461
4.453
4.446
4.450
4.459
4.474
4.492
4.509
4.526
4.541
4.550
4.562
4.555
4.554
4.551
4.553




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232934&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232934&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.873517735780965
beta1
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.873517735780965 \tabularnewline
beta & 1 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232934&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]0.873517735780965[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232934&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
alpha0.873517735780965
beta1
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.8763.8510.0249999999999999
43.8783.88267588678905-0.00467588678904773
53.8813.8843448901021-0.0033448901020976
63.8833.88425472179904-0.00125472179904307
73.8843.88489433083454-0.000894330834539048
83.8853.88506753392372-6.75339237190542e-05
93.8953.885903966698250.00909603330174669
103.9033.902690484381580.000309515618416523
113.9113.91207219041496-0.00107219041495998
123.9293.919310374378940.00968962562105569
133.9463.944413255352670.00158674464733055
143.9653.963824175676520.00117582432347652
153.9923.983903253210220.00809674678978345
164.014.0171005311892-0.00710053118919785
174.0154.03082027739072-0.0158202773907155
184.024.02310387774793-0.00310387774793419
194.0374.023784186465880.0132158135341154
204.0594.0502642824760.00873571752400171
214.0834.080461739355270.00253826064473461
224.1024.10746282342497-0.00546282342496518
234.1264.122702945505160.00329705449483875
244.1454.14847501188866-0.00347501188866151
254.1624.16529607366149-0.00329607366149176
264.1694.17939426234761-0.0103942623476101
274.1784.17821248481349-0.000212484813486569
284.1744.18573906128403-0.0117390612840316
294.1684.1729426905417-0.00494269054169916
304.174.161765542331090.00823445766891329
314.1594.16929181160779-0.0102918116077921
324.1594.151644976120720.00735502387928122
334.1434.15583770821766-0.0128377082176572
344.1594.131177764879140.0278222351208575
354.1674.166338219009810.000661780990193428
364.1764.17835161217761-0.00235161217760549
374.1854.18567857802363-0.000678578023634913
384.1954.193874218936970.00112578106303296
394.214.204629389239390.00537061076061196
404.2264.223783817319380.0022161826806153
414.254.242118671402510.00788132859749258
424.2594.27228661123124-0.0132866112312362
434.274.27235788963072-0.00235788963071659
444.2774.27991594176622-0.0029159417662159
454.2864.284439398614570.00156060138542546
464.3034.294236408289530.00876359171046648
474.324.317980510552310.00201948944769104
484.3364.33759757972641-0.00159757972641117
494.3524.35265956060004-0.000659560600043463
504.3714.36796477993510.00303522006490109
514.3924.38914877426950.00285122573050511
524.4154.412662642533820.00233735746617558
534.4424.437769360956970.00423063904302889
544.4574.4682254326541-0.0112254326540997
554.4724.47537473708311-0.00337473708311187
564.4744.4864338706359-0.0124338706359044
574.4614.47871848383466-0.0177184838346554
584.4534.450909483796830.00209051620316547
594.4464.442230099600540.0037699003994609
604.454.438310762145950.0116892378540454
614.4594.451519862996850.00748013700314498
624.4744.467586271941120.0064137280588783
634.4924.488323658970880.00367634102911829
644.5094.50988123897216-0.000881238972163523
654.5264.52668791413844-0.000687914138439716
664.5414.54306255677512-0.00206255677511802
674.554.55643474476418-0.00643474476417705
684.5624.560366885323890.0016331146761086
694.5554.57277299882863-0.0177729988286295
704.5544.552702498309580.00129750169042264
714.5514.550423808962930.000576191037072071
724.5534.548018355057650.00498164494235098

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.876 & 3.851 & 0.0249999999999999 \tabularnewline
4 & 3.878 & 3.88267588678905 & -0.00467588678904773 \tabularnewline
5 & 3.881 & 3.8843448901021 & -0.0033448901020976 \tabularnewline
6 & 3.883 & 3.88425472179904 & -0.00125472179904307 \tabularnewline
7 & 3.884 & 3.88489433083454 & -0.000894330834539048 \tabularnewline
8 & 3.885 & 3.88506753392372 & -6.75339237190542e-05 \tabularnewline
9 & 3.895 & 3.88590396669825 & 0.00909603330174669 \tabularnewline
10 & 3.903 & 3.90269048438158 & 0.000309515618416523 \tabularnewline
11 & 3.911 & 3.91207219041496 & -0.00107219041495998 \tabularnewline
12 & 3.929 & 3.91931037437894 & 0.00968962562105569 \tabularnewline
13 & 3.946 & 3.94441325535267 & 0.00158674464733055 \tabularnewline
14 & 3.965 & 3.96382417567652 & 0.00117582432347652 \tabularnewline
15 & 3.992 & 3.98390325321022 & 0.00809674678978345 \tabularnewline
16 & 4.01 & 4.0171005311892 & -0.00710053118919785 \tabularnewline
17 & 4.015 & 4.03082027739072 & -0.0158202773907155 \tabularnewline
18 & 4.02 & 4.02310387774793 & -0.00310387774793419 \tabularnewline
19 & 4.037 & 4.02378418646588 & 0.0132158135341154 \tabularnewline
20 & 4.059 & 4.050264282476 & 0.00873571752400171 \tabularnewline
21 & 4.083 & 4.08046173935527 & 0.00253826064473461 \tabularnewline
22 & 4.102 & 4.10746282342497 & -0.00546282342496518 \tabularnewline
23 & 4.126 & 4.12270294550516 & 0.00329705449483875 \tabularnewline
24 & 4.145 & 4.14847501188866 & -0.00347501188866151 \tabularnewline
25 & 4.162 & 4.16529607366149 & -0.00329607366149176 \tabularnewline
26 & 4.169 & 4.17939426234761 & -0.0103942623476101 \tabularnewline
27 & 4.178 & 4.17821248481349 & -0.000212484813486569 \tabularnewline
28 & 4.174 & 4.18573906128403 & -0.0117390612840316 \tabularnewline
29 & 4.168 & 4.1729426905417 & -0.00494269054169916 \tabularnewline
30 & 4.17 & 4.16176554233109 & 0.00823445766891329 \tabularnewline
31 & 4.159 & 4.16929181160779 & -0.0102918116077921 \tabularnewline
32 & 4.159 & 4.15164497612072 & 0.00735502387928122 \tabularnewline
33 & 4.143 & 4.15583770821766 & -0.0128377082176572 \tabularnewline
34 & 4.159 & 4.13117776487914 & 0.0278222351208575 \tabularnewline
35 & 4.167 & 4.16633821900981 & 0.000661780990193428 \tabularnewline
36 & 4.176 & 4.17835161217761 & -0.00235161217760549 \tabularnewline
37 & 4.185 & 4.18567857802363 & -0.000678578023634913 \tabularnewline
38 & 4.195 & 4.19387421893697 & 0.00112578106303296 \tabularnewline
39 & 4.21 & 4.20462938923939 & 0.00537061076061196 \tabularnewline
40 & 4.226 & 4.22378381731938 & 0.0022161826806153 \tabularnewline
41 & 4.25 & 4.24211867140251 & 0.00788132859749258 \tabularnewline
42 & 4.259 & 4.27228661123124 & -0.0132866112312362 \tabularnewline
43 & 4.27 & 4.27235788963072 & -0.00235788963071659 \tabularnewline
44 & 4.277 & 4.27991594176622 & -0.0029159417662159 \tabularnewline
45 & 4.286 & 4.28443939861457 & 0.00156060138542546 \tabularnewline
46 & 4.303 & 4.29423640828953 & 0.00876359171046648 \tabularnewline
47 & 4.32 & 4.31798051055231 & 0.00201948944769104 \tabularnewline
48 & 4.336 & 4.33759757972641 & -0.00159757972641117 \tabularnewline
49 & 4.352 & 4.35265956060004 & -0.000659560600043463 \tabularnewline
50 & 4.371 & 4.3679647799351 & 0.00303522006490109 \tabularnewline
51 & 4.392 & 4.3891487742695 & 0.00285122573050511 \tabularnewline
52 & 4.415 & 4.41266264253382 & 0.00233735746617558 \tabularnewline
53 & 4.442 & 4.43776936095697 & 0.00423063904302889 \tabularnewline
54 & 4.457 & 4.4682254326541 & -0.0112254326540997 \tabularnewline
55 & 4.472 & 4.47537473708311 & -0.00337473708311187 \tabularnewline
56 & 4.474 & 4.4864338706359 & -0.0124338706359044 \tabularnewline
57 & 4.461 & 4.47871848383466 & -0.0177184838346554 \tabularnewline
58 & 4.453 & 4.45090948379683 & 0.00209051620316547 \tabularnewline
59 & 4.446 & 4.44223009960054 & 0.0037699003994609 \tabularnewline
60 & 4.45 & 4.43831076214595 & 0.0116892378540454 \tabularnewline
61 & 4.459 & 4.45151986299685 & 0.00748013700314498 \tabularnewline
62 & 4.474 & 4.46758627194112 & 0.0064137280588783 \tabularnewline
63 & 4.492 & 4.48832365897088 & 0.00367634102911829 \tabularnewline
64 & 4.509 & 4.50988123897216 & -0.000881238972163523 \tabularnewline
65 & 4.526 & 4.52668791413844 & -0.000687914138439716 \tabularnewline
66 & 4.541 & 4.54306255677512 & -0.00206255677511802 \tabularnewline
67 & 4.55 & 4.55643474476418 & -0.00643474476417705 \tabularnewline
68 & 4.562 & 4.56036688532389 & 0.0016331146761086 \tabularnewline
69 & 4.555 & 4.57277299882863 & -0.0177729988286295 \tabularnewline
70 & 4.554 & 4.55270249830958 & 0.00129750169042264 \tabularnewline
71 & 4.551 & 4.55042380896293 & 0.000576191037072071 \tabularnewline
72 & 4.553 & 4.54801835505765 & 0.00498164494235098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232934&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]3[/C][C]3.876[/C][C]3.851[/C][C]0.0249999999999999[/C][/ROW]
[ROW][C]4[/C][C]3.878[/C][C]3.88267588678905[/C][C]-0.00467588678904773[/C][/ROW]
[ROW][C]5[/C][C]3.881[/C][C]3.8843448901021[/C][C]-0.0033448901020976[/C][/ROW]
[ROW][C]6[/C][C]3.883[/C][C]3.88425472179904[/C][C]-0.00125472179904307[/C][/ROW]
[ROW][C]7[/C][C]3.884[/C][C]3.88489433083454[/C][C]-0.000894330834539048[/C][/ROW]
[ROW][C]8[/C][C]3.885[/C][C]3.88506753392372[/C][C]-6.75339237190542e-05[/C][/ROW]
[ROW][C]9[/C][C]3.895[/C][C]3.88590396669825[/C][C]0.00909603330174669[/C][/ROW]
[ROW][C]10[/C][C]3.903[/C][C]3.90269048438158[/C][C]0.000309515618416523[/C][/ROW]
[ROW][C]11[/C][C]3.911[/C][C]3.91207219041496[/C][C]-0.00107219041495998[/C][/ROW]
[ROW][C]12[/C][C]3.929[/C][C]3.91931037437894[/C][C]0.00968962562105569[/C][/ROW]
[ROW][C]13[/C][C]3.946[/C][C]3.94441325535267[/C][C]0.00158674464733055[/C][/ROW]
[ROW][C]14[/C][C]3.965[/C][C]3.96382417567652[/C][C]0.00117582432347652[/C][/ROW]
[ROW][C]15[/C][C]3.992[/C][C]3.98390325321022[/C][C]0.00809674678978345[/C][/ROW]
[ROW][C]16[/C][C]4.01[/C][C]4.0171005311892[/C][C]-0.00710053118919785[/C][/ROW]
[ROW][C]17[/C][C]4.015[/C][C]4.03082027739072[/C][C]-0.0158202773907155[/C][/ROW]
[ROW][C]18[/C][C]4.02[/C][C]4.02310387774793[/C][C]-0.00310387774793419[/C][/ROW]
[ROW][C]19[/C][C]4.037[/C][C]4.02378418646588[/C][C]0.0132158135341154[/C][/ROW]
[ROW][C]20[/C][C]4.059[/C][C]4.050264282476[/C][C]0.00873571752400171[/C][/ROW]
[ROW][C]21[/C][C]4.083[/C][C]4.08046173935527[/C][C]0.00253826064473461[/C][/ROW]
[ROW][C]22[/C][C]4.102[/C][C]4.10746282342497[/C][C]-0.00546282342496518[/C][/ROW]
[ROW][C]23[/C][C]4.126[/C][C]4.12270294550516[/C][C]0.00329705449483875[/C][/ROW]
[ROW][C]24[/C][C]4.145[/C][C]4.14847501188866[/C][C]-0.00347501188866151[/C][/ROW]
[ROW][C]25[/C][C]4.162[/C][C]4.16529607366149[/C][C]-0.00329607366149176[/C][/ROW]
[ROW][C]26[/C][C]4.169[/C][C]4.17939426234761[/C][C]-0.0103942623476101[/C][/ROW]
[ROW][C]27[/C][C]4.178[/C][C]4.17821248481349[/C][C]-0.000212484813486569[/C][/ROW]
[ROW][C]28[/C][C]4.174[/C][C]4.18573906128403[/C][C]-0.0117390612840316[/C][/ROW]
[ROW][C]29[/C][C]4.168[/C][C]4.1729426905417[/C][C]-0.00494269054169916[/C][/ROW]
[ROW][C]30[/C][C]4.17[/C][C]4.16176554233109[/C][C]0.00823445766891329[/C][/ROW]
[ROW][C]31[/C][C]4.159[/C][C]4.16929181160779[/C][C]-0.0102918116077921[/C][/ROW]
[ROW][C]32[/C][C]4.159[/C][C]4.15164497612072[/C][C]0.00735502387928122[/C][/ROW]
[ROW][C]33[/C][C]4.143[/C][C]4.15583770821766[/C][C]-0.0128377082176572[/C][/ROW]
[ROW][C]34[/C][C]4.159[/C][C]4.13117776487914[/C][C]0.0278222351208575[/C][/ROW]
[ROW][C]35[/C][C]4.167[/C][C]4.16633821900981[/C][C]0.000661780990193428[/C][/ROW]
[ROW][C]36[/C][C]4.176[/C][C]4.17835161217761[/C][C]-0.00235161217760549[/C][/ROW]
[ROW][C]37[/C][C]4.185[/C][C]4.18567857802363[/C][C]-0.000678578023634913[/C][/ROW]
[ROW][C]38[/C][C]4.195[/C][C]4.19387421893697[/C][C]0.00112578106303296[/C][/ROW]
[ROW][C]39[/C][C]4.21[/C][C]4.20462938923939[/C][C]0.00537061076061196[/C][/ROW]
[ROW][C]40[/C][C]4.226[/C][C]4.22378381731938[/C][C]0.0022161826806153[/C][/ROW]
[ROW][C]41[/C][C]4.25[/C][C]4.24211867140251[/C][C]0.00788132859749258[/C][/ROW]
[ROW][C]42[/C][C]4.259[/C][C]4.27228661123124[/C][C]-0.0132866112312362[/C][/ROW]
[ROW][C]43[/C][C]4.27[/C][C]4.27235788963072[/C][C]-0.00235788963071659[/C][/ROW]
[ROW][C]44[/C][C]4.277[/C][C]4.27991594176622[/C][C]-0.0029159417662159[/C][/ROW]
[ROW][C]45[/C][C]4.286[/C][C]4.28443939861457[/C][C]0.00156060138542546[/C][/ROW]
[ROW][C]46[/C][C]4.303[/C][C]4.29423640828953[/C][C]0.00876359171046648[/C][/ROW]
[ROW][C]47[/C][C]4.32[/C][C]4.31798051055231[/C][C]0.00201948944769104[/C][/ROW]
[ROW][C]48[/C][C]4.336[/C][C]4.33759757972641[/C][C]-0.00159757972641117[/C][/ROW]
[ROW][C]49[/C][C]4.352[/C][C]4.35265956060004[/C][C]-0.000659560600043463[/C][/ROW]
[ROW][C]50[/C][C]4.371[/C][C]4.3679647799351[/C][C]0.00303522006490109[/C][/ROW]
[ROW][C]51[/C][C]4.392[/C][C]4.3891487742695[/C][C]0.00285122573050511[/C][/ROW]
[ROW][C]52[/C][C]4.415[/C][C]4.41266264253382[/C][C]0.00233735746617558[/C][/ROW]
[ROW][C]53[/C][C]4.442[/C][C]4.43776936095697[/C][C]0.00423063904302889[/C][/ROW]
[ROW][C]54[/C][C]4.457[/C][C]4.4682254326541[/C][C]-0.0112254326540997[/C][/ROW]
[ROW][C]55[/C][C]4.472[/C][C]4.47537473708311[/C][C]-0.00337473708311187[/C][/ROW]
[ROW][C]56[/C][C]4.474[/C][C]4.4864338706359[/C][C]-0.0124338706359044[/C][/ROW]
[ROW][C]57[/C][C]4.461[/C][C]4.47871848383466[/C][C]-0.0177184838346554[/C][/ROW]
[ROW][C]58[/C][C]4.453[/C][C]4.45090948379683[/C][C]0.00209051620316547[/C][/ROW]
[ROW][C]59[/C][C]4.446[/C][C]4.44223009960054[/C][C]0.0037699003994609[/C][/ROW]
[ROW][C]60[/C][C]4.45[/C][C]4.43831076214595[/C][C]0.0116892378540454[/C][/ROW]
[ROW][C]61[/C][C]4.459[/C][C]4.45151986299685[/C][C]0.00748013700314498[/C][/ROW]
[ROW][C]62[/C][C]4.474[/C][C]4.46758627194112[/C][C]0.0064137280588783[/C][/ROW]
[ROW][C]63[/C][C]4.492[/C][C]4.48832365897088[/C][C]0.00367634102911829[/C][/ROW]
[ROW][C]64[/C][C]4.509[/C][C]4.50988123897216[/C][C]-0.000881238972163523[/C][/ROW]
[ROW][C]65[/C][C]4.526[/C][C]4.52668791413844[/C][C]-0.000687914138439716[/C][/ROW]
[ROW][C]66[/C][C]4.541[/C][C]4.54306255677512[/C][C]-0.00206255677511802[/C][/ROW]
[ROW][C]67[/C][C]4.55[/C][C]4.55643474476418[/C][C]-0.00643474476417705[/C][/ROW]
[ROW][C]68[/C][C]4.562[/C][C]4.56036688532389[/C][C]0.0016331146761086[/C][/ROW]
[ROW][C]69[/C][C]4.555[/C][C]4.57277299882863[/C][C]-0.0177729988286295[/C][/ROW]
[ROW][C]70[/C][C]4.554[/C][C]4.55270249830958[/C][C]0.00129750169042264[/C][/ROW]
[ROW][C]71[/C][C]4.551[/C][C]4.55042380896293[/C][C]0.000576191037072071[/C][/ROW]
[ROW][C]72[/C][C]4.553[/C][C]4.54801835505765[/C][C]0.00498164494235098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232934&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232934&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
33.8763.8510.0249999999999999
43.8783.88267588678905-0.00467588678904773
53.8813.8843448901021-0.0033448901020976
63.8833.88425472179904-0.00125472179904307
73.8843.88489433083454-0.000894330834539048
83.8853.88506753392372-6.75339237190542e-05
93.8953.885903966698250.00909603330174669
103.9033.902690484381580.000309515618416523
113.9113.91207219041496-0.00107219041495998
123.9293.919310374378940.00968962562105569
133.9463.944413255352670.00158674464733055
143.9653.963824175676520.00117582432347652
153.9923.983903253210220.00809674678978345
164.014.0171005311892-0.00710053118919785
174.0154.03082027739072-0.0158202773907155
184.024.02310387774793-0.00310387774793419
194.0374.023784186465880.0132158135341154
204.0594.0502642824760.00873571752400171
214.0834.080461739355270.00253826064473461
224.1024.10746282342497-0.00546282342496518
234.1264.122702945505160.00329705449483875
244.1454.14847501188866-0.00347501188866151
254.1624.16529607366149-0.00329607366149176
264.1694.17939426234761-0.0103942623476101
274.1784.17821248481349-0.000212484813486569
284.1744.18573906128403-0.0117390612840316
294.1684.1729426905417-0.00494269054169916
304.174.161765542331090.00823445766891329
314.1594.16929181160779-0.0102918116077921
324.1594.151644976120720.00735502387928122
334.1434.15583770821766-0.0128377082176572
344.1594.131177764879140.0278222351208575
354.1674.166338219009810.000661780990193428
364.1764.17835161217761-0.00235161217760549
374.1854.18567857802363-0.000678578023634913
384.1954.193874218936970.00112578106303296
394.214.204629389239390.00537061076061196
404.2264.223783817319380.0022161826806153
414.254.242118671402510.00788132859749258
424.2594.27228661123124-0.0132866112312362
434.274.27235788963072-0.00235788963071659
444.2774.27991594176622-0.0029159417662159
454.2864.284439398614570.00156060138542546
464.3034.294236408289530.00876359171046648
474.324.317980510552310.00201948944769104
484.3364.33759757972641-0.00159757972641117
494.3524.35265956060004-0.000659560600043463
504.3714.36796477993510.00303522006490109
514.3924.38914877426950.00285122573050511
524.4154.412662642533820.00233735746617558
534.4424.437769360956970.00423063904302889
544.4574.4682254326541-0.0112254326540997
554.4724.47537473708311-0.00337473708311187
564.4744.4864338706359-0.0124338706359044
574.4614.47871848383466-0.0177184838346554
584.4534.450909483796830.00209051620316547
594.4464.442230099600540.0037699003994609
604.454.438310762145950.0116892378540454
614.4594.451519862996850.00748013700314498
624.4744.467586271941120.0064137280588783
634.4924.488323658970880.00367634102911829
644.5094.50988123897216-0.000881238972163523
654.5264.52668791413844-0.000687914138439716
664.5414.54306255677512-0.00206255677511802
674.554.55643474476418-0.00643474476417705
684.5624.560366885323890.0016331146761086
694.5554.57277299882863-0.0177729988286295
704.5544.552702498309580.00129750169042264
714.5514.550423808962930.000576191037072071
724.5534.548018355057650.00498164494235098







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734.55381269848334.537709032609494.56991636435712
744.555255486698454.522838951536214.5876720218607
754.55669827491364.503484413270594.60991213655661
764.558141063128754.48069605127934.63558607497819
774.55958385134394.45496727536864.6642004273192
784.561026639559044.426608778971464.69544450014662
794.562469427774194.395843854894534.72909500065385
804.563912215989344.362844713157414.76497971882127
814.565355004204494.327750099864534.80295990854444
824.566797792419634.290675205512774.8429203793265
834.568240580634784.25171780128874.88476335998086
844.569683368849934.210962303188114.92840443451175

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.5538126984833 & 4.53770903260949 & 4.56991636435712 \tabularnewline
74 & 4.55525548669845 & 4.52283895153621 & 4.5876720218607 \tabularnewline
75 & 4.5566982749136 & 4.50348441327059 & 4.60991213655661 \tabularnewline
76 & 4.55814106312875 & 4.4806960512793 & 4.63558607497819 \tabularnewline
77 & 4.5595838513439 & 4.4549672753686 & 4.6642004273192 \tabularnewline
78 & 4.56102663955904 & 4.42660877897146 & 4.69544450014662 \tabularnewline
79 & 4.56246942777419 & 4.39584385489453 & 4.72909500065385 \tabularnewline
80 & 4.56391221598934 & 4.36284471315741 & 4.76497971882127 \tabularnewline
81 & 4.56535500420449 & 4.32775009986453 & 4.80295990854444 \tabularnewline
82 & 4.56679779241963 & 4.29067520551277 & 4.8429203793265 \tabularnewline
83 & 4.56824058063478 & 4.2517178012887 & 4.88476335998086 \tabularnewline
84 & 4.56968336884993 & 4.21096230318811 & 4.92840443451175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232934&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]4.5538126984833[/C][C]4.53770903260949[/C][C]4.56991636435712[/C][/ROW]
[ROW][C]74[/C][C]4.55525548669845[/C][C]4.52283895153621[/C][C]4.5876720218607[/C][/ROW]
[ROW][C]75[/C][C]4.5566982749136[/C][C]4.50348441327059[/C][C]4.60991213655661[/C][/ROW]
[ROW][C]76[/C][C]4.55814106312875[/C][C]4.4806960512793[/C][C]4.63558607497819[/C][/ROW]
[ROW][C]77[/C][C]4.5595838513439[/C][C]4.4549672753686[/C][C]4.6642004273192[/C][/ROW]
[ROW][C]78[/C][C]4.56102663955904[/C][C]4.42660877897146[/C][C]4.69544450014662[/C][/ROW]
[ROW][C]79[/C][C]4.56246942777419[/C][C]4.39584385489453[/C][C]4.72909500065385[/C][/ROW]
[ROW][C]80[/C][C]4.56391221598934[/C][C]4.36284471315741[/C][C]4.76497971882127[/C][/ROW]
[ROW][C]81[/C][C]4.56535500420449[/C][C]4.32775009986453[/C][C]4.80295990854444[/C][/ROW]
[ROW][C]82[/C][C]4.56679779241963[/C][C]4.29067520551277[/C][C]4.8429203793265[/C][/ROW]
[ROW][C]83[/C][C]4.56824058063478[/C][C]4.2517178012887[/C][C]4.88476335998086[/C][/ROW]
[ROW][C]84[/C][C]4.56968336884993[/C][C]4.21096230318811[/C][C]4.92840443451175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232934&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232934&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
734.55381269848334.537709032609494.56991636435712
744.555255486698454.522838951536214.5876720218607
754.55669827491364.503484413270594.60991213655661
764.558141063128754.48069605127934.63558607497819
774.55958385134394.45496727536864.6642004273192
784.561026639559044.426608778971464.69544450014662
794.562469427774194.395843854894534.72909500065385
804.563912215989344.362844713157414.76497971882127
814.565355004204494.327750099864534.80295990854444
824.566797792419634.290675205512774.8429203793265
834.568240580634784.25171780128874.88476335998086
844.569683368849934.210962303188114.92840443451175



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')