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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 May 2008 08:38:30 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/21/t1211380795agtqcd3z19265r4.htm/, Retrieved Thu, 16 May 2024 00:33:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12984, Retrieved Thu, 16 May 2024 00:33:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact240
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde prijs ...] [2008-05-21 14:38:30] [10bf337d6aaebcf0c700ebf73b3b2ad5] [Current]
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Dataseries X:
58,1
57,9
57,3
55,9
55
55,9
56,6
57,3
56,2
57,7
56,8
57,9
58,3
58,2
56,9
57,1
56,7
54,2
54,2
52,1
51,5
51,8
53
52,4
52,41
52,36
52,94
52,34
51,84
51,42
50,85
50,66
51,53
51,59
52,32
51,98
51,17
50,57
49,84
50,12
49,08
48,57
47,22
46,78
46,04
45,05
44,42
44,09
44,46
44,34
43,04
42,87
42,32
42,49
41,94
41,6
41,42
41,12
41,28
40,21
39,69
39,16
38,8
38,44
37,02
36,75
35,95
36,29
36,35
36,07
36,6
36,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12984&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12984&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00765387410320782
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00765387410320782 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12984&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]0.00765387410320782[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12984&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
beta0.00765387410320782
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
357.357.7-0.399999999999999
455.957.0969384503587-1.19693845035872
55555.6877772341504-0.687777234150381
655.954.78251307378911.11748692621086
756.655.69106617803430.908933821965661
857.356.39802304307580.901976956924187
956.257.1049266611481-0.904926661148096
1057.755.9980004664111.70199953358896
1156.857.5110273565649-0.711027356564855
1257.956.60558524269381.29441475730624
1358.357.71549253028350.584507469716478
1458.258.11996627686910.0800337231308887
1556.958.02057884491-1.12057884490997
1657.156.71200207550830.387997924491692
1756.756.9149717627747-0.214971762774674
1854.256.5133263959667-2.31332639596666
1954.253.99562048697230.204379513027703
2052.153.9971847820343-1.89718478203429
2151.551.8826639685621-0.382663968562078
2251.851.27973510672290.52026489327713
235351.58371714871631.41628285128368
2452.452.7945571993546-0.394557199354587
2552.4152.19153730822420.218462691775784
2652.3652.20320939416330.15679060583669
2752.9452.1544094497210.785590550279046
2852.3452.7404222608895-0.400422260889449
2951.8452.1373574793165-0.297357479316489
3051.4251.6350815426062-0.21508154260615
3150.8551.2134353355571-0.363435335557121
3250.6650.64065364725410.0193463527458846
3351.5350.45080172180241.07919827819762
3451.5951.32906176955610.260938230443898
3552.3251.39105895792060.928941042079359
3651.9852.128168955706-0.148168955706019
3751.1751.787034889173-0.617034889173034
3850.5750.972312181814-0.402312181814018
3949.8450.3692329350242-0.529232935024226
4050.1249.63518225276830.484817747231709
4149.0849.9188929867686-0.838892986768592
4248.5748.8724722054618-0.302472205461804
4347.2248.3601571212815-1.14015712128148
4446.7847.0014305022173-0.221430502217316
4546.0446.5597357010307-0.519735701030733
4645.0545.8157577094081-0.765757709408106
4744.4244.8198966963067-0.399896696306726
4844.0944.1868359373389-0.0968359373389092
4944.4643.85609476726590.603905232734142
5044.3444.23071698188750.109283018112535
5143.0444.1115534203497-1.07155342034972
5242.8742.80335188537550.066648114624499
5342.3242.6338620016541-0.313862001654051
5442.4942.08145974140760.408540258592389
5541.9442.254586657113-0.314586657112976
5641.641.7021788504449-0.102178850444879
5741.4241.36139678638760.0586032136124359
5841.1241.1818453280066-0.0618453280066049
5941.2840.88137197165220.398628028347844
6040.2141.0444230203952-0.83442302039515
6139.6939.9680364516482-0.278036451648227
6239.1639.4459083956512-0.285908395651205
6338.838.9137200887858-0.113720088785840
6438.4438.5528496895433-0.112849689543268
6537.0238.1919859522269-1.17198595222691
6636.7536.7630157192978-0.0130157192978473
6735.9536.492916098621-0.542916098620978
6836.2935.68876068715350.601239312846467
6936.3536.03336249716000.316637502840045
7036.0736.0957860007430-0.0257860007430466
7136.635.81558863793970.784411362060268
7236.536.35159242375010.148407576249930

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 57.3 & 57.7 & -0.399999999999999 \tabularnewline
4 & 55.9 & 57.0969384503587 & -1.19693845035872 \tabularnewline
5 & 55 & 55.6877772341504 & -0.687777234150381 \tabularnewline
6 & 55.9 & 54.7825130737891 & 1.11748692621086 \tabularnewline
7 & 56.6 & 55.6910661780343 & 0.908933821965661 \tabularnewline
8 & 57.3 & 56.3980230430758 & 0.901976956924187 \tabularnewline
9 & 56.2 & 57.1049266611481 & -0.904926661148096 \tabularnewline
10 & 57.7 & 55.998000466411 & 1.70199953358896 \tabularnewline
11 & 56.8 & 57.5110273565649 & -0.711027356564855 \tabularnewline
12 & 57.9 & 56.6055852426938 & 1.29441475730624 \tabularnewline
13 & 58.3 & 57.7154925302835 & 0.584507469716478 \tabularnewline
14 & 58.2 & 58.1199662768691 & 0.0800337231308887 \tabularnewline
15 & 56.9 & 58.02057884491 & -1.12057884490997 \tabularnewline
16 & 57.1 & 56.7120020755083 & 0.387997924491692 \tabularnewline
17 & 56.7 & 56.9149717627747 & -0.214971762774674 \tabularnewline
18 & 54.2 & 56.5133263959667 & -2.31332639596666 \tabularnewline
19 & 54.2 & 53.9956204869723 & 0.204379513027703 \tabularnewline
20 & 52.1 & 53.9971847820343 & -1.89718478203429 \tabularnewline
21 & 51.5 & 51.8826639685621 & -0.382663968562078 \tabularnewline
22 & 51.8 & 51.2797351067229 & 0.52026489327713 \tabularnewline
23 & 53 & 51.5837171487163 & 1.41628285128368 \tabularnewline
24 & 52.4 & 52.7945571993546 & -0.394557199354587 \tabularnewline
25 & 52.41 & 52.1915373082242 & 0.218462691775784 \tabularnewline
26 & 52.36 & 52.2032093941633 & 0.15679060583669 \tabularnewline
27 & 52.94 & 52.154409449721 & 0.785590550279046 \tabularnewline
28 & 52.34 & 52.7404222608895 & -0.400422260889449 \tabularnewline
29 & 51.84 & 52.1373574793165 & -0.297357479316489 \tabularnewline
30 & 51.42 & 51.6350815426062 & -0.21508154260615 \tabularnewline
31 & 50.85 & 51.2134353355571 & -0.363435335557121 \tabularnewline
32 & 50.66 & 50.6406536472541 & 0.0193463527458846 \tabularnewline
33 & 51.53 & 50.4508017218024 & 1.07919827819762 \tabularnewline
34 & 51.59 & 51.3290617695561 & 0.260938230443898 \tabularnewline
35 & 52.32 & 51.3910589579206 & 0.928941042079359 \tabularnewline
36 & 51.98 & 52.128168955706 & -0.148168955706019 \tabularnewline
37 & 51.17 & 51.787034889173 & -0.617034889173034 \tabularnewline
38 & 50.57 & 50.972312181814 & -0.402312181814018 \tabularnewline
39 & 49.84 & 50.3692329350242 & -0.529232935024226 \tabularnewline
40 & 50.12 & 49.6351822527683 & 0.484817747231709 \tabularnewline
41 & 49.08 & 49.9188929867686 & -0.838892986768592 \tabularnewline
42 & 48.57 & 48.8724722054618 & -0.302472205461804 \tabularnewline
43 & 47.22 & 48.3601571212815 & -1.14015712128148 \tabularnewline
44 & 46.78 & 47.0014305022173 & -0.221430502217316 \tabularnewline
45 & 46.04 & 46.5597357010307 & -0.519735701030733 \tabularnewline
46 & 45.05 & 45.8157577094081 & -0.765757709408106 \tabularnewline
47 & 44.42 & 44.8198966963067 & -0.399896696306726 \tabularnewline
48 & 44.09 & 44.1868359373389 & -0.0968359373389092 \tabularnewline
49 & 44.46 & 43.8560947672659 & 0.603905232734142 \tabularnewline
50 & 44.34 & 44.2307169818875 & 0.109283018112535 \tabularnewline
51 & 43.04 & 44.1115534203497 & -1.07155342034972 \tabularnewline
52 & 42.87 & 42.8033518853755 & 0.066648114624499 \tabularnewline
53 & 42.32 & 42.6338620016541 & -0.313862001654051 \tabularnewline
54 & 42.49 & 42.0814597414076 & 0.408540258592389 \tabularnewline
55 & 41.94 & 42.254586657113 & -0.314586657112976 \tabularnewline
56 & 41.6 & 41.7021788504449 & -0.102178850444879 \tabularnewline
57 & 41.42 & 41.3613967863876 & 0.0586032136124359 \tabularnewline
58 & 41.12 & 41.1818453280066 & -0.0618453280066049 \tabularnewline
59 & 41.28 & 40.8813719716522 & 0.398628028347844 \tabularnewline
60 & 40.21 & 41.0444230203952 & -0.83442302039515 \tabularnewline
61 & 39.69 & 39.9680364516482 & -0.278036451648227 \tabularnewline
62 & 39.16 & 39.4459083956512 & -0.285908395651205 \tabularnewline
63 & 38.8 & 38.9137200887858 & -0.113720088785840 \tabularnewline
64 & 38.44 & 38.5528496895433 & -0.112849689543268 \tabularnewline
65 & 37.02 & 38.1919859522269 & -1.17198595222691 \tabularnewline
66 & 36.75 & 36.7630157192978 & -0.0130157192978473 \tabularnewline
67 & 35.95 & 36.492916098621 & -0.542916098620978 \tabularnewline
68 & 36.29 & 35.6887606871535 & 0.601239312846467 \tabularnewline
69 & 36.35 & 36.0333624971600 & 0.316637502840045 \tabularnewline
70 & 36.07 & 36.0957860007430 & -0.0257860007430466 \tabularnewline
71 & 36.6 & 35.8155886379397 & 0.784411362060268 \tabularnewline
72 & 36.5 & 36.3515924237501 & 0.148407576249930 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12984&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]57.3[/C][C]57.7[/C][C]-0.399999999999999[/C][/ROW]
[ROW][C]4[/C][C]55.9[/C][C]57.0969384503587[/C][C]-1.19693845035872[/C][/ROW]
[ROW][C]5[/C][C]55[/C][C]55.6877772341504[/C][C]-0.687777234150381[/C][/ROW]
[ROW][C]6[/C][C]55.9[/C][C]54.7825130737891[/C][C]1.11748692621086[/C][/ROW]
[ROW][C]7[/C][C]56.6[/C][C]55.6910661780343[/C][C]0.908933821965661[/C][/ROW]
[ROW][C]8[/C][C]57.3[/C][C]56.3980230430758[/C][C]0.901976956924187[/C][/ROW]
[ROW][C]9[/C][C]56.2[/C][C]57.1049266611481[/C][C]-0.904926661148096[/C][/ROW]
[ROW][C]10[/C][C]57.7[/C][C]55.998000466411[/C][C]1.70199953358896[/C][/ROW]
[ROW][C]11[/C][C]56.8[/C][C]57.5110273565649[/C][C]-0.711027356564855[/C][/ROW]
[ROW][C]12[/C][C]57.9[/C][C]56.6055852426938[/C][C]1.29441475730624[/C][/ROW]
[ROW][C]13[/C][C]58.3[/C][C]57.7154925302835[/C][C]0.584507469716478[/C][/ROW]
[ROW][C]14[/C][C]58.2[/C][C]58.1199662768691[/C][C]0.0800337231308887[/C][/ROW]
[ROW][C]15[/C][C]56.9[/C][C]58.02057884491[/C][C]-1.12057884490997[/C][/ROW]
[ROW][C]16[/C][C]57.1[/C][C]56.7120020755083[/C][C]0.387997924491692[/C][/ROW]
[ROW][C]17[/C][C]56.7[/C][C]56.9149717627747[/C][C]-0.214971762774674[/C][/ROW]
[ROW][C]18[/C][C]54.2[/C][C]56.5133263959667[/C][C]-2.31332639596666[/C][/ROW]
[ROW][C]19[/C][C]54.2[/C][C]53.9956204869723[/C][C]0.204379513027703[/C][/ROW]
[ROW][C]20[/C][C]52.1[/C][C]53.9971847820343[/C][C]-1.89718478203429[/C][/ROW]
[ROW][C]21[/C][C]51.5[/C][C]51.8826639685621[/C][C]-0.382663968562078[/C][/ROW]
[ROW][C]22[/C][C]51.8[/C][C]51.2797351067229[/C][C]0.52026489327713[/C][/ROW]
[ROW][C]23[/C][C]53[/C][C]51.5837171487163[/C][C]1.41628285128368[/C][/ROW]
[ROW][C]24[/C][C]52.4[/C][C]52.7945571993546[/C][C]-0.394557199354587[/C][/ROW]
[ROW][C]25[/C][C]52.41[/C][C]52.1915373082242[/C][C]0.218462691775784[/C][/ROW]
[ROW][C]26[/C][C]52.36[/C][C]52.2032093941633[/C][C]0.15679060583669[/C][/ROW]
[ROW][C]27[/C][C]52.94[/C][C]52.154409449721[/C][C]0.785590550279046[/C][/ROW]
[ROW][C]28[/C][C]52.34[/C][C]52.7404222608895[/C][C]-0.400422260889449[/C][/ROW]
[ROW][C]29[/C][C]51.84[/C][C]52.1373574793165[/C][C]-0.297357479316489[/C][/ROW]
[ROW][C]30[/C][C]51.42[/C][C]51.6350815426062[/C][C]-0.21508154260615[/C][/ROW]
[ROW][C]31[/C][C]50.85[/C][C]51.2134353355571[/C][C]-0.363435335557121[/C][/ROW]
[ROW][C]32[/C][C]50.66[/C][C]50.6406536472541[/C][C]0.0193463527458846[/C][/ROW]
[ROW][C]33[/C][C]51.53[/C][C]50.4508017218024[/C][C]1.07919827819762[/C][/ROW]
[ROW][C]34[/C][C]51.59[/C][C]51.3290617695561[/C][C]0.260938230443898[/C][/ROW]
[ROW][C]35[/C][C]52.32[/C][C]51.3910589579206[/C][C]0.928941042079359[/C][/ROW]
[ROW][C]36[/C][C]51.98[/C][C]52.128168955706[/C][C]-0.148168955706019[/C][/ROW]
[ROW][C]37[/C][C]51.17[/C][C]51.787034889173[/C][C]-0.617034889173034[/C][/ROW]
[ROW][C]38[/C][C]50.57[/C][C]50.972312181814[/C][C]-0.402312181814018[/C][/ROW]
[ROW][C]39[/C][C]49.84[/C][C]50.3692329350242[/C][C]-0.529232935024226[/C][/ROW]
[ROW][C]40[/C][C]50.12[/C][C]49.6351822527683[/C][C]0.484817747231709[/C][/ROW]
[ROW][C]41[/C][C]49.08[/C][C]49.9188929867686[/C][C]-0.838892986768592[/C][/ROW]
[ROW][C]42[/C][C]48.57[/C][C]48.8724722054618[/C][C]-0.302472205461804[/C][/ROW]
[ROW][C]43[/C][C]47.22[/C][C]48.3601571212815[/C][C]-1.14015712128148[/C][/ROW]
[ROW][C]44[/C][C]46.78[/C][C]47.0014305022173[/C][C]-0.221430502217316[/C][/ROW]
[ROW][C]45[/C][C]46.04[/C][C]46.5597357010307[/C][C]-0.519735701030733[/C][/ROW]
[ROW][C]46[/C][C]45.05[/C][C]45.8157577094081[/C][C]-0.765757709408106[/C][/ROW]
[ROW][C]47[/C][C]44.42[/C][C]44.8198966963067[/C][C]-0.399896696306726[/C][/ROW]
[ROW][C]48[/C][C]44.09[/C][C]44.1868359373389[/C][C]-0.0968359373389092[/C][/ROW]
[ROW][C]49[/C][C]44.46[/C][C]43.8560947672659[/C][C]0.603905232734142[/C][/ROW]
[ROW][C]50[/C][C]44.34[/C][C]44.2307169818875[/C][C]0.109283018112535[/C][/ROW]
[ROW][C]51[/C][C]43.04[/C][C]44.1115534203497[/C][C]-1.07155342034972[/C][/ROW]
[ROW][C]52[/C][C]42.87[/C][C]42.8033518853755[/C][C]0.066648114624499[/C][/ROW]
[ROW][C]53[/C][C]42.32[/C][C]42.6338620016541[/C][C]-0.313862001654051[/C][/ROW]
[ROW][C]54[/C][C]42.49[/C][C]42.0814597414076[/C][C]0.408540258592389[/C][/ROW]
[ROW][C]55[/C][C]41.94[/C][C]42.254586657113[/C][C]-0.314586657112976[/C][/ROW]
[ROW][C]56[/C][C]41.6[/C][C]41.7021788504449[/C][C]-0.102178850444879[/C][/ROW]
[ROW][C]57[/C][C]41.42[/C][C]41.3613967863876[/C][C]0.0586032136124359[/C][/ROW]
[ROW][C]58[/C][C]41.12[/C][C]41.1818453280066[/C][C]-0.0618453280066049[/C][/ROW]
[ROW][C]59[/C][C]41.28[/C][C]40.8813719716522[/C][C]0.398628028347844[/C][/ROW]
[ROW][C]60[/C][C]40.21[/C][C]41.0444230203952[/C][C]-0.83442302039515[/C][/ROW]
[ROW][C]61[/C][C]39.69[/C][C]39.9680364516482[/C][C]-0.278036451648227[/C][/ROW]
[ROW][C]62[/C][C]39.16[/C][C]39.4459083956512[/C][C]-0.285908395651205[/C][/ROW]
[ROW][C]63[/C][C]38.8[/C][C]38.9137200887858[/C][C]-0.113720088785840[/C][/ROW]
[ROW][C]64[/C][C]38.44[/C][C]38.5528496895433[/C][C]-0.112849689543268[/C][/ROW]
[ROW][C]65[/C][C]37.02[/C][C]38.1919859522269[/C][C]-1.17198595222691[/C][/ROW]
[ROW][C]66[/C][C]36.75[/C][C]36.7630157192978[/C][C]-0.0130157192978473[/C][/ROW]
[ROW][C]67[/C][C]35.95[/C][C]36.492916098621[/C][C]-0.542916098620978[/C][/ROW]
[ROW][C]68[/C][C]36.29[/C][C]35.6887606871535[/C][C]0.601239312846467[/C][/ROW]
[ROW][C]69[/C][C]36.35[/C][C]36.0333624971600[/C][C]0.316637502840045[/C][/ROW]
[ROW][C]70[/C][C]36.07[/C][C]36.0957860007430[/C][C]-0.0257860007430466[/C][/ROW]
[ROW][C]71[/C][C]36.6[/C][C]35.8155886379397[/C][C]0.784411362060268[/C][/ROW]
[ROW][C]72[/C][C]36.5[/C][C]36.3515924237501[/C][C]0.148407576249930[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12984&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
357.357.7-0.399999999999999
455.957.0969384503587-1.19693845035872
55555.6877772341504-0.687777234150381
655.954.78251307378911.11748692621086
756.655.69106617803430.908933821965661
857.356.39802304307580.901976956924187
956.257.1049266611481-0.904926661148096
1057.755.9980004664111.70199953358896
1156.857.5110273565649-0.711027356564855
1257.956.60558524269381.29441475730624
1358.357.71549253028350.584507469716478
1458.258.11996627686910.0800337231308887
1556.958.02057884491-1.12057884490997
1657.156.71200207550830.387997924491692
1756.756.9149717627747-0.214971762774674
1854.256.5133263959667-2.31332639596666
1954.253.99562048697230.204379513027703
2052.153.9971847820343-1.89718478203429
2151.551.8826639685621-0.382663968562078
2251.851.27973510672290.52026489327713
235351.58371714871631.41628285128368
2452.452.7945571993546-0.394557199354587
2552.4152.19153730822420.218462691775784
2652.3652.20320939416330.15679060583669
2752.9452.1544094497210.785590550279046
2852.3452.7404222608895-0.400422260889449
2951.8452.1373574793165-0.297357479316489
3051.4251.6350815426062-0.21508154260615
3150.8551.2134353355571-0.363435335557121
3250.6650.64065364725410.0193463527458846
3351.5350.45080172180241.07919827819762
3451.5951.32906176955610.260938230443898
3552.3251.39105895792060.928941042079359
3651.9852.128168955706-0.148168955706019
3751.1751.787034889173-0.617034889173034
3850.5750.972312181814-0.402312181814018
3949.8450.3692329350242-0.529232935024226
4050.1249.63518225276830.484817747231709
4149.0849.9188929867686-0.838892986768592
4248.5748.8724722054618-0.302472205461804
4347.2248.3601571212815-1.14015712128148
4446.7847.0014305022173-0.221430502217316
4546.0446.5597357010307-0.519735701030733
4645.0545.8157577094081-0.765757709408106
4744.4244.8198966963067-0.399896696306726
4844.0944.1868359373389-0.0968359373389092
4944.4643.85609476726590.603905232734142
5044.3444.23071698188750.109283018112535
5143.0444.1115534203497-1.07155342034972
5242.8742.80335188537550.066648114624499
5342.3242.6338620016541-0.313862001654051
5442.4942.08145974140760.408540258592389
5541.9442.254586657113-0.314586657112976
5641.641.7021788504449-0.102178850444879
5741.4241.36139678638760.0586032136124359
5841.1241.1818453280066-0.0618453280066049
5941.2840.88137197165220.398628028347844
6040.2141.0444230203952-0.83442302039515
6139.6939.9680364516482-0.278036451648227
6239.1639.4459083956512-0.285908395651205
6338.838.9137200887858-0.113720088785840
6438.4438.5528496895433-0.112849689543268
6537.0238.1919859522269-1.17198595222691
6636.7536.7630157192978-0.0130157192978473
6735.9536.492916098621-0.542916098620978
6836.2935.68876068715350.601239312846467
6936.3536.03336249716000.316637502840045
7036.0736.0957860007430-0.0257860007430466
7136.635.81558863793970.784411362060268
7236.536.35159242375010.148407576249930







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7336.252728316654634.820215129234337.685241504075
7436.005456633309333.971809363415738.0391039032028
7535.758184949963933.257960562170938.2584093377570
7635.510913266618632.612890358544938.4089361746923
7735.263641583273232.011226171884538.516056994662
7835.016369899927931.440007206135438.5927325937203
7934.769098216582530.891564266462738.6466321667024
8034.521826533237230.360919818437838.6827332480366
8134.274554849891829.844629792622738.704479907161
8234.027283166546529.340196231542538.7143701015504
8333.780011483201128.845740626252638.7142823401497
8433.532739799855828.35980916973538.7056704299765

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 36.2527283166546 & 34.8202151292343 & 37.685241504075 \tabularnewline
74 & 36.0054566333093 & 33.9718093634157 & 38.0391039032028 \tabularnewline
75 & 35.7581849499639 & 33.2579605621709 & 38.2584093377570 \tabularnewline
76 & 35.5109132666186 & 32.6128903585449 & 38.4089361746923 \tabularnewline
77 & 35.2636415832732 & 32.0112261718845 & 38.516056994662 \tabularnewline
78 & 35.0163698999279 & 31.4400072061354 & 38.5927325937203 \tabularnewline
79 & 34.7690982165825 & 30.8915642664627 & 38.6466321667024 \tabularnewline
80 & 34.5218265332372 & 30.3609198184378 & 38.6827332480366 \tabularnewline
81 & 34.2745548498918 & 29.8446297926227 & 38.704479907161 \tabularnewline
82 & 34.0272831665465 & 29.3401962315425 & 38.7143701015504 \tabularnewline
83 & 33.7800114832011 & 28.8457406262526 & 38.7142823401497 \tabularnewline
84 & 33.5327397998558 & 28.359809169735 & 38.7056704299765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12984&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]36.2527283166546[/C][C]34.8202151292343[/C][C]37.685241504075[/C][/ROW]
[ROW][C]74[/C][C]36.0054566333093[/C][C]33.9718093634157[/C][C]38.0391039032028[/C][/ROW]
[ROW][C]75[/C][C]35.7581849499639[/C][C]33.2579605621709[/C][C]38.2584093377570[/C][/ROW]
[ROW][C]76[/C][C]35.5109132666186[/C][C]32.6128903585449[/C][C]38.4089361746923[/C][/ROW]
[ROW][C]77[/C][C]35.2636415832732[/C][C]32.0112261718845[/C][C]38.516056994662[/C][/ROW]
[ROW][C]78[/C][C]35.0163698999279[/C][C]31.4400072061354[/C][C]38.5927325937203[/C][/ROW]
[ROW][C]79[/C][C]34.7690982165825[/C][C]30.8915642664627[/C][C]38.6466321667024[/C][/ROW]
[ROW][C]80[/C][C]34.5218265332372[/C][C]30.3609198184378[/C][C]38.6827332480366[/C][/ROW]
[ROW][C]81[/C][C]34.2745548498918[/C][C]29.8446297926227[/C][C]38.704479907161[/C][/ROW]
[ROW][C]82[/C][C]34.0272831665465[/C][C]29.3401962315425[/C][C]38.7143701015504[/C][/ROW]
[ROW][C]83[/C][C]33.7800114832011[/C][C]28.8457406262526[/C][C]38.7142823401497[/C][/ROW]
[ROW][C]84[/C][C]33.5327397998558[/C][C]28.359809169735[/C][C]38.7056704299765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12984&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12984&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
7336.252728316654634.820215129234337.685241504075
7436.005456633309333.971809363415738.0391039032028
7535.758184949963933.257960562170938.2584093377570
7635.510913266618632.612890358544938.4089361746923
7735.263641583273232.011226171884538.516056994662
7835.016369899927931.440007206135438.5927325937203
7934.769098216582530.891564266462738.6466321667024
8034.521826533237230.360919818437838.6827332480366
8134.274554849891829.844629792622738.704479907161
8234.027283166546529.340196231542538.7143701015504
8333.780011483201128.845740626252638.7142823401497
8433.532739799855828.35980916973538.7056704299765



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')