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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 08:42:01 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/26/t13695721969g0ylemjrbfxks8.htm/, Retrieved Mon, 29 Apr 2024 11:19:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210604, Retrieved Mon, 29 Apr 2024 11:19:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [additief model ei...] [2013-05-04 09:39:34] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [Voorspellen van t...] [2013-05-26 12:42:01] [74bc874243339b3c42d25470eb033c43] [Current]
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Dataseries X:
8,27
8,25
8,22
8,21
8,12
8,16
8,15
8,1
8,09
8,02
8,03
7,98
7,95
7,92
7,96
7,96
7,94
7,83
7,77
7,8
7,78
7,78
7,8
7,81
7,95
8,02
7,99
8,01
8,03
8,05
8,05
8,06
8,07
7,99
8
8,01
8
8,09
8,1
8,12
8,29
8,32
8,36
8,38
8,48
8,45
8,41
8,38
8,38
8,34
8,41
8,34
8,22
8,27
8,18
8,19
8,19
8,13
8,06
7,99
8
7,98
7,92
7,93
7,9
7,86
7,88
7,88
7,93
7,91
7,89
7,93




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210604&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210604&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210604&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.938589004712726
beta0.185994942007099
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.938589004712726 \tabularnewline
beta & 0.185994942007099 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210604&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]0.938589004712726[/C][/ROW]
[ROW][C]beta[/C][C]0.185994942007099[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210604&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210604&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
alpha0.938589004712726
beta0.185994942007099
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.228.23-0.00999999999999979
48.218.198868381877870.0111316181221284
58.128.18951394600456-0.0695139460045624
68.168.092331225648660.0676687743513398
78.158.135719826173990.0142801738260108
88.18.13149140330564-0.0314914033056404
98.098.078804738725980.01119526127402
108.028.06813769635995-0.0481376963599534
118.037.993377859541450.0366221404585492
127.988.00456590347855-0.0245659034785479
137.957.95403498341738-0.00403498341738295
147.927.92206976079888-0.00206976079887511
157.967.89158775056840.0684122494316028
167.967.939202298620970.0207977013790348
177.947.94575706852631-0.00575706852631175
187.837.92638279576022-0.0963827957602161
197.777.80512239661772-0.0351223966177194
207.87.7352289191510.0647710808490034
217.787.770401630705680.00959836929431912
227.787.755465456110080.0245345438899154
237.87.758831274969980.0411687250300208
247.817.784996693260060.0250033067399347
257.957.800354325140870.149645674859132
268.027.95882397885010.0611760211498957
277.998.04493665810093-0.0549366581009263
288.018.01247680665984-0.0024768066598444
298.038.028822811877980.0011771881220195
308.058.048803921457070.00119607854293236
318.058.06901156416675-0.0190115641667479
328.068.06693363348641-0.00693363348640474
338.078.07498149187841-0.00498149187841435
347.998.08399197589657-0.0939919758965733
3587.993049755196390.00695024480361006
368.017.998064116704860.0119358832951377
3788.00984162433978-0.00984162433977964
388.097.999460922767160.0905390772328394
398.18.099102104876950.000897895123047832
408.128.114763807161510.00523619283848831
418.298.135411484865380.154588515134618
428.328.32322656119902-0.00322656119902298
438.368.36235487226093-0.00235487226092701
448.388.40189024431376-0.0218902443137612
458.488.419268489548120.0607315104518804
468.458.52479667563888-0.0747966756388845
478.418.49006213077824-0.0800621307782432
488.388.4364088166746-0.0564088166745993
498.388.39510879761901-0.0151087976190123
508.348.38993493712513-0.0499349371251263
518.418.343356362847940.0666436371520636
528.348.41783132341205-0.0778313234120542
538.228.3431164418949-0.123116441894897
548.278.204404663181630.0655953368183742
558.188.25426684713571-0.0742668471357053
568.198.159890951046720.03010904895328
578.198.168737344590830.0212626554091742
588.138.17299249187276-0.0429924918727558
598.068.10943314441202-0.0494331444120206
607.998.0311989884912-0.0411989884911961
6187.953501097693680.0464989023063227
627.987.966232926856490.0137670731435087
637.927.95064637767267-0.0306463776726744
647.937.888023827701410.041976172298587
657.97.90089190287365-0.000891902873647155
667.867.87336877204735-0.0133687720473539
677.887.831801164932250.0481988350677529
687.887.856434442857860.0235655571421391
697.937.862061102443070.0679388975569326
707.917.92119637552894-0.0111963755289439
717.897.90410156870157-0.0141015687015669
727.937.881818229067410.0481817709325885

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.22 & 8.23 & -0.00999999999999979 \tabularnewline
4 & 8.21 & 8.19886838187787 & 0.0111316181221284 \tabularnewline
5 & 8.12 & 8.18951394600456 & -0.0695139460045624 \tabularnewline
6 & 8.16 & 8.09233122564866 & 0.0676687743513398 \tabularnewline
7 & 8.15 & 8.13571982617399 & 0.0142801738260108 \tabularnewline
8 & 8.1 & 8.13149140330564 & -0.0314914033056404 \tabularnewline
9 & 8.09 & 8.07880473872598 & 0.01119526127402 \tabularnewline
10 & 8.02 & 8.06813769635995 & -0.0481376963599534 \tabularnewline
11 & 8.03 & 7.99337785954145 & 0.0366221404585492 \tabularnewline
12 & 7.98 & 8.00456590347855 & -0.0245659034785479 \tabularnewline
13 & 7.95 & 7.95403498341738 & -0.00403498341738295 \tabularnewline
14 & 7.92 & 7.92206976079888 & -0.00206976079887511 \tabularnewline
15 & 7.96 & 7.8915877505684 & 0.0684122494316028 \tabularnewline
16 & 7.96 & 7.93920229862097 & 0.0207977013790348 \tabularnewline
17 & 7.94 & 7.94575706852631 & -0.00575706852631175 \tabularnewline
18 & 7.83 & 7.92638279576022 & -0.0963827957602161 \tabularnewline
19 & 7.77 & 7.80512239661772 & -0.0351223966177194 \tabularnewline
20 & 7.8 & 7.735228919151 & 0.0647710808490034 \tabularnewline
21 & 7.78 & 7.77040163070568 & 0.00959836929431912 \tabularnewline
22 & 7.78 & 7.75546545611008 & 0.0245345438899154 \tabularnewline
23 & 7.8 & 7.75883127496998 & 0.0411687250300208 \tabularnewline
24 & 7.81 & 7.78499669326006 & 0.0250033067399347 \tabularnewline
25 & 7.95 & 7.80035432514087 & 0.149645674859132 \tabularnewline
26 & 8.02 & 7.9588239788501 & 0.0611760211498957 \tabularnewline
27 & 7.99 & 8.04493665810093 & -0.0549366581009263 \tabularnewline
28 & 8.01 & 8.01247680665984 & -0.0024768066598444 \tabularnewline
29 & 8.03 & 8.02882281187798 & 0.0011771881220195 \tabularnewline
30 & 8.05 & 8.04880392145707 & 0.00119607854293236 \tabularnewline
31 & 8.05 & 8.06901156416675 & -0.0190115641667479 \tabularnewline
32 & 8.06 & 8.06693363348641 & -0.00693363348640474 \tabularnewline
33 & 8.07 & 8.07498149187841 & -0.00498149187841435 \tabularnewline
34 & 7.99 & 8.08399197589657 & -0.0939919758965733 \tabularnewline
35 & 8 & 7.99304975519639 & 0.00695024480361006 \tabularnewline
36 & 8.01 & 7.99806411670486 & 0.0119358832951377 \tabularnewline
37 & 8 & 8.00984162433978 & -0.00984162433977964 \tabularnewline
38 & 8.09 & 7.99946092276716 & 0.0905390772328394 \tabularnewline
39 & 8.1 & 8.09910210487695 & 0.000897895123047832 \tabularnewline
40 & 8.12 & 8.11476380716151 & 0.00523619283848831 \tabularnewline
41 & 8.29 & 8.13541148486538 & 0.154588515134618 \tabularnewline
42 & 8.32 & 8.32322656119902 & -0.00322656119902298 \tabularnewline
43 & 8.36 & 8.36235487226093 & -0.00235487226092701 \tabularnewline
44 & 8.38 & 8.40189024431376 & -0.0218902443137612 \tabularnewline
45 & 8.48 & 8.41926848954812 & 0.0607315104518804 \tabularnewline
46 & 8.45 & 8.52479667563888 & -0.0747966756388845 \tabularnewline
47 & 8.41 & 8.49006213077824 & -0.0800621307782432 \tabularnewline
48 & 8.38 & 8.4364088166746 & -0.0564088166745993 \tabularnewline
49 & 8.38 & 8.39510879761901 & -0.0151087976190123 \tabularnewline
50 & 8.34 & 8.38993493712513 & -0.0499349371251263 \tabularnewline
51 & 8.41 & 8.34335636284794 & 0.0666436371520636 \tabularnewline
52 & 8.34 & 8.41783132341205 & -0.0778313234120542 \tabularnewline
53 & 8.22 & 8.3431164418949 & -0.123116441894897 \tabularnewline
54 & 8.27 & 8.20440466318163 & 0.0655953368183742 \tabularnewline
55 & 8.18 & 8.25426684713571 & -0.0742668471357053 \tabularnewline
56 & 8.19 & 8.15989095104672 & 0.03010904895328 \tabularnewline
57 & 8.19 & 8.16873734459083 & 0.0212626554091742 \tabularnewline
58 & 8.13 & 8.17299249187276 & -0.0429924918727558 \tabularnewline
59 & 8.06 & 8.10943314441202 & -0.0494331444120206 \tabularnewline
60 & 7.99 & 8.0311989884912 & -0.0411989884911961 \tabularnewline
61 & 8 & 7.95350109769368 & 0.0464989023063227 \tabularnewline
62 & 7.98 & 7.96623292685649 & 0.0137670731435087 \tabularnewline
63 & 7.92 & 7.95064637767267 & -0.0306463776726744 \tabularnewline
64 & 7.93 & 7.88802382770141 & 0.041976172298587 \tabularnewline
65 & 7.9 & 7.90089190287365 & -0.000891902873647155 \tabularnewline
66 & 7.86 & 7.87336877204735 & -0.0133687720473539 \tabularnewline
67 & 7.88 & 7.83180116493225 & 0.0481988350677529 \tabularnewline
68 & 7.88 & 7.85643444285786 & 0.0235655571421391 \tabularnewline
69 & 7.93 & 7.86206110244307 & 0.0679388975569326 \tabularnewline
70 & 7.91 & 7.92119637552894 & -0.0111963755289439 \tabularnewline
71 & 7.89 & 7.90410156870157 & -0.0141015687015669 \tabularnewline
72 & 7.93 & 7.88181822906741 & 0.0481817709325885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210604&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]8.22[/C][C]8.23[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]8.21[/C][C]8.19886838187787[/C][C]0.0111316181221284[/C][/ROW]
[ROW][C]5[/C][C]8.12[/C][C]8.18951394600456[/C][C]-0.0695139460045624[/C][/ROW]
[ROW][C]6[/C][C]8.16[/C][C]8.09233122564866[/C][C]0.0676687743513398[/C][/ROW]
[ROW][C]7[/C][C]8.15[/C][C]8.13571982617399[/C][C]0.0142801738260108[/C][/ROW]
[ROW][C]8[/C][C]8.1[/C][C]8.13149140330564[/C][C]-0.0314914033056404[/C][/ROW]
[ROW][C]9[/C][C]8.09[/C][C]8.07880473872598[/C][C]0.01119526127402[/C][/ROW]
[ROW][C]10[/C][C]8.02[/C][C]8.06813769635995[/C][C]-0.0481376963599534[/C][/ROW]
[ROW][C]11[/C][C]8.03[/C][C]7.99337785954145[/C][C]0.0366221404585492[/C][/ROW]
[ROW][C]12[/C][C]7.98[/C][C]8.00456590347855[/C][C]-0.0245659034785479[/C][/ROW]
[ROW][C]13[/C][C]7.95[/C][C]7.95403498341738[/C][C]-0.00403498341738295[/C][/ROW]
[ROW][C]14[/C][C]7.92[/C][C]7.92206976079888[/C][C]-0.00206976079887511[/C][/ROW]
[ROW][C]15[/C][C]7.96[/C][C]7.8915877505684[/C][C]0.0684122494316028[/C][/ROW]
[ROW][C]16[/C][C]7.96[/C][C]7.93920229862097[/C][C]0.0207977013790348[/C][/ROW]
[ROW][C]17[/C][C]7.94[/C][C]7.94575706852631[/C][C]-0.00575706852631175[/C][/ROW]
[ROW][C]18[/C][C]7.83[/C][C]7.92638279576022[/C][C]-0.0963827957602161[/C][/ROW]
[ROW][C]19[/C][C]7.77[/C][C]7.80512239661772[/C][C]-0.0351223966177194[/C][/ROW]
[ROW][C]20[/C][C]7.8[/C][C]7.735228919151[/C][C]0.0647710808490034[/C][/ROW]
[ROW][C]21[/C][C]7.78[/C][C]7.77040163070568[/C][C]0.00959836929431912[/C][/ROW]
[ROW][C]22[/C][C]7.78[/C][C]7.75546545611008[/C][C]0.0245345438899154[/C][/ROW]
[ROW][C]23[/C][C]7.8[/C][C]7.75883127496998[/C][C]0.0411687250300208[/C][/ROW]
[ROW][C]24[/C][C]7.81[/C][C]7.78499669326006[/C][C]0.0250033067399347[/C][/ROW]
[ROW][C]25[/C][C]7.95[/C][C]7.80035432514087[/C][C]0.149645674859132[/C][/ROW]
[ROW][C]26[/C][C]8.02[/C][C]7.9588239788501[/C][C]0.0611760211498957[/C][/ROW]
[ROW][C]27[/C][C]7.99[/C][C]8.04493665810093[/C][C]-0.0549366581009263[/C][/ROW]
[ROW][C]28[/C][C]8.01[/C][C]8.01247680665984[/C][C]-0.0024768066598444[/C][/ROW]
[ROW][C]29[/C][C]8.03[/C][C]8.02882281187798[/C][C]0.0011771881220195[/C][/ROW]
[ROW][C]30[/C][C]8.05[/C][C]8.04880392145707[/C][C]0.00119607854293236[/C][/ROW]
[ROW][C]31[/C][C]8.05[/C][C]8.06901156416675[/C][C]-0.0190115641667479[/C][/ROW]
[ROW][C]32[/C][C]8.06[/C][C]8.06693363348641[/C][C]-0.00693363348640474[/C][/ROW]
[ROW][C]33[/C][C]8.07[/C][C]8.07498149187841[/C][C]-0.00498149187841435[/C][/ROW]
[ROW][C]34[/C][C]7.99[/C][C]8.08399197589657[/C][C]-0.0939919758965733[/C][/ROW]
[ROW][C]35[/C][C]8[/C][C]7.99304975519639[/C][C]0.00695024480361006[/C][/ROW]
[ROW][C]36[/C][C]8.01[/C][C]7.99806411670486[/C][C]0.0119358832951377[/C][/ROW]
[ROW][C]37[/C][C]8[/C][C]8.00984162433978[/C][C]-0.00984162433977964[/C][/ROW]
[ROW][C]38[/C][C]8.09[/C][C]7.99946092276716[/C][C]0.0905390772328394[/C][/ROW]
[ROW][C]39[/C][C]8.1[/C][C]8.09910210487695[/C][C]0.000897895123047832[/C][/ROW]
[ROW][C]40[/C][C]8.12[/C][C]8.11476380716151[/C][C]0.00523619283848831[/C][/ROW]
[ROW][C]41[/C][C]8.29[/C][C]8.13541148486538[/C][C]0.154588515134618[/C][/ROW]
[ROW][C]42[/C][C]8.32[/C][C]8.32322656119902[/C][C]-0.00322656119902298[/C][/ROW]
[ROW][C]43[/C][C]8.36[/C][C]8.36235487226093[/C][C]-0.00235487226092701[/C][/ROW]
[ROW][C]44[/C][C]8.38[/C][C]8.40189024431376[/C][C]-0.0218902443137612[/C][/ROW]
[ROW][C]45[/C][C]8.48[/C][C]8.41926848954812[/C][C]0.0607315104518804[/C][/ROW]
[ROW][C]46[/C][C]8.45[/C][C]8.52479667563888[/C][C]-0.0747966756388845[/C][/ROW]
[ROW][C]47[/C][C]8.41[/C][C]8.49006213077824[/C][C]-0.0800621307782432[/C][/ROW]
[ROW][C]48[/C][C]8.38[/C][C]8.4364088166746[/C][C]-0.0564088166745993[/C][/ROW]
[ROW][C]49[/C][C]8.38[/C][C]8.39510879761901[/C][C]-0.0151087976190123[/C][/ROW]
[ROW][C]50[/C][C]8.34[/C][C]8.38993493712513[/C][C]-0.0499349371251263[/C][/ROW]
[ROW][C]51[/C][C]8.41[/C][C]8.34335636284794[/C][C]0.0666436371520636[/C][/ROW]
[ROW][C]52[/C][C]8.34[/C][C]8.41783132341205[/C][C]-0.0778313234120542[/C][/ROW]
[ROW][C]53[/C][C]8.22[/C][C]8.3431164418949[/C][C]-0.123116441894897[/C][/ROW]
[ROW][C]54[/C][C]8.27[/C][C]8.20440466318163[/C][C]0.0655953368183742[/C][/ROW]
[ROW][C]55[/C][C]8.18[/C][C]8.25426684713571[/C][C]-0.0742668471357053[/C][/ROW]
[ROW][C]56[/C][C]8.19[/C][C]8.15989095104672[/C][C]0.03010904895328[/C][/ROW]
[ROW][C]57[/C][C]8.19[/C][C]8.16873734459083[/C][C]0.0212626554091742[/C][/ROW]
[ROW][C]58[/C][C]8.13[/C][C]8.17299249187276[/C][C]-0.0429924918727558[/C][/ROW]
[ROW][C]59[/C][C]8.06[/C][C]8.10943314441202[/C][C]-0.0494331444120206[/C][/ROW]
[ROW][C]60[/C][C]7.99[/C][C]8.0311989884912[/C][C]-0.0411989884911961[/C][/ROW]
[ROW][C]61[/C][C]8[/C][C]7.95350109769368[/C][C]0.0464989023063227[/C][/ROW]
[ROW][C]62[/C][C]7.98[/C][C]7.96623292685649[/C][C]0.0137670731435087[/C][/ROW]
[ROW][C]63[/C][C]7.92[/C][C]7.95064637767267[/C][C]-0.0306463776726744[/C][/ROW]
[ROW][C]64[/C][C]7.93[/C][C]7.88802382770141[/C][C]0.041976172298587[/C][/ROW]
[ROW][C]65[/C][C]7.9[/C][C]7.90089190287365[/C][C]-0.000891902873647155[/C][/ROW]
[ROW][C]66[/C][C]7.86[/C][C]7.87336877204735[/C][C]-0.0133687720473539[/C][/ROW]
[ROW][C]67[/C][C]7.88[/C][C]7.83180116493225[/C][C]0.0481988350677529[/C][/ROW]
[ROW][C]68[/C][C]7.88[/C][C]7.85643444285786[/C][C]0.0235655571421391[/C][/ROW]
[ROW][C]69[/C][C]7.93[/C][C]7.86206110244307[/C][C]0.0679388975569326[/C][/ROW]
[ROW][C]70[/C][C]7.91[/C][C]7.92119637552894[/C][C]-0.0111963755289439[/C][/ROW]
[ROW][C]71[/C][C]7.89[/C][C]7.90410156870157[/C][C]-0.0141015687015669[/C][/ROW]
[ROW][C]72[/C][C]7.93[/C][C]7.88181822906741[/C][C]0.0481817709325885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210604&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210604&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
38.228.23-0.00999999999999979
48.218.198868381877870.0111316181221284
58.128.18951394600456-0.0695139460045624
68.168.092331225648660.0676687743513398
78.158.135719826173990.0142801738260108
88.18.13149140330564-0.0314914033056404
98.098.078804738725980.01119526127402
108.028.06813769635995-0.0481376963599534
118.037.993377859541450.0366221404585492
127.988.00456590347855-0.0245659034785479
137.957.95403498341738-0.00403498341738295
147.927.92206976079888-0.00206976079887511
157.967.89158775056840.0684122494316028
167.967.939202298620970.0207977013790348
177.947.94575706852631-0.00575706852631175
187.837.92638279576022-0.0963827957602161
197.777.80512239661772-0.0351223966177194
207.87.7352289191510.0647710808490034
217.787.770401630705680.00959836929431912
227.787.755465456110080.0245345438899154
237.87.758831274969980.0411687250300208
247.817.784996693260060.0250033067399347
257.957.800354325140870.149645674859132
268.027.95882397885010.0611760211498957
277.998.04493665810093-0.0549366581009263
288.018.01247680665984-0.0024768066598444
298.038.028822811877980.0011771881220195
308.058.048803921457070.00119607854293236
318.058.06901156416675-0.0190115641667479
328.068.06693363348641-0.00693363348640474
338.078.07498149187841-0.00498149187841435
347.998.08399197589657-0.0939919758965733
3587.993049755196390.00695024480361006
368.017.998064116704860.0119358832951377
3788.00984162433978-0.00984162433977964
388.097.999460922767160.0905390772328394
398.18.099102104876950.000897895123047832
408.128.114763807161510.00523619283848831
418.298.135411484865380.154588515134618
428.328.32322656119902-0.00322656119902298
438.368.36235487226093-0.00235487226092701
448.388.40189024431376-0.0218902443137612
458.488.419268489548120.0607315104518804
468.458.52479667563888-0.0747966756388845
478.418.49006213077824-0.0800621307782432
488.388.4364088166746-0.0564088166745993
498.388.39510879761901-0.0151087976190123
508.348.38993493712513-0.0499349371251263
518.418.343356362847940.0666436371520636
528.348.41783132341205-0.0778313234120542
538.228.3431164418949-0.123116441894897
548.278.204404663181630.0655953368183742
558.188.25426684713571-0.0742668471357053
568.198.159890951046720.03010904895328
578.198.168737344590830.0212626554091742
588.138.17299249187276-0.0429924918727558
598.068.10943314441202-0.0494331444120206
607.998.0311989884912-0.0411989884911961
6187.953501097693680.0464989023063227
627.987.966232926856490.0137670731435087
637.927.95064637767267-0.0306463776726744
647.937.888023827701410.041976172298587
657.97.90089190287365-0.000891902873647155
667.867.87336877204735-0.0133687720473539
677.887.831801164932250.0481988350677529
687.887.856434442857860.0235655571421391
697.937.862061102443070.0679388975569326
707.917.92119637552894-0.0111963755289439
717.897.90410156870157-0.0141015687015669
727.937.881818229067410.0481817709325885







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
737.926404574212697.823807175343488.0290019730819
747.925768038933057.772244162011358.07929191585476
757.925131503653417.722585692836378.12767731447045
767.924494968373787.672436467563528.17655346918403
777.923858433094147.620976912807398.22673995338089
787.92322189781457.567866335773288.27857745985573
797.922585362534867.512956071894448.33221465317528
807.921948827255227.45618650197058.38771115253995
817.921312291975597.397542947055128.44508163689606
827.920675756695957.337034520734578.50431699265732
837.920039221416317.2746831739088.56539526892462
847.919402686136677.210517701534738.62828767073861

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 7.92640457421269 & 7.82380717534348 & 8.0290019730819 \tabularnewline
74 & 7.92576803893305 & 7.77224416201135 & 8.07929191585476 \tabularnewline
75 & 7.92513150365341 & 7.72258569283637 & 8.12767731447045 \tabularnewline
76 & 7.92449496837378 & 7.67243646756352 & 8.17655346918403 \tabularnewline
77 & 7.92385843309414 & 7.62097691280739 & 8.22673995338089 \tabularnewline
78 & 7.9232218978145 & 7.56786633577328 & 8.27857745985573 \tabularnewline
79 & 7.92258536253486 & 7.51295607189444 & 8.33221465317528 \tabularnewline
80 & 7.92194882725522 & 7.4561865019705 & 8.38771115253995 \tabularnewline
81 & 7.92131229197559 & 7.39754294705512 & 8.44508163689606 \tabularnewline
82 & 7.92067575669595 & 7.33703452073457 & 8.50431699265732 \tabularnewline
83 & 7.92003922141631 & 7.274683173908 & 8.56539526892462 \tabularnewline
84 & 7.91940268613667 & 7.21051770153473 & 8.62828767073861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210604&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]7.92640457421269[/C][C]7.82380717534348[/C][C]8.0290019730819[/C][/ROW]
[ROW][C]74[/C][C]7.92576803893305[/C][C]7.77224416201135[/C][C]8.07929191585476[/C][/ROW]
[ROW][C]75[/C][C]7.92513150365341[/C][C]7.72258569283637[/C][C]8.12767731447045[/C][/ROW]
[ROW][C]76[/C][C]7.92449496837378[/C][C]7.67243646756352[/C][C]8.17655346918403[/C][/ROW]
[ROW][C]77[/C][C]7.92385843309414[/C][C]7.62097691280739[/C][C]8.22673995338089[/C][/ROW]
[ROW][C]78[/C][C]7.9232218978145[/C][C]7.56786633577328[/C][C]8.27857745985573[/C][/ROW]
[ROW][C]79[/C][C]7.92258536253486[/C][C]7.51295607189444[/C][C]8.33221465317528[/C][/ROW]
[ROW][C]80[/C][C]7.92194882725522[/C][C]7.4561865019705[/C][C]8.38771115253995[/C][/ROW]
[ROW][C]81[/C][C]7.92131229197559[/C][C]7.39754294705512[/C][C]8.44508163689606[/C][/ROW]
[ROW][C]82[/C][C]7.92067575669595[/C][C]7.33703452073457[/C][C]8.50431699265732[/C][/ROW]
[ROW][C]83[/C][C]7.92003922141631[/C][C]7.274683173908[/C][C]8.56539526892462[/C][/ROW]
[ROW][C]84[/C][C]7.91940268613667[/C][C]7.21051770153473[/C][C]8.62828767073861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210604&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210604&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
737.926404574212697.823807175343488.0290019730819
747.925768038933057.772244162011358.07929191585476
757.925131503653417.722585692836378.12767731447045
767.924494968373787.672436467563528.17655346918403
777.923858433094147.620976912807398.22673995338089
787.92322189781457.567866335773288.27857745985573
797.922585362534867.512956071894448.33221465317528
807.921948827255227.45618650197058.38771115253995
817.921312291975597.397542947055128.44508163689606
827.920675756695957.337034520734578.50431699265732
837.920039221416317.2746831739088.56539526892462
847.919402686136677.210517701534738.62828767073861



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