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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Dec 2013 11:49:32 -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/2013/Dec/19/t1387471789e4z5uek7mon1xyx.htm/, Retrieved Thu, 25 Apr 2024 18:07:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232448, Retrieved Thu, 25 Apr 2024 18:07:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-19 16:49:32] [4b42de28d069c82084b3ad7a06d83fce] [Current]
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Dataseries X:
9,27
9,30
9,35
9,33
9,37
9,42
9,45
9,38
9,40
9,43
9,45
9,49
9,47
9,48
9,52
9,53
9,53
9,54
9,57
9,61
9,61
9,63
9,64
9,60
9,64
9,66
9,67
9,70
9,72
9,73
9,77
9,72
9,68
9,62
9,79
9,77
9,79
9,77
9,78
9,81
9,74
9,70
9,78
9,85
9,83
9,90
9,93
9,85
9,95
9,97
10,02
9,97
9,95
9,95
9,98
10,00
10,04
10,05
10,06
10,09
10,14
10,13
10,12
10,10
10,12
10,06
10,21
10,18
10,26
10,39
10,41
10,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232448&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232448&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.761122450067448
beta0.0552770057358704
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.761122450067448 \tabularnewline
beta & 0.0552770057358704 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232448&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]0.761122450067448[/C][/ROW]
[ROW][C]beta[/C][C]0.0552770057358704[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232448&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
alpha0.761122450067448
beta0.0552770057358704
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39.359.330.0199999999999978
49.339.37606390040211-0.0460639004021122
59.379.369907056393269.29436067380607e-05
69.429.398885132960210.0211148670397883
79.459.444751824118030.00524817588196846
89.389.47876282467471-0.0987628246747132
99.49.42945351179544-0.0294535117954435
109.439.43165788800945-0.00165788800945244
119.459.45494838589121-0.00494838589121471
129.499.475526220651280.014473779348716
139.479.51149565049975-0.0414956504997495
149.489.50311966211115-0.0231196621111476
159.529.507757347423860.0122426525761394
169.539.53982516418938-0.00982516418937962
179.539.55468330028219-0.0246833002821933
189.549.55719408554871-0.0171940855487147
199.579.564681680913770.00531831908622671
209.619.589527728203730.0204722717962689
219.619.62676911019755-0.0167691101975489
229.639.63495972072107-0.00495972072106987
239.649.65193005449933-0.0119300544993255
249.69.66309318270101-0.0630931827010066
259.649.632660413064590.00733958693540693
269.669.656144400904280.00385559909572386
279.679.67713886234641-0.00713886234640526
289.79.689464842072470.0105351579275297
299.729.715686156581740.00431384341826124
309.739.73735378342842-0.00735378342842274
319.779.749831524974750.0201684750252511
329.729.78410561488479-0.0641056148847863
339.689.75153971503322-0.071539715033218
349.629.71030569499139-0.0903056949913896
359.799.650989073628520.139010926371483
369.779.77205902789437-0.00205902789436685
379.799.785670844343190.0043291556568068
389.779.80432698941254-0.0343269894125449
399.789.7921168499703-0.0121168499702957
409.819.796301559257650.0136984407423473
419.749.82071119446897-0.0807111944689662
429.79.76986780943612-0.0698678094361185
439.789.724338049880590.0556619501194131
449.859.776693649769190.0733063502308049
459.839.84556298525488-0.0155629852548778
469.99.846137099592690.0538629004073066
479.939.901818964773660.0281810352263445
489.859.93913943438409-0.0891394343840854
499.959.883414335625280.0665856643747169
509.979.949016535598710.0209834644012883
5110.029.980792705675570.0392072943244344
529.9710.0280889934696-0.0580889934696032
539.959.99888693906918-0.0488869390691846
549.959.97463197569173-0.0246319756917313
559.989.967801678943950.0121983210560472
56109.989516962610540.0104830373894647
5710.0410.0103677536950.0296322463049705
5810.0510.04704014234420.00295985765580475
5910.0610.0635361060141-0.00353610601408505
6010.0910.07493907283210.0150609271679407
6110.1410.10113031102260.0388696889773676
6210.1310.1470782800465-0.0170782800465279
6310.1210.1497244666773-0.0297244666772727
6410.110.1414947720495-0.0414947720494894
6510.1210.1225606420555-0.00256064205549578
6610.0610.1331524196816-0.0731524196815521
6710.2110.08693750026570.123062499734258
6810.1810.1952437166946-0.0152437166946111
6910.2610.19764062447730.0623593755226945
7010.3910.26172660713550.128273392864545
7110.4110.38137801947190.0286219805280616
7210.4610.42638670497860.0336132950214107

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9.35 & 9.33 & 0.0199999999999978 \tabularnewline
4 & 9.33 & 9.37606390040211 & -0.0460639004021122 \tabularnewline
5 & 9.37 & 9.36990705639326 & 9.29436067380607e-05 \tabularnewline
6 & 9.42 & 9.39888513296021 & 0.0211148670397883 \tabularnewline
7 & 9.45 & 9.44475182411803 & 0.00524817588196846 \tabularnewline
8 & 9.38 & 9.47876282467471 & -0.0987628246747132 \tabularnewline
9 & 9.4 & 9.42945351179544 & -0.0294535117954435 \tabularnewline
10 & 9.43 & 9.43165788800945 & -0.00165788800945244 \tabularnewline
11 & 9.45 & 9.45494838589121 & -0.00494838589121471 \tabularnewline
12 & 9.49 & 9.47552622065128 & 0.014473779348716 \tabularnewline
13 & 9.47 & 9.51149565049975 & -0.0414956504997495 \tabularnewline
14 & 9.48 & 9.50311966211115 & -0.0231196621111476 \tabularnewline
15 & 9.52 & 9.50775734742386 & 0.0122426525761394 \tabularnewline
16 & 9.53 & 9.53982516418938 & -0.00982516418937962 \tabularnewline
17 & 9.53 & 9.55468330028219 & -0.0246833002821933 \tabularnewline
18 & 9.54 & 9.55719408554871 & -0.0171940855487147 \tabularnewline
19 & 9.57 & 9.56468168091377 & 0.00531831908622671 \tabularnewline
20 & 9.61 & 9.58952772820373 & 0.0204722717962689 \tabularnewline
21 & 9.61 & 9.62676911019755 & -0.0167691101975489 \tabularnewline
22 & 9.63 & 9.63495972072107 & -0.00495972072106987 \tabularnewline
23 & 9.64 & 9.65193005449933 & -0.0119300544993255 \tabularnewline
24 & 9.6 & 9.66309318270101 & -0.0630931827010066 \tabularnewline
25 & 9.64 & 9.63266041306459 & 0.00733958693540693 \tabularnewline
26 & 9.66 & 9.65614440090428 & 0.00385559909572386 \tabularnewline
27 & 9.67 & 9.67713886234641 & -0.00713886234640526 \tabularnewline
28 & 9.7 & 9.68946484207247 & 0.0105351579275297 \tabularnewline
29 & 9.72 & 9.71568615658174 & 0.00431384341826124 \tabularnewline
30 & 9.73 & 9.73735378342842 & -0.00735378342842274 \tabularnewline
31 & 9.77 & 9.74983152497475 & 0.0201684750252511 \tabularnewline
32 & 9.72 & 9.78410561488479 & -0.0641056148847863 \tabularnewline
33 & 9.68 & 9.75153971503322 & -0.071539715033218 \tabularnewline
34 & 9.62 & 9.71030569499139 & -0.0903056949913896 \tabularnewline
35 & 9.79 & 9.65098907362852 & 0.139010926371483 \tabularnewline
36 & 9.77 & 9.77205902789437 & -0.00205902789436685 \tabularnewline
37 & 9.79 & 9.78567084434319 & 0.0043291556568068 \tabularnewline
38 & 9.77 & 9.80432698941254 & -0.0343269894125449 \tabularnewline
39 & 9.78 & 9.7921168499703 & -0.0121168499702957 \tabularnewline
40 & 9.81 & 9.79630155925765 & 0.0136984407423473 \tabularnewline
41 & 9.74 & 9.82071119446897 & -0.0807111944689662 \tabularnewline
42 & 9.7 & 9.76986780943612 & -0.0698678094361185 \tabularnewline
43 & 9.78 & 9.72433804988059 & 0.0556619501194131 \tabularnewline
44 & 9.85 & 9.77669364976919 & 0.0733063502308049 \tabularnewline
45 & 9.83 & 9.84556298525488 & -0.0155629852548778 \tabularnewline
46 & 9.9 & 9.84613709959269 & 0.0538629004073066 \tabularnewline
47 & 9.93 & 9.90181896477366 & 0.0281810352263445 \tabularnewline
48 & 9.85 & 9.93913943438409 & -0.0891394343840854 \tabularnewline
49 & 9.95 & 9.88341433562528 & 0.0665856643747169 \tabularnewline
50 & 9.97 & 9.94901653559871 & 0.0209834644012883 \tabularnewline
51 & 10.02 & 9.98079270567557 & 0.0392072943244344 \tabularnewline
52 & 9.97 & 10.0280889934696 & -0.0580889934696032 \tabularnewline
53 & 9.95 & 9.99888693906918 & -0.0488869390691846 \tabularnewline
54 & 9.95 & 9.97463197569173 & -0.0246319756917313 \tabularnewline
55 & 9.98 & 9.96780167894395 & 0.0121983210560472 \tabularnewline
56 & 10 & 9.98951696261054 & 0.0104830373894647 \tabularnewline
57 & 10.04 & 10.010367753695 & 0.0296322463049705 \tabularnewline
58 & 10.05 & 10.0470401423442 & 0.00295985765580475 \tabularnewline
59 & 10.06 & 10.0635361060141 & -0.00353610601408505 \tabularnewline
60 & 10.09 & 10.0749390728321 & 0.0150609271679407 \tabularnewline
61 & 10.14 & 10.1011303110226 & 0.0388696889773676 \tabularnewline
62 & 10.13 & 10.1470782800465 & -0.0170782800465279 \tabularnewline
63 & 10.12 & 10.1497244666773 & -0.0297244666772727 \tabularnewline
64 & 10.1 & 10.1414947720495 & -0.0414947720494894 \tabularnewline
65 & 10.12 & 10.1225606420555 & -0.00256064205549578 \tabularnewline
66 & 10.06 & 10.1331524196816 & -0.0731524196815521 \tabularnewline
67 & 10.21 & 10.0869375002657 & 0.123062499734258 \tabularnewline
68 & 10.18 & 10.1952437166946 & -0.0152437166946111 \tabularnewline
69 & 10.26 & 10.1976406244773 & 0.0623593755226945 \tabularnewline
70 & 10.39 & 10.2617266071355 & 0.128273392864545 \tabularnewline
71 & 10.41 & 10.3813780194719 & 0.0286219805280616 \tabularnewline
72 & 10.46 & 10.4263867049786 & 0.0336132950214107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232448&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]9.35[/C][C]9.33[/C][C]0.0199999999999978[/C][/ROW]
[ROW][C]4[/C][C]9.33[/C][C]9.37606390040211[/C][C]-0.0460639004021122[/C][/ROW]
[ROW][C]5[/C][C]9.37[/C][C]9.36990705639326[/C][C]9.29436067380607e-05[/C][/ROW]
[ROW][C]6[/C][C]9.42[/C][C]9.39888513296021[/C][C]0.0211148670397883[/C][/ROW]
[ROW][C]7[/C][C]9.45[/C][C]9.44475182411803[/C][C]0.00524817588196846[/C][/ROW]
[ROW][C]8[/C][C]9.38[/C][C]9.47876282467471[/C][C]-0.0987628246747132[/C][/ROW]
[ROW][C]9[/C][C]9.4[/C][C]9.42945351179544[/C][C]-0.0294535117954435[/C][/ROW]
[ROW][C]10[/C][C]9.43[/C][C]9.43165788800945[/C][C]-0.00165788800945244[/C][/ROW]
[ROW][C]11[/C][C]9.45[/C][C]9.45494838589121[/C][C]-0.00494838589121471[/C][/ROW]
[ROW][C]12[/C][C]9.49[/C][C]9.47552622065128[/C][C]0.014473779348716[/C][/ROW]
[ROW][C]13[/C][C]9.47[/C][C]9.51149565049975[/C][C]-0.0414956504997495[/C][/ROW]
[ROW][C]14[/C][C]9.48[/C][C]9.50311966211115[/C][C]-0.0231196621111476[/C][/ROW]
[ROW][C]15[/C][C]9.52[/C][C]9.50775734742386[/C][C]0.0122426525761394[/C][/ROW]
[ROW][C]16[/C][C]9.53[/C][C]9.53982516418938[/C][C]-0.00982516418937962[/C][/ROW]
[ROW][C]17[/C][C]9.53[/C][C]9.55468330028219[/C][C]-0.0246833002821933[/C][/ROW]
[ROW][C]18[/C][C]9.54[/C][C]9.55719408554871[/C][C]-0.0171940855487147[/C][/ROW]
[ROW][C]19[/C][C]9.57[/C][C]9.56468168091377[/C][C]0.00531831908622671[/C][/ROW]
[ROW][C]20[/C][C]9.61[/C][C]9.58952772820373[/C][C]0.0204722717962689[/C][/ROW]
[ROW][C]21[/C][C]9.61[/C][C]9.62676911019755[/C][C]-0.0167691101975489[/C][/ROW]
[ROW][C]22[/C][C]9.63[/C][C]9.63495972072107[/C][C]-0.00495972072106987[/C][/ROW]
[ROW][C]23[/C][C]9.64[/C][C]9.65193005449933[/C][C]-0.0119300544993255[/C][/ROW]
[ROW][C]24[/C][C]9.6[/C][C]9.66309318270101[/C][C]-0.0630931827010066[/C][/ROW]
[ROW][C]25[/C][C]9.64[/C][C]9.63266041306459[/C][C]0.00733958693540693[/C][/ROW]
[ROW][C]26[/C][C]9.66[/C][C]9.65614440090428[/C][C]0.00385559909572386[/C][/ROW]
[ROW][C]27[/C][C]9.67[/C][C]9.67713886234641[/C][C]-0.00713886234640526[/C][/ROW]
[ROW][C]28[/C][C]9.7[/C][C]9.68946484207247[/C][C]0.0105351579275297[/C][/ROW]
[ROW][C]29[/C][C]9.72[/C][C]9.71568615658174[/C][C]0.00431384341826124[/C][/ROW]
[ROW][C]30[/C][C]9.73[/C][C]9.73735378342842[/C][C]-0.00735378342842274[/C][/ROW]
[ROW][C]31[/C][C]9.77[/C][C]9.74983152497475[/C][C]0.0201684750252511[/C][/ROW]
[ROW][C]32[/C][C]9.72[/C][C]9.78410561488479[/C][C]-0.0641056148847863[/C][/ROW]
[ROW][C]33[/C][C]9.68[/C][C]9.75153971503322[/C][C]-0.071539715033218[/C][/ROW]
[ROW][C]34[/C][C]9.62[/C][C]9.71030569499139[/C][C]-0.0903056949913896[/C][/ROW]
[ROW][C]35[/C][C]9.79[/C][C]9.65098907362852[/C][C]0.139010926371483[/C][/ROW]
[ROW][C]36[/C][C]9.77[/C][C]9.77205902789437[/C][C]-0.00205902789436685[/C][/ROW]
[ROW][C]37[/C][C]9.79[/C][C]9.78567084434319[/C][C]0.0043291556568068[/C][/ROW]
[ROW][C]38[/C][C]9.77[/C][C]9.80432698941254[/C][C]-0.0343269894125449[/C][/ROW]
[ROW][C]39[/C][C]9.78[/C][C]9.7921168499703[/C][C]-0.0121168499702957[/C][/ROW]
[ROW][C]40[/C][C]9.81[/C][C]9.79630155925765[/C][C]0.0136984407423473[/C][/ROW]
[ROW][C]41[/C][C]9.74[/C][C]9.82071119446897[/C][C]-0.0807111944689662[/C][/ROW]
[ROW][C]42[/C][C]9.7[/C][C]9.76986780943612[/C][C]-0.0698678094361185[/C][/ROW]
[ROW][C]43[/C][C]9.78[/C][C]9.72433804988059[/C][C]0.0556619501194131[/C][/ROW]
[ROW][C]44[/C][C]9.85[/C][C]9.77669364976919[/C][C]0.0733063502308049[/C][/ROW]
[ROW][C]45[/C][C]9.83[/C][C]9.84556298525488[/C][C]-0.0155629852548778[/C][/ROW]
[ROW][C]46[/C][C]9.9[/C][C]9.84613709959269[/C][C]0.0538629004073066[/C][/ROW]
[ROW][C]47[/C][C]9.93[/C][C]9.90181896477366[/C][C]0.0281810352263445[/C][/ROW]
[ROW][C]48[/C][C]9.85[/C][C]9.93913943438409[/C][C]-0.0891394343840854[/C][/ROW]
[ROW][C]49[/C][C]9.95[/C][C]9.88341433562528[/C][C]0.0665856643747169[/C][/ROW]
[ROW][C]50[/C][C]9.97[/C][C]9.94901653559871[/C][C]0.0209834644012883[/C][/ROW]
[ROW][C]51[/C][C]10.02[/C][C]9.98079270567557[/C][C]0.0392072943244344[/C][/ROW]
[ROW][C]52[/C][C]9.97[/C][C]10.0280889934696[/C][C]-0.0580889934696032[/C][/ROW]
[ROW][C]53[/C][C]9.95[/C][C]9.99888693906918[/C][C]-0.0488869390691846[/C][/ROW]
[ROW][C]54[/C][C]9.95[/C][C]9.97463197569173[/C][C]-0.0246319756917313[/C][/ROW]
[ROW][C]55[/C][C]9.98[/C][C]9.96780167894395[/C][C]0.0121983210560472[/C][/ROW]
[ROW][C]56[/C][C]10[/C][C]9.98951696261054[/C][C]0.0104830373894647[/C][/ROW]
[ROW][C]57[/C][C]10.04[/C][C]10.010367753695[/C][C]0.0296322463049705[/C][/ROW]
[ROW][C]58[/C][C]10.05[/C][C]10.0470401423442[/C][C]0.00295985765580475[/C][/ROW]
[ROW][C]59[/C][C]10.06[/C][C]10.0635361060141[/C][C]-0.00353610601408505[/C][/ROW]
[ROW][C]60[/C][C]10.09[/C][C]10.0749390728321[/C][C]0.0150609271679407[/C][/ROW]
[ROW][C]61[/C][C]10.14[/C][C]10.1011303110226[/C][C]0.0388696889773676[/C][/ROW]
[ROW][C]62[/C][C]10.13[/C][C]10.1470782800465[/C][C]-0.0170782800465279[/C][/ROW]
[ROW][C]63[/C][C]10.12[/C][C]10.1497244666773[/C][C]-0.0297244666772727[/C][/ROW]
[ROW][C]64[/C][C]10.1[/C][C]10.1414947720495[/C][C]-0.0414947720494894[/C][/ROW]
[ROW][C]65[/C][C]10.12[/C][C]10.1225606420555[/C][C]-0.00256064205549578[/C][/ROW]
[ROW][C]66[/C][C]10.06[/C][C]10.1331524196816[/C][C]-0.0731524196815521[/C][/ROW]
[ROW][C]67[/C][C]10.21[/C][C]10.0869375002657[/C][C]0.123062499734258[/C][/ROW]
[ROW][C]68[/C][C]10.18[/C][C]10.1952437166946[/C][C]-0.0152437166946111[/C][/ROW]
[ROW][C]69[/C][C]10.26[/C][C]10.1976406244773[/C][C]0.0623593755226945[/C][/ROW]
[ROW][C]70[/C][C]10.39[/C][C]10.2617266071355[/C][C]0.128273392864545[/C][/ROW]
[ROW][C]71[/C][C]10.41[/C][C]10.3813780194719[/C][C]0.0286219805280616[/C][/ROW]
[ROW][C]72[/C][C]10.46[/C][C]10.4263867049786[/C][C]0.0336132950214107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232448&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232448&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
39.359.330.0199999999999978
49.339.37606390040211-0.0460639004021122
59.379.369907056393269.29436067380607e-05
69.429.398885132960210.0211148670397883
79.459.444751824118030.00524817588196846
89.389.47876282467471-0.0987628246747132
99.49.42945351179544-0.0294535117954435
109.439.43165788800945-0.00165788800945244
119.459.45494838589121-0.00494838589121471
129.499.475526220651280.014473779348716
139.479.51149565049975-0.0414956504997495
149.489.50311966211115-0.0231196621111476
159.529.507757347423860.0122426525761394
169.539.53982516418938-0.00982516418937962
179.539.55468330028219-0.0246833002821933
189.549.55719408554871-0.0171940855487147
199.579.564681680913770.00531831908622671
209.619.589527728203730.0204722717962689
219.619.62676911019755-0.0167691101975489
229.639.63495972072107-0.00495972072106987
239.649.65193005449933-0.0119300544993255
249.69.66309318270101-0.0630931827010066
259.649.632660413064590.00733958693540693
269.669.656144400904280.00385559909572386
279.679.67713886234641-0.00713886234640526
289.79.689464842072470.0105351579275297
299.729.715686156581740.00431384341826124
309.739.73735378342842-0.00735378342842274
319.779.749831524974750.0201684750252511
329.729.78410561488479-0.0641056148847863
339.689.75153971503322-0.071539715033218
349.629.71030569499139-0.0903056949913896
359.799.650989073628520.139010926371483
369.779.77205902789437-0.00205902789436685
379.799.785670844343190.0043291556568068
389.779.80432698941254-0.0343269894125449
399.789.7921168499703-0.0121168499702957
409.819.796301559257650.0136984407423473
419.749.82071119446897-0.0807111944689662
429.79.76986780943612-0.0698678094361185
439.789.724338049880590.0556619501194131
449.859.776693649769190.0733063502308049
459.839.84556298525488-0.0155629852548778
469.99.846137099592690.0538629004073066
479.939.901818964773660.0281810352263445
489.859.93913943438409-0.0891394343840854
499.959.883414335625280.0665856643747169
509.979.949016535598710.0209834644012883
5110.029.980792705675570.0392072943244344
529.9710.0280889934696-0.0580889934696032
539.959.99888693906918-0.0488869390691846
549.959.97463197569173-0.0246319756917313
559.989.967801678943950.0121983210560472
56109.989516962610540.0104830373894647
5710.0410.0103677536950.0296322463049705
5810.0510.04704014234420.00295985765580475
5910.0610.0635361060141-0.00353610601408505
6010.0910.07493907283210.0150609271679407
6110.1410.10113031102260.0388696889773676
6210.1310.1470782800465-0.0170782800465279
6310.1210.1497244666773-0.0297244666772727
6410.110.1414947720495-0.0414947720494894
6510.1210.1225606420555-0.00256064205549578
6610.0610.1331524196816-0.0731524196815521
6710.2110.08693750026570.123062499734258
6810.1810.1952437166946-0.0152437166946111
6910.2610.19764062447730.0623593755226945
7010.3910.26172660713550.128273392864545
7110.4110.38137801947190.0286219805280616
7210.4610.42638670497860.0336132950214107







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7310.476608589710510.383951028512510.5692661509085
7410.501246640980810.382401904519610.620091377442
7510.525884692251210.383553523204210.6682158612981
7610.550522743521510.386150943394810.7148945436483
7710.575160794791910.38959612545810.7607254641258
7810.599798846062210.393553775083410.806043917041
7910.624436897332610.397816441045810.8510573536193
8010.649074948602910.402246979451910.895902917754
8110.673712999873310.406750326672710.9406756730739
8210.698351051143610.411258221338110.9854438809491
8310.72298910241410.415720307021911.030257897806
8410.747627153684310.420098647891611.0751556594771

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 10.4766085897105 & 10.3839510285125 & 10.5692661509085 \tabularnewline
74 & 10.5012466409808 & 10.3824019045196 & 10.620091377442 \tabularnewline
75 & 10.5258846922512 & 10.3835535232042 & 10.6682158612981 \tabularnewline
76 & 10.5505227435215 & 10.3861509433948 & 10.7148945436483 \tabularnewline
77 & 10.5751607947919 & 10.389596125458 & 10.7607254641258 \tabularnewline
78 & 10.5997988460622 & 10.3935537750834 & 10.806043917041 \tabularnewline
79 & 10.6244368973326 & 10.3978164410458 & 10.8510573536193 \tabularnewline
80 & 10.6490749486029 & 10.4022469794519 & 10.895902917754 \tabularnewline
81 & 10.6737129998733 & 10.4067503266727 & 10.9406756730739 \tabularnewline
82 & 10.6983510511436 & 10.4112582213381 & 10.9854438809491 \tabularnewline
83 & 10.722989102414 & 10.4157203070219 & 11.030257897806 \tabularnewline
84 & 10.7476271536843 & 10.4200986478916 & 11.0751556594771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232448&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]10.4766085897105[/C][C]10.3839510285125[/C][C]10.5692661509085[/C][/ROW]
[ROW][C]74[/C][C]10.5012466409808[/C][C]10.3824019045196[/C][C]10.620091377442[/C][/ROW]
[ROW][C]75[/C][C]10.5258846922512[/C][C]10.3835535232042[/C][C]10.6682158612981[/C][/ROW]
[ROW][C]76[/C][C]10.5505227435215[/C][C]10.3861509433948[/C][C]10.7148945436483[/C][/ROW]
[ROW][C]77[/C][C]10.5751607947919[/C][C]10.389596125458[/C][C]10.7607254641258[/C][/ROW]
[ROW][C]78[/C][C]10.5997988460622[/C][C]10.3935537750834[/C][C]10.806043917041[/C][/ROW]
[ROW][C]79[/C][C]10.6244368973326[/C][C]10.3978164410458[/C][C]10.8510573536193[/C][/ROW]
[ROW][C]80[/C][C]10.6490749486029[/C][C]10.4022469794519[/C][C]10.895902917754[/C][/ROW]
[ROW][C]81[/C][C]10.6737129998733[/C][C]10.4067503266727[/C][C]10.9406756730739[/C][/ROW]
[ROW][C]82[/C][C]10.6983510511436[/C][C]10.4112582213381[/C][C]10.9854438809491[/C][/ROW]
[ROW][C]83[/C][C]10.722989102414[/C][C]10.4157203070219[/C][C]11.030257897806[/C][/ROW]
[ROW][C]84[/C][C]10.7476271536843[/C][C]10.4200986478916[/C][C]11.0751556594771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232448&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232448&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
7310.476608589710510.383951028512510.5692661509085
7410.501246640980810.382401904519610.620091377442
7510.525884692251210.383553523204210.6682158612981
7610.550522743521510.386150943394810.7148945436483
7710.575160794791910.38959612545810.7607254641258
7810.599798846062210.393553775083410.806043917041
7910.624436897332610.397816441045810.8510573536193
8010.649074948602910.402246979451910.895902917754
8110.673712999873310.406750326672710.9406756730739
8210.698351051143610.411258221338110.9854438809491
8310.72298910241410.415720307021911.030257897806
8410.747627153684310.420098647891611.0751556594771



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')