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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 14:34:07 +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/30/t14173580685uhw3viegt3vqt0.htm/, Retrieved Sun, 19 May 2024 16:09:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261475, Retrieved Sun, 19 May 2024 16:09:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [eigen reeks decom...] [2014-11-30 14:34:07] [6e93958bb59fd6ca90246553243cf8d9] [Current]
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Dataseries X:
389,09
391,76
390,96
391,76
392,8
393,06
393,06
393,26
393,87
394,47
394,57
394,57
394,57
399,57
406,13
407,03
409,46
409,9
409,9
410,14
410,54
410,69
410,79
410,97
410,97
413,8
423,31
423,85
426,6
426,26
426,26
426,32
427,14
427,55
428,29
428,8
428,8
434,87
435,66
440,75
440,99
441,04
441,04
441,88
441,92
442,48
442,81
442,81
442,81
447,19
446,52
448,57
448,71
448,73
449,07
449,03
448,68
450,08
449,96
449,96
449,96
452,56
455,31
456,2
456,75
457,63
457,63
457,65
458,32
459,64
460,16
459,89




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=261475&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=261475&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261475&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
beta0.0858026750297081
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0858026750297081 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261475&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]0.0858026750297081[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261475&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261475&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
beta0.0858026750297081
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3390.96394.43-3.47000000000003
4391.76393.332264717647-1.57226471764693
5392.8393.997360199018-1.19736019901796
6393.06394.934623490968-1.87462349096813
7393.06395.03377578077-1.97377578076953
8393.26394.864420538871-1.60442053887067
9393.87394.926756964763-1.05675696476294
10394.47395.44608439033-0.976084390330016
11394.57395.962333738585-1.39233373858502
12394.57395.94286777928-1.37286777928028
13394.57395.825072051356-1.25507205135591
14399.57395.7173835119953.85261648800542
15406.13401.0479483125295.08205168747099
16407.03408.044001941953-1.01400194195327
17409.46408.8569978628480.603002137151691
18409.9411.338737059265-1.43873705926455
19409.9411.655289570915-1.75528957091529
20410.14411.504681030279-1.36468103027903
21410.54411.627587747319-1.08758774731876
22410.69411.934269809269-1.24426980926933
23410.79411.977508131175-1.18750813117526
24410.97411.975616756901-1.00561675690091
25410.97412.069332149104-1.0993321491041
26413.8411.9750065099651.82499349003513
27423.31414.9615958333228.34840416667834
28423.85425.187911243052-1.33791124305179
29426.6425.6131148794460.986885120554348
30426.26428.447792262736-2.18779226273625
31426.26427.920073834184-1.66007383418417
32426.32427.777635058464-1.45763505846435
33427.14427.712566071231-0.572566071230995
34427.55428.483438370688-0.933438370688123
35428.29428.813346861508-0.523346861507719
36428.8429.508442300822-0.708442300821957
37428.8429.957656056307-1.15765605630725
38434.87429.8583260699125.01167393008825
39435.66436.35834109949-0.698341099489937
40440.75437.0884215650713.66157843492942
41440.99442.492594789619-1.50259478961857
42441.04442.603668137184-1.56366813718358
43441.04442.519501228155-1.4795012281545
44441.88442.392556065069-0.512556065069134
45441.92443.188577383583-1.26857738358348
46442.48443.11973005059-0.639730050589833
47442.81443.624839500952-0.81483950095236
48442.81443.884924092051-1.07492409205076
49442.81443.792692729499-0.982692729498922
50447.19443.7083750645763.48162493542435
51446.52448.387107797485-1.86710779748523
52448.57447.5569049538921.01309504610788
53448.71449.693831218908-0.98383121890754
54448.73449.749415868548-1.01941586854753
55449.07449.681947260058-0.611947260058457
56449.03449.969440548168-0.939440548168363
57448.68449.848834036104-1.16883403610404
58450.08449.3985449491410.68145505085937
59449.96450.857015615417-0.897015615416819
60449.96450.660049276071-0.700049276070672
61449.96450.599983175531-0.639983175531199
62452.56450.5450709070972.0149290929034
63455.31453.3179572132631.9920427867371
64456.2456.238879813139-0.0388798131385784
65456.75457.125543821167-0.375543821166616
66457.63457.64332115672-0.0133211567196554
67457.63458.522178165839-0.892178165838629
68457.65458.445626892607-0.795626892606606
69458.32458.397359976895-0.077359976895309
70459.64459.0607222839370.579277716062506
71460.16460.430425861561-0.270425861560739
72459.89460.927222599242-1.03722259924166

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 390.96 & 394.43 & -3.47000000000003 \tabularnewline
4 & 391.76 & 393.332264717647 & -1.57226471764693 \tabularnewline
5 & 392.8 & 393.997360199018 & -1.19736019901796 \tabularnewline
6 & 393.06 & 394.934623490968 & -1.87462349096813 \tabularnewline
7 & 393.06 & 395.03377578077 & -1.97377578076953 \tabularnewline
8 & 393.26 & 394.864420538871 & -1.60442053887067 \tabularnewline
9 & 393.87 & 394.926756964763 & -1.05675696476294 \tabularnewline
10 & 394.47 & 395.44608439033 & -0.976084390330016 \tabularnewline
11 & 394.57 & 395.962333738585 & -1.39233373858502 \tabularnewline
12 & 394.57 & 395.94286777928 & -1.37286777928028 \tabularnewline
13 & 394.57 & 395.825072051356 & -1.25507205135591 \tabularnewline
14 & 399.57 & 395.717383511995 & 3.85261648800542 \tabularnewline
15 & 406.13 & 401.047948312529 & 5.08205168747099 \tabularnewline
16 & 407.03 & 408.044001941953 & -1.01400194195327 \tabularnewline
17 & 409.46 & 408.856997862848 & 0.603002137151691 \tabularnewline
18 & 409.9 & 411.338737059265 & -1.43873705926455 \tabularnewline
19 & 409.9 & 411.655289570915 & -1.75528957091529 \tabularnewline
20 & 410.14 & 411.504681030279 & -1.36468103027903 \tabularnewline
21 & 410.54 & 411.627587747319 & -1.08758774731876 \tabularnewline
22 & 410.69 & 411.934269809269 & -1.24426980926933 \tabularnewline
23 & 410.79 & 411.977508131175 & -1.18750813117526 \tabularnewline
24 & 410.97 & 411.975616756901 & -1.00561675690091 \tabularnewline
25 & 410.97 & 412.069332149104 & -1.0993321491041 \tabularnewline
26 & 413.8 & 411.975006509965 & 1.82499349003513 \tabularnewline
27 & 423.31 & 414.961595833322 & 8.34840416667834 \tabularnewline
28 & 423.85 & 425.187911243052 & -1.33791124305179 \tabularnewline
29 & 426.6 & 425.613114879446 & 0.986885120554348 \tabularnewline
30 & 426.26 & 428.447792262736 & -2.18779226273625 \tabularnewline
31 & 426.26 & 427.920073834184 & -1.66007383418417 \tabularnewline
32 & 426.32 & 427.777635058464 & -1.45763505846435 \tabularnewline
33 & 427.14 & 427.712566071231 & -0.572566071230995 \tabularnewline
34 & 427.55 & 428.483438370688 & -0.933438370688123 \tabularnewline
35 & 428.29 & 428.813346861508 & -0.523346861507719 \tabularnewline
36 & 428.8 & 429.508442300822 & -0.708442300821957 \tabularnewline
37 & 428.8 & 429.957656056307 & -1.15765605630725 \tabularnewline
38 & 434.87 & 429.858326069912 & 5.01167393008825 \tabularnewline
39 & 435.66 & 436.35834109949 & -0.698341099489937 \tabularnewline
40 & 440.75 & 437.088421565071 & 3.66157843492942 \tabularnewline
41 & 440.99 & 442.492594789619 & -1.50259478961857 \tabularnewline
42 & 441.04 & 442.603668137184 & -1.56366813718358 \tabularnewline
43 & 441.04 & 442.519501228155 & -1.4795012281545 \tabularnewline
44 & 441.88 & 442.392556065069 & -0.512556065069134 \tabularnewline
45 & 441.92 & 443.188577383583 & -1.26857738358348 \tabularnewline
46 & 442.48 & 443.11973005059 & -0.639730050589833 \tabularnewline
47 & 442.81 & 443.624839500952 & -0.81483950095236 \tabularnewline
48 & 442.81 & 443.884924092051 & -1.07492409205076 \tabularnewline
49 & 442.81 & 443.792692729499 & -0.982692729498922 \tabularnewline
50 & 447.19 & 443.708375064576 & 3.48162493542435 \tabularnewline
51 & 446.52 & 448.387107797485 & -1.86710779748523 \tabularnewline
52 & 448.57 & 447.556904953892 & 1.01309504610788 \tabularnewline
53 & 448.71 & 449.693831218908 & -0.98383121890754 \tabularnewline
54 & 448.73 & 449.749415868548 & -1.01941586854753 \tabularnewline
55 & 449.07 & 449.681947260058 & -0.611947260058457 \tabularnewline
56 & 449.03 & 449.969440548168 & -0.939440548168363 \tabularnewline
57 & 448.68 & 449.848834036104 & -1.16883403610404 \tabularnewline
58 & 450.08 & 449.398544949141 & 0.68145505085937 \tabularnewline
59 & 449.96 & 450.857015615417 & -0.897015615416819 \tabularnewline
60 & 449.96 & 450.660049276071 & -0.700049276070672 \tabularnewline
61 & 449.96 & 450.599983175531 & -0.639983175531199 \tabularnewline
62 & 452.56 & 450.545070907097 & 2.0149290929034 \tabularnewline
63 & 455.31 & 453.317957213263 & 1.9920427867371 \tabularnewline
64 & 456.2 & 456.238879813139 & -0.0388798131385784 \tabularnewline
65 & 456.75 & 457.125543821167 & -0.375543821166616 \tabularnewline
66 & 457.63 & 457.64332115672 & -0.0133211567196554 \tabularnewline
67 & 457.63 & 458.522178165839 & -0.892178165838629 \tabularnewline
68 & 457.65 & 458.445626892607 & -0.795626892606606 \tabularnewline
69 & 458.32 & 458.397359976895 & -0.077359976895309 \tabularnewline
70 & 459.64 & 459.060722283937 & 0.579277716062506 \tabularnewline
71 & 460.16 & 460.430425861561 & -0.270425861560739 \tabularnewline
72 & 459.89 & 460.927222599242 & -1.03722259924166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261475&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]390.96[/C][C]394.43[/C][C]-3.47000000000003[/C][/ROW]
[ROW][C]4[/C][C]391.76[/C][C]393.332264717647[/C][C]-1.57226471764693[/C][/ROW]
[ROW][C]5[/C][C]392.8[/C][C]393.997360199018[/C][C]-1.19736019901796[/C][/ROW]
[ROW][C]6[/C][C]393.06[/C][C]394.934623490968[/C][C]-1.87462349096813[/C][/ROW]
[ROW][C]7[/C][C]393.06[/C][C]395.03377578077[/C][C]-1.97377578076953[/C][/ROW]
[ROW][C]8[/C][C]393.26[/C][C]394.864420538871[/C][C]-1.60442053887067[/C][/ROW]
[ROW][C]9[/C][C]393.87[/C][C]394.926756964763[/C][C]-1.05675696476294[/C][/ROW]
[ROW][C]10[/C][C]394.47[/C][C]395.44608439033[/C][C]-0.976084390330016[/C][/ROW]
[ROW][C]11[/C][C]394.57[/C][C]395.962333738585[/C][C]-1.39233373858502[/C][/ROW]
[ROW][C]12[/C][C]394.57[/C][C]395.94286777928[/C][C]-1.37286777928028[/C][/ROW]
[ROW][C]13[/C][C]394.57[/C][C]395.825072051356[/C][C]-1.25507205135591[/C][/ROW]
[ROW][C]14[/C][C]399.57[/C][C]395.717383511995[/C][C]3.85261648800542[/C][/ROW]
[ROW][C]15[/C][C]406.13[/C][C]401.047948312529[/C][C]5.08205168747099[/C][/ROW]
[ROW][C]16[/C][C]407.03[/C][C]408.044001941953[/C][C]-1.01400194195327[/C][/ROW]
[ROW][C]17[/C][C]409.46[/C][C]408.856997862848[/C][C]0.603002137151691[/C][/ROW]
[ROW][C]18[/C][C]409.9[/C][C]411.338737059265[/C][C]-1.43873705926455[/C][/ROW]
[ROW][C]19[/C][C]409.9[/C][C]411.655289570915[/C][C]-1.75528957091529[/C][/ROW]
[ROW][C]20[/C][C]410.14[/C][C]411.504681030279[/C][C]-1.36468103027903[/C][/ROW]
[ROW][C]21[/C][C]410.54[/C][C]411.627587747319[/C][C]-1.08758774731876[/C][/ROW]
[ROW][C]22[/C][C]410.69[/C][C]411.934269809269[/C][C]-1.24426980926933[/C][/ROW]
[ROW][C]23[/C][C]410.79[/C][C]411.977508131175[/C][C]-1.18750813117526[/C][/ROW]
[ROW][C]24[/C][C]410.97[/C][C]411.975616756901[/C][C]-1.00561675690091[/C][/ROW]
[ROW][C]25[/C][C]410.97[/C][C]412.069332149104[/C][C]-1.0993321491041[/C][/ROW]
[ROW][C]26[/C][C]413.8[/C][C]411.975006509965[/C][C]1.82499349003513[/C][/ROW]
[ROW][C]27[/C][C]423.31[/C][C]414.961595833322[/C][C]8.34840416667834[/C][/ROW]
[ROW][C]28[/C][C]423.85[/C][C]425.187911243052[/C][C]-1.33791124305179[/C][/ROW]
[ROW][C]29[/C][C]426.6[/C][C]425.613114879446[/C][C]0.986885120554348[/C][/ROW]
[ROW][C]30[/C][C]426.26[/C][C]428.447792262736[/C][C]-2.18779226273625[/C][/ROW]
[ROW][C]31[/C][C]426.26[/C][C]427.920073834184[/C][C]-1.66007383418417[/C][/ROW]
[ROW][C]32[/C][C]426.32[/C][C]427.777635058464[/C][C]-1.45763505846435[/C][/ROW]
[ROW][C]33[/C][C]427.14[/C][C]427.712566071231[/C][C]-0.572566071230995[/C][/ROW]
[ROW][C]34[/C][C]427.55[/C][C]428.483438370688[/C][C]-0.933438370688123[/C][/ROW]
[ROW][C]35[/C][C]428.29[/C][C]428.813346861508[/C][C]-0.523346861507719[/C][/ROW]
[ROW][C]36[/C][C]428.8[/C][C]429.508442300822[/C][C]-0.708442300821957[/C][/ROW]
[ROW][C]37[/C][C]428.8[/C][C]429.957656056307[/C][C]-1.15765605630725[/C][/ROW]
[ROW][C]38[/C][C]434.87[/C][C]429.858326069912[/C][C]5.01167393008825[/C][/ROW]
[ROW][C]39[/C][C]435.66[/C][C]436.35834109949[/C][C]-0.698341099489937[/C][/ROW]
[ROW][C]40[/C][C]440.75[/C][C]437.088421565071[/C][C]3.66157843492942[/C][/ROW]
[ROW][C]41[/C][C]440.99[/C][C]442.492594789619[/C][C]-1.50259478961857[/C][/ROW]
[ROW][C]42[/C][C]441.04[/C][C]442.603668137184[/C][C]-1.56366813718358[/C][/ROW]
[ROW][C]43[/C][C]441.04[/C][C]442.519501228155[/C][C]-1.4795012281545[/C][/ROW]
[ROW][C]44[/C][C]441.88[/C][C]442.392556065069[/C][C]-0.512556065069134[/C][/ROW]
[ROW][C]45[/C][C]441.92[/C][C]443.188577383583[/C][C]-1.26857738358348[/C][/ROW]
[ROW][C]46[/C][C]442.48[/C][C]443.11973005059[/C][C]-0.639730050589833[/C][/ROW]
[ROW][C]47[/C][C]442.81[/C][C]443.624839500952[/C][C]-0.81483950095236[/C][/ROW]
[ROW][C]48[/C][C]442.81[/C][C]443.884924092051[/C][C]-1.07492409205076[/C][/ROW]
[ROW][C]49[/C][C]442.81[/C][C]443.792692729499[/C][C]-0.982692729498922[/C][/ROW]
[ROW][C]50[/C][C]447.19[/C][C]443.708375064576[/C][C]3.48162493542435[/C][/ROW]
[ROW][C]51[/C][C]446.52[/C][C]448.387107797485[/C][C]-1.86710779748523[/C][/ROW]
[ROW][C]52[/C][C]448.57[/C][C]447.556904953892[/C][C]1.01309504610788[/C][/ROW]
[ROW][C]53[/C][C]448.71[/C][C]449.693831218908[/C][C]-0.98383121890754[/C][/ROW]
[ROW][C]54[/C][C]448.73[/C][C]449.749415868548[/C][C]-1.01941586854753[/C][/ROW]
[ROW][C]55[/C][C]449.07[/C][C]449.681947260058[/C][C]-0.611947260058457[/C][/ROW]
[ROW][C]56[/C][C]449.03[/C][C]449.969440548168[/C][C]-0.939440548168363[/C][/ROW]
[ROW][C]57[/C][C]448.68[/C][C]449.848834036104[/C][C]-1.16883403610404[/C][/ROW]
[ROW][C]58[/C][C]450.08[/C][C]449.398544949141[/C][C]0.68145505085937[/C][/ROW]
[ROW][C]59[/C][C]449.96[/C][C]450.857015615417[/C][C]-0.897015615416819[/C][/ROW]
[ROW][C]60[/C][C]449.96[/C][C]450.660049276071[/C][C]-0.700049276070672[/C][/ROW]
[ROW][C]61[/C][C]449.96[/C][C]450.599983175531[/C][C]-0.639983175531199[/C][/ROW]
[ROW][C]62[/C][C]452.56[/C][C]450.545070907097[/C][C]2.0149290929034[/C][/ROW]
[ROW][C]63[/C][C]455.31[/C][C]453.317957213263[/C][C]1.9920427867371[/C][/ROW]
[ROW][C]64[/C][C]456.2[/C][C]456.238879813139[/C][C]-0.0388798131385784[/C][/ROW]
[ROW][C]65[/C][C]456.75[/C][C]457.125543821167[/C][C]-0.375543821166616[/C][/ROW]
[ROW][C]66[/C][C]457.63[/C][C]457.64332115672[/C][C]-0.0133211567196554[/C][/ROW]
[ROW][C]67[/C][C]457.63[/C][C]458.522178165839[/C][C]-0.892178165838629[/C][/ROW]
[ROW][C]68[/C][C]457.65[/C][C]458.445626892607[/C][C]-0.795626892606606[/C][/ROW]
[ROW][C]69[/C][C]458.32[/C][C]458.397359976895[/C][C]-0.077359976895309[/C][/ROW]
[ROW][C]70[/C][C]459.64[/C][C]459.060722283937[/C][C]0.579277716062506[/C][/ROW]
[ROW][C]71[/C][C]460.16[/C][C]460.430425861561[/C][C]-0.270425861560739[/C][/ROW]
[ROW][C]72[/C][C]459.89[/C][C]460.927222599242[/C][C]-1.03722259924166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261475&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261475&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
3390.96394.43-3.47000000000003
4391.76393.332264717647-1.57226471764693
5392.8393.997360199018-1.19736019901796
6393.06394.934623490968-1.87462349096813
7393.06395.03377578077-1.97377578076953
8393.26394.864420538871-1.60442053887067
9393.87394.926756964763-1.05675696476294
10394.47395.44608439033-0.976084390330016
11394.57395.962333738585-1.39233373858502
12394.57395.94286777928-1.37286777928028
13394.57395.825072051356-1.25507205135591
14399.57395.7173835119953.85261648800542
15406.13401.0479483125295.08205168747099
16407.03408.044001941953-1.01400194195327
17409.46408.8569978628480.603002137151691
18409.9411.338737059265-1.43873705926455
19409.9411.655289570915-1.75528957091529
20410.14411.504681030279-1.36468103027903
21410.54411.627587747319-1.08758774731876
22410.69411.934269809269-1.24426980926933
23410.79411.977508131175-1.18750813117526
24410.97411.975616756901-1.00561675690091
25410.97412.069332149104-1.0993321491041
26413.8411.9750065099651.82499349003513
27423.31414.9615958333228.34840416667834
28423.85425.187911243052-1.33791124305179
29426.6425.6131148794460.986885120554348
30426.26428.447792262736-2.18779226273625
31426.26427.920073834184-1.66007383418417
32426.32427.777635058464-1.45763505846435
33427.14427.712566071231-0.572566071230995
34427.55428.483438370688-0.933438370688123
35428.29428.813346861508-0.523346861507719
36428.8429.508442300822-0.708442300821957
37428.8429.957656056307-1.15765605630725
38434.87429.8583260699125.01167393008825
39435.66436.35834109949-0.698341099489937
40440.75437.0884215650713.66157843492942
41440.99442.492594789619-1.50259478961857
42441.04442.603668137184-1.56366813718358
43441.04442.519501228155-1.4795012281545
44441.88442.392556065069-0.512556065069134
45441.92443.188577383583-1.26857738358348
46442.48443.11973005059-0.639730050589833
47442.81443.624839500952-0.81483950095236
48442.81443.884924092051-1.07492409205076
49442.81443.792692729499-0.982692729498922
50447.19443.7083750645763.48162493542435
51446.52448.387107797485-1.86710779748523
52448.57447.5569049538921.01309504610788
53448.71449.693831218908-0.98383121890754
54448.73449.749415868548-1.01941586854753
55449.07449.681947260058-0.611947260058457
56449.03449.969440548168-0.939440548168363
57448.68449.848834036104-1.16883403610404
58450.08449.3985449491410.68145505085937
59449.96450.857015615417-0.897015615416819
60449.96450.660049276071-0.700049276070672
61449.96450.599983175531-0.639983175531199
62452.56450.5450709070972.0149290929034
63455.31453.3179572132631.9920427867371
64456.2456.238879813139-0.0388798131385784
65456.75457.125543821167-0.375543821166616
66457.63457.64332115672-0.0133211567196554
67457.63458.522178165839-0.892178165838629
68457.65458.445626892607-0.795626892606606
69458.32458.397359976895-0.077359976895309
70459.64459.0607222839370.579277716062506
71460.16460.430425861561-0.270425861560739
72459.89460.927222599242-1.03722259924166







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73460.568226125625456.797401524148464.339050727103
74461.246452251251455.68021513283466.812689369671
75461.924678376876454.818272987178469.031083766575
76462.602904502502454.059925572383471.14588343262
77463.281130628127453.349522748019473.212738508236
78463.959356753753452.660091249894475.258622257611
79464.637582879378451.976557974561477.298607784195
80465.315809005003451.289738552523479.341879457484
81465.994035130629450.593708246697481.394362014561
82466.672261256254449.88449296696483.460029545549
83467.35048738188449.159354776686485.541619987074
84468.028713507505448.416374095321487.641052919689

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 460.568226125625 & 456.797401524148 & 464.339050727103 \tabularnewline
74 & 461.246452251251 & 455.68021513283 & 466.812689369671 \tabularnewline
75 & 461.924678376876 & 454.818272987178 & 469.031083766575 \tabularnewline
76 & 462.602904502502 & 454.059925572383 & 471.14588343262 \tabularnewline
77 & 463.281130628127 & 453.349522748019 & 473.212738508236 \tabularnewline
78 & 463.959356753753 & 452.660091249894 & 475.258622257611 \tabularnewline
79 & 464.637582879378 & 451.976557974561 & 477.298607784195 \tabularnewline
80 & 465.315809005003 & 451.289738552523 & 479.341879457484 \tabularnewline
81 & 465.994035130629 & 450.593708246697 & 481.394362014561 \tabularnewline
82 & 466.672261256254 & 449.88449296696 & 483.460029545549 \tabularnewline
83 & 467.35048738188 & 449.159354776686 & 485.541619987074 \tabularnewline
84 & 468.028713507505 & 448.416374095321 & 487.641052919689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261475&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]460.568226125625[/C][C]456.797401524148[/C][C]464.339050727103[/C][/ROW]
[ROW][C]74[/C][C]461.246452251251[/C][C]455.68021513283[/C][C]466.812689369671[/C][/ROW]
[ROW][C]75[/C][C]461.924678376876[/C][C]454.818272987178[/C][C]469.031083766575[/C][/ROW]
[ROW][C]76[/C][C]462.602904502502[/C][C]454.059925572383[/C][C]471.14588343262[/C][/ROW]
[ROW][C]77[/C][C]463.281130628127[/C][C]453.349522748019[/C][C]473.212738508236[/C][/ROW]
[ROW][C]78[/C][C]463.959356753753[/C][C]452.660091249894[/C][C]475.258622257611[/C][/ROW]
[ROW][C]79[/C][C]464.637582879378[/C][C]451.976557974561[/C][C]477.298607784195[/C][/ROW]
[ROW][C]80[/C][C]465.315809005003[/C][C]451.289738552523[/C][C]479.341879457484[/C][/ROW]
[ROW][C]81[/C][C]465.994035130629[/C][C]450.593708246697[/C][C]481.394362014561[/C][/ROW]
[ROW][C]82[/C][C]466.672261256254[/C][C]449.88449296696[/C][C]483.460029545549[/C][/ROW]
[ROW][C]83[/C][C]467.35048738188[/C][C]449.159354776686[/C][C]485.541619987074[/C][/ROW]
[ROW][C]84[/C][C]468.028713507505[/C][C]448.416374095321[/C][C]487.641052919689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261475&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261475&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
73460.568226125625456.797401524148464.339050727103
74461.246452251251455.68021513283466.812689369671
75461.924678376876454.818272987178469.031083766575
76462.602904502502454.059925572383471.14588343262
77463.281130628127453.349522748019473.212738508236
78463.959356753753452.660091249894475.258622257611
79464.637582879378451.976557974561477.298607784195
80465.315809005003451.289738552523479.341879457484
81465.994035130629450.593708246697481.394362014561
82466.672261256254449.88449296696483.460029545549
83467.35048738188449.159354776686485.541619987074
84468.028713507505448.416374095321487.641052919689



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')