Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 21:03:35 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/28/t1417208725uryge6eab94oryr.htm/, Retrieved Sun, 19 May 2024 14:07:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261026, Retrieved Sun, 19 May 2024 14:07:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde consum...] [2014-11-28 21:03:35] [34904d4daa687a283c33410e9d0f3c21] [Current]
Feedback Forum

Post a new message
Dataseries X:
4,53
4,53
4,53
4,61
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,66
4,7
4,72
4,73
4,73
4,74
4,74
4,74
4,76
4,88
4,88
4,88
4,88
4,89
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,98
5
5,03
5,04
5,04
5,05
5,05
5,05
5,06
5,06
5,06
5,07
5,09
5,18
5,23
5,25
5,26
5,28
5,29
5,29
5,29
5,29
5,3
5,3
5,3
5,32
5,33
5,33
5,37
5,45
5,47
5,5
5,51




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261026&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261026&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261026&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0199635626507471
gamma0.241448120250782

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0199635626507471 \tabularnewline
gamma & 0.241448120250782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261026&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0199635626507471[/C][/ROW]
[ROW][C]gamma[/C][C]0.241448120250782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261026&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261026&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
alpha1
beta0.0199635626507471
gamma0.241448120250782







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134.634.579620726495730.0503792735042712
144.634.631238850016-0.00123885001600144
154.664.66079745148943-0.000797451489424894
164.74.70078153151666-0.000781531516656386
174.724.719932596029936.7403970073876e-05
184.734.724100608319970.00589939168002829
194.734.74380171452871-0.0138017145287108
204.744.73144284980270.00855715019730319
214.744.74036368100677-0.000363681006772865
224.744.74077308730487-0.000773087304873243
234.764.74242432039470.0175756796053035
244.884.762358526908960.11764147309104
254.884.88429040316067-0.0042904031606712
264.884.88378808476171-0.00378808476171066
274.884.91329579442758-0.0332957944275769
284.894.92263109174952-0.0326310917495158
294.974.911146325571680.0588536744283221
304.974.97648792125502-0.00648792125502151
314.974.98594173256591-0.0159417325659073
324.974.97354014545573-0.00354014545573378
334.974.97221947154013-0.00221947154013513
344.974.97259182964766-0.00259182964765703
354.974.97420675416077-0.00420675416077376
364.974.97370610569386-0.00370610569386365
374.974.97321545195399-0.00321545195398532
384.974.97273459341079-0.00273459341078564
394.975.00226333451724-0.0322633345172383
404.985.01161924341728-0.0316192434172811
4155.00015467733702-0.000154677337017795
425.035.004318256092980.0256817439070236
435.045.04441428852978-0.00441428852977843
445.045.04224283027082-0.00224283027082262
455.055.04094805538820.00905194461180336
465.055.05154543111823-0.00154543111822925
475.055.05318124547395-0.00318124547394572
485.065.052701069813950.00729893018604599
495.065.06243011579734-0.00243011579733832
505.065.0619649353617-0.00196493536170372
515.075.09150904158484-0.0215090415848378
525.095.1110796444856-0.021079644485603
535.185.109825486348930.0701745136510743
545.235.185393086315350.0446069136846496
555.255.245866932564680.0041330674353155
565.265.253866109982040.00613389001796349
575.285.26273856427970.0172614357202976
585.295.283499830699810.00650016930018893
595.295.29529626390354-0.00529626390354387
605.295.29477386494063-0.00477386494062504
615.295.29426189492213-0.00426189492212892
625.35.293760145649170.00623985435082641
635.35.33346804870577-0.033468048705771
645.35.34279990721864-0.0427999072186358
655.325.3211121352561-0.0011121352560961
665.335.32525659974090.00474340025909736
675.335.34493462824249-0.0149346282424858
685.375.332553146522570.0374468534774319
695.455.372050719128040.0779492808719615
705.475.454023531146970.0159764688530286
715.55.476009145050520.0239908549494761
725.515.506071421319690.00392857868031271

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.63 & 4.57962072649573 & 0.0503792735042712 \tabularnewline
14 & 4.63 & 4.631238850016 & -0.00123885001600144 \tabularnewline
15 & 4.66 & 4.66079745148943 & -0.000797451489424894 \tabularnewline
16 & 4.7 & 4.70078153151666 & -0.000781531516656386 \tabularnewline
17 & 4.72 & 4.71993259602993 & 6.7403970073876e-05 \tabularnewline
18 & 4.73 & 4.72410060831997 & 0.00589939168002829 \tabularnewline
19 & 4.73 & 4.74380171452871 & -0.0138017145287108 \tabularnewline
20 & 4.74 & 4.7314428498027 & 0.00855715019730319 \tabularnewline
21 & 4.74 & 4.74036368100677 & -0.000363681006772865 \tabularnewline
22 & 4.74 & 4.74077308730487 & -0.000773087304873243 \tabularnewline
23 & 4.76 & 4.7424243203947 & 0.0175756796053035 \tabularnewline
24 & 4.88 & 4.76235852690896 & 0.11764147309104 \tabularnewline
25 & 4.88 & 4.88429040316067 & -0.0042904031606712 \tabularnewline
26 & 4.88 & 4.88378808476171 & -0.00378808476171066 \tabularnewline
27 & 4.88 & 4.91329579442758 & -0.0332957944275769 \tabularnewline
28 & 4.89 & 4.92263109174952 & -0.0326310917495158 \tabularnewline
29 & 4.97 & 4.91114632557168 & 0.0588536744283221 \tabularnewline
30 & 4.97 & 4.97648792125502 & -0.00648792125502151 \tabularnewline
31 & 4.97 & 4.98594173256591 & -0.0159417325659073 \tabularnewline
32 & 4.97 & 4.97354014545573 & -0.00354014545573378 \tabularnewline
33 & 4.97 & 4.97221947154013 & -0.00221947154013513 \tabularnewline
34 & 4.97 & 4.97259182964766 & -0.00259182964765703 \tabularnewline
35 & 4.97 & 4.97420675416077 & -0.00420675416077376 \tabularnewline
36 & 4.97 & 4.97370610569386 & -0.00370610569386365 \tabularnewline
37 & 4.97 & 4.97321545195399 & -0.00321545195398532 \tabularnewline
38 & 4.97 & 4.97273459341079 & -0.00273459341078564 \tabularnewline
39 & 4.97 & 5.00226333451724 & -0.0322633345172383 \tabularnewline
40 & 4.98 & 5.01161924341728 & -0.0316192434172811 \tabularnewline
41 & 5 & 5.00015467733702 & -0.000154677337017795 \tabularnewline
42 & 5.03 & 5.00431825609298 & 0.0256817439070236 \tabularnewline
43 & 5.04 & 5.04441428852978 & -0.00441428852977843 \tabularnewline
44 & 5.04 & 5.04224283027082 & -0.00224283027082262 \tabularnewline
45 & 5.05 & 5.0409480553882 & 0.00905194461180336 \tabularnewline
46 & 5.05 & 5.05154543111823 & -0.00154543111822925 \tabularnewline
47 & 5.05 & 5.05318124547395 & -0.00318124547394572 \tabularnewline
48 & 5.06 & 5.05270106981395 & 0.00729893018604599 \tabularnewline
49 & 5.06 & 5.06243011579734 & -0.00243011579733832 \tabularnewline
50 & 5.06 & 5.0619649353617 & -0.00196493536170372 \tabularnewline
51 & 5.07 & 5.09150904158484 & -0.0215090415848378 \tabularnewline
52 & 5.09 & 5.1110796444856 & -0.021079644485603 \tabularnewline
53 & 5.18 & 5.10982548634893 & 0.0701745136510743 \tabularnewline
54 & 5.23 & 5.18539308631535 & 0.0446069136846496 \tabularnewline
55 & 5.25 & 5.24586693256468 & 0.0041330674353155 \tabularnewline
56 & 5.26 & 5.25386610998204 & 0.00613389001796349 \tabularnewline
57 & 5.28 & 5.2627385642797 & 0.0172614357202976 \tabularnewline
58 & 5.29 & 5.28349983069981 & 0.00650016930018893 \tabularnewline
59 & 5.29 & 5.29529626390354 & -0.00529626390354387 \tabularnewline
60 & 5.29 & 5.29477386494063 & -0.00477386494062504 \tabularnewline
61 & 5.29 & 5.29426189492213 & -0.00426189492212892 \tabularnewline
62 & 5.3 & 5.29376014564917 & 0.00623985435082641 \tabularnewline
63 & 5.3 & 5.33346804870577 & -0.033468048705771 \tabularnewline
64 & 5.3 & 5.34279990721864 & -0.0427999072186358 \tabularnewline
65 & 5.32 & 5.3211121352561 & -0.0011121352560961 \tabularnewline
66 & 5.33 & 5.3252565997409 & 0.00474340025909736 \tabularnewline
67 & 5.33 & 5.34493462824249 & -0.0149346282424858 \tabularnewline
68 & 5.37 & 5.33255314652257 & 0.0374468534774319 \tabularnewline
69 & 5.45 & 5.37205071912804 & 0.0779492808719615 \tabularnewline
70 & 5.47 & 5.45402353114697 & 0.0159764688530286 \tabularnewline
71 & 5.5 & 5.47600914505052 & 0.0239908549494761 \tabularnewline
72 & 5.51 & 5.50607142131969 & 0.00392857868031271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261026&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]4.63[/C][C]4.57962072649573[/C][C]0.0503792735042712[/C][/ROW]
[ROW][C]14[/C][C]4.63[/C][C]4.631238850016[/C][C]-0.00123885001600144[/C][/ROW]
[ROW][C]15[/C][C]4.66[/C][C]4.66079745148943[/C][C]-0.000797451489424894[/C][/ROW]
[ROW][C]16[/C][C]4.7[/C][C]4.70078153151666[/C][C]-0.000781531516656386[/C][/ROW]
[ROW][C]17[/C][C]4.72[/C][C]4.71993259602993[/C][C]6.7403970073876e-05[/C][/ROW]
[ROW][C]18[/C][C]4.73[/C][C]4.72410060831997[/C][C]0.00589939168002829[/C][/ROW]
[ROW][C]19[/C][C]4.73[/C][C]4.74380171452871[/C][C]-0.0138017145287108[/C][/ROW]
[ROW][C]20[/C][C]4.74[/C][C]4.7314428498027[/C][C]0.00855715019730319[/C][/ROW]
[ROW][C]21[/C][C]4.74[/C][C]4.74036368100677[/C][C]-0.000363681006772865[/C][/ROW]
[ROW][C]22[/C][C]4.74[/C][C]4.74077308730487[/C][C]-0.000773087304873243[/C][/ROW]
[ROW][C]23[/C][C]4.76[/C][C]4.7424243203947[/C][C]0.0175756796053035[/C][/ROW]
[ROW][C]24[/C][C]4.88[/C][C]4.76235852690896[/C][C]0.11764147309104[/C][/ROW]
[ROW][C]25[/C][C]4.88[/C][C]4.88429040316067[/C][C]-0.0042904031606712[/C][/ROW]
[ROW][C]26[/C][C]4.88[/C][C]4.88378808476171[/C][C]-0.00378808476171066[/C][/ROW]
[ROW][C]27[/C][C]4.88[/C][C]4.91329579442758[/C][C]-0.0332957944275769[/C][/ROW]
[ROW][C]28[/C][C]4.89[/C][C]4.92263109174952[/C][C]-0.0326310917495158[/C][/ROW]
[ROW][C]29[/C][C]4.97[/C][C]4.91114632557168[/C][C]0.0588536744283221[/C][/ROW]
[ROW][C]30[/C][C]4.97[/C][C]4.97648792125502[/C][C]-0.00648792125502151[/C][/ROW]
[ROW][C]31[/C][C]4.97[/C][C]4.98594173256591[/C][C]-0.0159417325659073[/C][/ROW]
[ROW][C]32[/C][C]4.97[/C][C]4.97354014545573[/C][C]-0.00354014545573378[/C][/ROW]
[ROW][C]33[/C][C]4.97[/C][C]4.97221947154013[/C][C]-0.00221947154013513[/C][/ROW]
[ROW][C]34[/C][C]4.97[/C][C]4.97259182964766[/C][C]-0.00259182964765703[/C][/ROW]
[ROW][C]35[/C][C]4.97[/C][C]4.97420675416077[/C][C]-0.00420675416077376[/C][/ROW]
[ROW][C]36[/C][C]4.97[/C][C]4.97370610569386[/C][C]-0.00370610569386365[/C][/ROW]
[ROW][C]37[/C][C]4.97[/C][C]4.97321545195399[/C][C]-0.00321545195398532[/C][/ROW]
[ROW][C]38[/C][C]4.97[/C][C]4.97273459341079[/C][C]-0.00273459341078564[/C][/ROW]
[ROW][C]39[/C][C]4.97[/C][C]5.00226333451724[/C][C]-0.0322633345172383[/C][/ROW]
[ROW][C]40[/C][C]4.98[/C][C]5.01161924341728[/C][C]-0.0316192434172811[/C][/ROW]
[ROW][C]41[/C][C]5[/C][C]5.00015467733702[/C][C]-0.000154677337017795[/C][/ROW]
[ROW][C]42[/C][C]5.03[/C][C]5.00431825609298[/C][C]0.0256817439070236[/C][/ROW]
[ROW][C]43[/C][C]5.04[/C][C]5.04441428852978[/C][C]-0.00441428852977843[/C][/ROW]
[ROW][C]44[/C][C]5.04[/C][C]5.04224283027082[/C][C]-0.00224283027082262[/C][/ROW]
[ROW][C]45[/C][C]5.05[/C][C]5.0409480553882[/C][C]0.00905194461180336[/C][/ROW]
[ROW][C]46[/C][C]5.05[/C][C]5.05154543111823[/C][C]-0.00154543111822925[/C][/ROW]
[ROW][C]47[/C][C]5.05[/C][C]5.05318124547395[/C][C]-0.00318124547394572[/C][/ROW]
[ROW][C]48[/C][C]5.06[/C][C]5.05270106981395[/C][C]0.00729893018604599[/C][/ROW]
[ROW][C]49[/C][C]5.06[/C][C]5.06243011579734[/C][C]-0.00243011579733832[/C][/ROW]
[ROW][C]50[/C][C]5.06[/C][C]5.0619649353617[/C][C]-0.00196493536170372[/C][/ROW]
[ROW][C]51[/C][C]5.07[/C][C]5.09150904158484[/C][C]-0.0215090415848378[/C][/ROW]
[ROW][C]52[/C][C]5.09[/C][C]5.1110796444856[/C][C]-0.021079644485603[/C][/ROW]
[ROW][C]53[/C][C]5.18[/C][C]5.10982548634893[/C][C]0.0701745136510743[/C][/ROW]
[ROW][C]54[/C][C]5.23[/C][C]5.18539308631535[/C][C]0.0446069136846496[/C][/ROW]
[ROW][C]55[/C][C]5.25[/C][C]5.24586693256468[/C][C]0.0041330674353155[/C][/ROW]
[ROW][C]56[/C][C]5.26[/C][C]5.25386610998204[/C][C]0.00613389001796349[/C][/ROW]
[ROW][C]57[/C][C]5.28[/C][C]5.2627385642797[/C][C]0.0172614357202976[/C][/ROW]
[ROW][C]58[/C][C]5.29[/C][C]5.28349983069981[/C][C]0.00650016930018893[/C][/ROW]
[ROW][C]59[/C][C]5.29[/C][C]5.29529626390354[/C][C]-0.00529626390354387[/C][/ROW]
[ROW][C]60[/C][C]5.29[/C][C]5.29477386494063[/C][C]-0.00477386494062504[/C][/ROW]
[ROW][C]61[/C][C]5.29[/C][C]5.29426189492213[/C][C]-0.00426189492212892[/C][/ROW]
[ROW][C]62[/C][C]5.3[/C][C]5.29376014564917[/C][C]0.00623985435082641[/C][/ROW]
[ROW][C]63[/C][C]5.3[/C][C]5.33346804870577[/C][C]-0.033468048705771[/C][/ROW]
[ROW][C]64[/C][C]5.3[/C][C]5.34279990721864[/C][C]-0.0427999072186358[/C][/ROW]
[ROW][C]65[/C][C]5.32[/C][C]5.3211121352561[/C][C]-0.0011121352560961[/C][/ROW]
[ROW][C]66[/C][C]5.33[/C][C]5.3252565997409[/C][C]0.00474340025909736[/C][/ROW]
[ROW][C]67[/C][C]5.33[/C][C]5.34493462824249[/C][C]-0.0149346282424858[/C][/ROW]
[ROW][C]68[/C][C]5.37[/C][C]5.33255314652257[/C][C]0.0374468534774319[/C][/ROW]
[ROW][C]69[/C][C]5.45[/C][C]5.37205071912804[/C][C]0.0779492808719615[/C][/ROW]
[ROW][C]70[/C][C]5.47[/C][C]5.45402353114697[/C][C]0.0159764688530286[/C][/ROW]
[ROW][C]71[/C][C]5.5[/C][C]5.47600914505052[/C][C]0.0239908549494761[/C][/ROW]
[ROW][C]72[/C][C]5.51[/C][C]5.50607142131969[/C][C]0.00392857868031271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261026&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261026&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
134.634.579620726495730.0503792735042712
144.634.631238850016-0.00123885001600144
154.664.66079745148943-0.000797451489424894
164.74.70078153151666-0.000781531516656386
174.724.719932596029936.7403970073876e-05
184.734.724100608319970.00589939168002829
194.734.74380171452871-0.0138017145287108
204.744.73144284980270.00855715019730319
214.744.74036368100677-0.000363681006772865
224.744.74077308730487-0.000773087304873243
234.764.74242432039470.0175756796053035
244.884.762358526908960.11764147309104
254.884.88429040316067-0.0042904031606712
264.884.88378808476171-0.00378808476171066
274.884.91329579442758-0.0332957944275769
284.894.92263109174952-0.0326310917495158
294.974.911146325571680.0588536744283221
304.974.97648792125502-0.00648792125502151
314.974.98594173256591-0.0159417325659073
324.974.97354014545573-0.00354014545573378
334.974.97221947154013-0.00221947154013513
344.974.97259182964766-0.00259182964765703
354.974.97420675416077-0.00420675416077376
364.974.97370610569386-0.00370610569386365
374.974.97321545195399-0.00321545195398532
384.974.97273459341079-0.00273459341078564
394.975.00226333451724-0.0322633345172383
404.985.01161924341728-0.0316192434172811
4155.00015467733702-0.000154677337017795
425.035.004318256092980.0256817439070236
435.045.04441428852978-0.00441428852977843
445.045.04224283027082-0.00224283027082262
455.055.04094805538820.00905194461180336
465.055.05154543111823-0.00154543111822925
475.055.05318124547395-0.00318124547394572
485.065.052701069813950.00729893018604599
495.065.06243011579734-0.00243011579733832
505.065.0619649353617-0.00196493536170372
515.075.09150904158484-0.0215090415848378
525.095.1110796444856-0.021079644485603
535.185.109825486348930.0701745136510743
545.235.185393086315350.0446069136846496
555.255.245866932564680.0041330674353155
565.265.253866109982040.00613389001796349
575.285.26273856427970.0172614357202976
585.295.283499830699810.00650016930018893
595.295.29529626390354-0.00529626390354387
605.295.29477386494063-0.00477386494062504
615.295.29426189492213-0.00426189492212892
625.35.293760145649170.00623985435082641
635.35.33346804870577-0.033468048705771
645.35.34279990721864-0.0427999072186358
655.325.3211121352561-0.0011121352560961
665.335.32525659974090.00474340025909736
675.335.34493462824249-0.0149346282424858
685.375.332553146522570.0374468534774319
695.455.372050719128040.0779492808719615
705.475.454023531146970.0159764688530286
715.55.476009145050520.0239908549494761
725.515.506071421319690.00392857868031271







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.515733183079635.461798924524345.56966744163492
745.52104969949265.444010021391085.59808937759411
755.55594954923895.460655572934375.65124352554342
765.60084939898525.48972463733675.7119741606337
775.624915915398165.499453798214485.75037803258184
785.63314909847785.494371034065755.77192716288984
795.650965614890765.499615503412895.80231572636864
805.656698797970395.493341591985655.82005600395514
815.661181981050035.486259623068025.83610433903204
825.666081830796335.479947635602115.85221602599054
835.672648347209295.475589428876025.86970726554256
845.678798196955595.471050787835945.88654560607524

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.51573318307963 & 5.46179892452434 & 5.56966744163492 \tabularnewline
74 & 5.5210496994926 & 5.44401002139108 & 5.59808937759411 \tabularnewline
75 & 5.5559495492389 & 5.46065557293437 & 5.65124352554342 \tabularnewline
76 & 5.6008493989852 & 5.4897246373367 & 5.7119741606337 \tabularnewline
77 & 5.62491591539816 & 5.49945379821448 & 5.75037803258184 \tabularnewline
78 & 5.6331490984778 & 5.49437103406575 & 5.77192716288984 \tabularnewline
79 & 5.65096561489076 & 5.49961550341289 & 5.80231572636864 \tabularnewline
80 & 5.65669879797039 & 5.49334159198565 & 5.82005600395514 \tabularnewline
81 & 5.66118198105003 & 5.48625962306802 & 5.83610433903204 \tabularnewline
82 & 5.66608183079633 & 5.47994763560211 & 5.85221602599054 \tabularnewline
83 & 5.67264834720929 & 5.47558942887602 & 5.86970726554256 \tabularnewline
84 & 5.67879819695559 & 5.47105078783594 & 5.88654560607524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261026&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]5.51573318307963[/C][C]5.46179892452434[/C][C]5.56966744163492[/C][/ROW]
[ROW][C]74[/C][C]5.5210496994926[/C][C]5.44401002139108[/C][C]5.59808937759411[/C][/ROW]
[ROW][C]75[/C][C]5.5559495492389[/C][C]5.46065557293437[/C][C]5.65124352554342[/C][/ROW]
[ROW][C]76[/C][C]5.6008493989852[/C][C]5.4897246373367[/C][C]5.7119741606337[/C][/ROW]
[ROW][C]77[/C][C]5.62491591539816[/C][C]5.49945379821448[/C][C]5.75037803258184[/C][/ROW]
[ROW][C]78[/C][C]5.6331490984778[/C][C]5.49437103406575[/C][C]5.77192716288984[/C][/ROW]
[ROW][C]79[/C][C]5.65096561489076[/C][C]5.49961550341289[/C][C]5.80231572636864[/C][/ROW]
[ROW][C]80[/C][C]5.65669879797039[/C][C]5.49334159198565[/C][C]5.82005600395514[/C][/ROW]
[ROW][C]81[/C][C]5.66118198105003[/C][C]5.48625962306802[/C][C]5.83610433903204[/C][/ROW]
[ROW][C]82[/C][C]5.66608183079633[/C][C]5.47994763560211[/C][C]5.85221602599054[/C][/ROW]
[ROW][C]83[/C][C]5.67264834720929[/C][C]5.47558942887602[/C][C]5.86970726554256[/C][/ROW]
[ROW][C]84[/C][C]5.67879819695559[/C][C]5.47105078783594[/C][C]5.88654560607524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261026&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261026&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
735.515733183079635.461798924524345.56966744163492
745.52104969949265.444010021391085.59808937759411
755.55594954923895.460655572934375.65124352554342
765.60084939898525.48972463733675.7119741606337
775.624915915398165.499453798214485.75037803258184
785.63314909847785.494371034065755.77192716288984
795.650965614890765.499615503412895.80231572636864
805.656698797970395.493341591985655.82005600395514
815.661181981050035.486259623068025.83610433903204
825.666081830796335.479947635602115.85221602599054
835.672648347209295.475589428876025.86970726554256
845.678798196955595.471050787835945.88654560607524



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')