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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 27 Apr 2016 20:53:29 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/27/t1461786865dyd9wh2ggpyiprm.htm/, Retrieved Fri, 03 May 2024 04:45:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294998, Retrieved Fri, 03 May 2024 04:45:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-27 19:53:29] [d0e43a2339caadb8d5bf1f89f27a021a] [Current]
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Dataseries X:
86,88
90,65
90,68
89,64
102,62
101,84
92,51
94,29
94,68
96,94
94,03
89,65
84,9
89,07
89,8
93,22
92,23
98,41
96,63
89,8
90
92,13
93,27
90,81
85,42
88,28
88,73
90,18
92,74
96,13
94,85
94,25
96,94
101,22
98,71
95,51
93,91
98,17
97,59
99,64
107,88
108,49
100,25
99,27
101,73
101,25
97,09
94,74
94,53
93,48
96,05
106,22
98,33
99,86
93,78
88,96
83,77
89,46
86,78
88,4
87,19
92,23
95,99
104,75
105,63
108,71
96,4
93,31
93,77
98,7
95,04
95,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294998&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294998&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0750134915724138
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0750134915724138 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294998&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]0.0750134915724138[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294998&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
beta0.0750134915724138
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
390.6894.42-3.74000000000001
489.6494.1694495415192-4.52944954151918
5102.6292.78967971650889.83032028349125
6101.84106.507086364249-4.66708636424856
792.51105.376991920596-12.8669919205963
894.2995.0817939305983-0.791793930598303
994.6896.8023987032583-2.12239870325828
1096.9497.0331901660181-0.0931901660181182
1194.0399.2861996462849-5.25619964628488
1289.6595.9819137584154-6.33191375841537
1384.991.1269347990612-6.22693479906123
1489.0785.90983067798993.16016932201012
1589.890.3168860127939-0.516886012793876
1693.2291.00811258822932.21188741177073
1792.2394.5940339859513-2.36403398595125
1898.4193.42669954246924.98330045753079
1996.6399.980514309343-3.350514309343
2089.897.9491805324358-8.14918053243585
219090.5078820472439-0.507882047243882
2292.1390.66978404157321.46021595842682
2393.2792.90931993906450.360680060935465
2490.8194.0763758097759-3.26637580977585
2585.4291.3713535554969-5.95135355549689
2688.2885.53492174571722.74507825428283
2788.7388.60083965021040.129160349789572
2890.1889.06052841902091.11947158097914
2992.7490.59450389102622.14549610897379
3096.1393.31544504531532.81455495468465
3194.8596.9165746396887-2.06657463968868
3294.2595.4815536603706-1.23155366037062
3396.9494.78917052024752.15082947975255
34101.2297.64051174930063.57948825069944
3598.71102.189021661028-3.47902166102797
3695.5199.4180480989782-3.90804809897818
3793.9195.9248917658409-2.01489176584091
3898.1794.17374769934473.99625230065533
3997.5998.7335205376211-1.14352053762111
4099.6498.06774106940941.57225893059061
41107.88100.2356817014497.64431829855108
42108.49109.049108707714-0.559108707714117
43100.25109.61716801138-9.36716801137993
4499.27100.674504032701-1.40450403270091
45101.7399.58914728128052.14085271871953
46101.25102.209740118654-0.959740118653926
4797.09101.657746661352-4.56774666135156
4894.7497.1551040356654-2.41510403566537
4994.5394.6239386494395-0.0939386494394654
5093.4894.4068919833514-0.92689198335141
5196.0593.28736257936982.76263742063024
52106.2296.064597658239810.1554023417602
5398.33106.996389846218-8.66638984621792
5499.8698.45629368452541.40370631547459
5593.78100.091590596391-6.3115905963914
5688.9693.5381361483805-4.57813614838048
5783.7788.3747141709966-4.60471417099657
5889.4682.83929848333716.62070151666285
5986.7889.0259404207608-2.24594042076079
6088.486.17746458793592.22253541206409
6187.1987.9641847293382-0.774184729338188
6292.2386.69611042966855.53388957033152
6395.9992.15122680831523.83877319168478
64104.7596.19918658877818.55081341122194
65105.63105.6006129585380.0293870414619448
66108.71106.4828173831252.22718261687491
6796.4109.729886127586-13.3298861275862
6893.3196.4199648268933-3.10996482689333
6993.7793.09667550656070.673324493439324
7098.793.60718392777485.09281607222523
7195.0498.9192138432885-3.8792138432885
7295.6194.96822046834740.641779531652602

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 90.68 & 94.42 & -3.74000000000001 \tabularnewline
4 & 89.64 & 94.1694495415192 & -4.52944954151918 \tabularnewline
5 & 102.62 & 92.7896797165088 & 9.83032028349125 \tabularnewline
6 & 101.84 & 106.507086364249 & -4.66708636424856 \tabularnewline
7 & 92.51 & 105.376991920596 & -12.8669919205963 \tabularnewline
8 & 94.29 & 95.0817939305983 & -0.791793930598303 \tabularnewline
9 & 94.68 & 96.8023987032583 & -2.12239870325828 \tabularnewline
10 & 96.94 & 97.0331901660181 & -0.0931901660181182 \tabularnewline
11 & 94.03 & 99.2861996462849 & -5.25619964628488 \tabularnewline
12 & 89.65 & 95.9819137584154 & -6.33191375841537 \tabularnewline
13 & 84.9 & 91.1269347990612 & -6.22693479906123 \tabularnewline
14 & 89.07 & 85.9098306779899 & 3.16016932201012 \tabularnewline
15 & 89.8 & 90.3168860127939 & -0.516886012793876 \tabularnewline
16 & 93.22 & 91.0081125882293 & 2.21188741177073 \tabularnewline
17 & 92.23 & 94.5940339859513 & -2.36403398595125 \tabularnewline
18 & 98.41 & 93.4266995424692 & 4.98330045753079 \tabularnewline
19 & 96.63 & 99.980514309343 & -3.350514309343 \tabularnewline
20 & 89.8 & 97.9491805324358 & -8.14918053243585 \tabularnewline
21 & 90 & 90.5078820472439 & -0.507882047243882 \tabularnewline
22 & 92.13 & 90.6697840415732 & 1.46021595842682 \tabularnewline
23 & 93.27 & 92.9093199390645 & 0.360680060935465 \tabularnewline
24 & 90.81 & 94.0763758097759 & -3.26637580977585 \tabularnewline
25 & 85.42 & 91.3713535554969 & -5.95135355549689 \tabularnewline
26 & 88.28 & 85.5349217457172 & 2.74507825428283 \tabularnewline
27 & 88.73 & 88.6008396502104 & 0.129160349789572 \tabularnewline
28 & 90.18 & 89.0605284190209 & 1.11947158097914 \tabularnewline
29 & 92.74 & 90.5945038910262 & 2.14549610897379 \tabularnewline
30 & 96.13 & 93.3154450453153 & 2.81455495468465 \tabularnewline
31 & 94.85 & 96.9165746396887 & -2.06657463968868 \tabularnewline
32 & 94.25 & 95.4815536603706 & -1.23155366037062 \tabularnewline
33 & 96.94 & 94.7891705202475 & 2.15082947975255 \tabularnewline
34 & 101.22 & 97.6405117493006 & 3.57948825069944 \tabularnewline
35 & 98.71 & 102.189021661028 & -3.47902166102797 \tabularnewline
36 & 95.51 & 99.4180480989782 & -3.90804809897818 \tabularnewline
37 & 93.91 & 95.9248917658409 & -2.01489176584091 \tabularnewline
38 & 98.17 & 94.1737476993447 & 3.99625230065533 \tabularnewline
39 & 97.59 & 98.7335205376211 & -1.14352053762111 \tabularnewline
40 & 99.64 & 98.0677410694094 & 1.57225893059061 \tabularnewline
41 & 107.88 & 100.235681701449 & 7.64431829855108 \tabularnewline
42 & 108.49 & 109.049108707714 & -0.559108707714117 \tabularnewline
43 & 100.25 & 109.61716801138 & -9.36716801137993 \tabularnewline
44 & 99.27 & 100.674504032701 & -1.40450403270091 \tabularnewline
45 & 101.73 & 99.5891472812805 & 2.14085271871953 \tabularnewline
46 & 101.25 & 102.209740118654 & -0.959740118653926 \tabularnewline
47 & 97.09 & 101.657746661352 & -4.56774666135156 \tabularnewline
48 & 94.74 & 97.1551040356654 & -2.41510403566537 \tabularnewline
49 & 94.53 & 94.6239386494395 & -0.0939386494394654 \tabularnewline
50 & 93.48 & 94.4068919833514 & -0.92689198335141 \tabularnewline
51 & 96.05 & 93.2873625793698 & 2.76263742063024 \tabularnewline
52 & 106.22 & 96.0645976582398 & 10.1554023417602 \tabularnewline
53 & 98.33 & 106.996389846218 & -8.66638984621792 \tabularnewline
54 & 99.86 & 98.4562936845254 & 1.40370631547459 \tabularnewline
55 & 93.78 & 100.091590596391 & -6.3115905963914 \tabularnewline
56 & 88.96 & 93.5381361483805 & -4.57813614838048 \tabularnewline
57 & 83.77 & 88.3747141709966 & -4.60471417099657 \tabularnewline
58 & 89.46 & 82.8392984833371 & 6.62070151666285 \tabularnewline
59 & 86.78 & 89.0259404207608 & -2.24594042076079 \tabularnewline
60 & 88.4 & 86.1774645879359 & 2.22253541206409 \tabularnewline
61 & 87.19 & 87.9641847293382 & -0.774184729338188 \tabularnewline
62 & 92.23 & 86.6961104296685 & 5.53388957033152 \tabularnewline
63 & 95.99 & 92.1512268083152 & 3.83877319168478 \tabularnewline
64 & 104.75 & 96.1991865887781 & 8.55081341122194 \tabularnewline
65 & 105.63 & 105.600612958538 & 0.0293870414619448 \tabularnewline
66 & 108.71 & 106.482817383125 & 2.22718261687491 \tabularnewline
67 & 96.4 & 109.729886127586 & -13.3298861275862 \tabularnewline
68 & 93.31 & 96.4199648268933 & -3.10996482689333 \tabularnewline
69 & 93.77 & 93.0966755065607 & 0.673324493439324 \tabularnewline
70 & 98.7 & 93.6071839277748 & 5.09281607222523 \tabularnewline
71 & 95.04 & 98.9192138432885 & -3.8792138432885 \tabularnewline
72 & 95.61 & 94.9682204683474 & 0.641779531652602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294998&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]90.68[/C][C]94.42[/C][C]-3.74000000000001[/C][/ROW]
[ROW][C]4[/C][C]89.64[/C][C]94.1694495415192[/C][C]-4.52944954151918[/C][/ROW]
[ROW][C]5[/C][C]102.62[/C][C]92.7896797165088[/C][C]9.83032028349125[/C][/ROW]
[ROW][C]6[/C][C]101.84[/C][C]106.507086364249[/C][C]-4.66708636424856[/C][/ROW]
[ROW][C]7[/C][C]92.51[/C][C]105.376991920596[/C][C]-12.8669919205963[/C][/ROW]
[ROW][C]8[/C][C]94.29[/C][C]95.0817939305983[/C][C]-0.791793930598303[/C][/ROW]
[ROW][C]9[/C][C]94.68[/C][C]96.8023987032583[/C][C]-2.12239870325828[/C][/ROW]
[ROW][C]10[/C][C]96.94[/C][C]97.0331901660181[/C][C]-0.0931901660181182[/C][/ROW]
[ROW][C]11[/C][C]94.03[/C][C]99.2861996462849[/C][C]-5.25619964628488[/C][/ROW]
[ROW][C]12[/C][C]89.65[/C][C]95.9819137584154[/C][C]-6.33191375841537[/C][/ROW]
[ROW][C]13[/C][C]84.9[/C][C]91.1269347990612[/C][C]-6.22693479906123[/C][/ROW]
[ROW][C]14[/C][C]89.07[/C][C]85.9098306779899[/C][C]3.16016932201012[/C][/ROW]
[ROW][C]15[/C][C]89.8[/C][C]90.3168860127939[/C][C]-0.516886012793876[/C][/ROW]
[ROW][C]16[/C][C]93.22[/C][C]91.0081125882293[/C][C]2.21188741177073[/C][/ROW]
[ROW][C]17[/C][C]92.23[/C][C]94.5940339859513[/C][C]-2.36403398595125[/C][/ROW]
[ROW][C]18[/C][C]98.41[/C][C]93.4266995424692[/C][C]4.98330045753079[/C][/ROW]
[ROW][C]19[/C][C]96.63[/C][C]99.980514309343[/C][C]-3.350514309343[/C][/ROW]
[ROW][C]20[/C][C]89.8[/C][C]97.9491805324358[/C][C]-8.14918053243585[/C][/ROW]
[ROW][C]21[/C][C]90[/C][C]90.5078820472439[/C][C]-0.507882047243882[/C][/ROW]
[ROW][C]22[/C][C]92.13[/C][C]90.6697840415732[/C][C]1.46021595842682[/C][/ROW]
[ROW][C]23[/C][C]93.27[/C][C]92.9093199390645[/C][C]0.360680060935465[/C][/ROW]
[ROW][C]24[/C][C]90.81[/C][C]94.0763758097759[/C][C]-3.26637580977585[/C][/ROW]
[ROW][C]25[/C][C]85.42[/C][C]91.3713535554969[/C][C]-5.95135355549689[/C][/ROW]
[ROW][C]26[/C][C]88.28[/C][C]85.5349217457172[/C][C]2.74507825428283[/C][/ROW]
[ROW][C]27[/C][C]88.73[/C][C]88.6008396502104[/C][C]0.129160349789572[/C][/ROW]
[ROW][C]28[/C][C]90.18[/C][C]89.0605284190209[/C][C]1.11947158097914[/C][/ROW]
[ROW][C]29[/C][C]92.74[/C][C]90.5945038910262[/C][C]2.14549610897379[/C][/ROW]
[ROW][C]30[/C][C]96.13[/C][C]93.3154450453153[/C][C]2.81455495468465[/C][/ROW]
[ROW][C]31[/C][C]94.85[/C][C]96.9165746396887[/C][C]-2.06657463968868[/C][/ROW]
[ROW][C]32[/C][C]94.25[/C][C]95.4815536603706[/C][C]-1.23155366037062[/C][/ROW]
[ROW][C]33[/C][C]96.94[/C][C]94.7891705202475[/C][C]2.15082947975255[/C][/ROW]
[ROW][C]34[/C][C]101.22[/C][C]97.6405117493006[/C][C]3.57948825069944[/C][/ROW]
[ROW][C]35[/C][C]98.71[/C][C]102.189021661028[/C][C]-3.47902166102797[/C][/ROW]
[ROW][C]36[/C][C]95.51[/C][C]99.4180480989782[/C][C]-3.90804809897818[/C][/ROW]
[ROW][C]37[/C][C]93.91[/C][C]95.9248917658409[/C][C]-2.01489176584091[/C][/ROW]
[ROW][C]38[/C][C]98.17[/C][C]94.1737476993447[/C][C]3.99625230065533[/C][/ROW]
[ROW][C]39[/C][C]97.59[/C][C]98.7335205376211[/C][C]-1.14352053762111[/C][/ROW]
[ROW][C]40[/C][C]99.64[/C][C]98.0677410694094[/C][C]1.57225893059061[/C][/ROW]
[ROW][C]41[/C][C]107.88[/C][C]100.235681701449[/C][C]7.64431829855108[/C][/ROW]
[ROW][C]42[/C][C]108.49[/C][C]109.049108707714[/C][C]-0.559108707714117[/C][/ROW]
[ROW][C]43[/C][C]100.25[/C][C]109.61716801138[/C][C]-9.36716801137993[/C][/ROW]
[ROW][C]44[/C][C]99.27[/C][C]100.674504032701[/C][C]-1.40450403270091[/C][/ROW]
[ROW][C]45[/C][C]101.73[/C][C]99.5891472812805[/C][C]2.14085271871953[/C][/ROW]
[ROW][C]46[/C][C]101.25[/C][C]102.209740118654[/C][C]-0.959740118653926[/C][/ROW]
[ROW][C]47[/C][C]97.09[/C][C]101.657746661352[/C][C]-4.56774666135156[/C][/ROW]
[ROW][C]48[/C][C]94.74[/C][C]97.1551040356654[/C][C]-2.41510403566537[/C][/ROW]
[ROW][C]49[/C][C]94.53[/C][C]94.6239386494395[/C][C]-0.0939386494394654[/C][/ROW]
[ROW][C]50[/C][C]93.48[/C][C]94.4068919833514[/C][C]-0.92689198335141[/C][/ROW]
[ROW][C]51[/C][C]96.05[/C][C]93.2873625793698[/C][C]2.76263742063024[/C][/ROW]
[ROW][C]52[/C][C]106.22[/C][C]96.0645976582398[/C][C]10.1554023417602[/C][/ROW]
[ROW][C]53[/C][C]98.33[/C][C]106.996389846218[/C][C]-8.66638984621792[/C][/ROW]
[ROW][C]54[/C][C]99.86[/C][C]98.4562936845254[/C][C]1.40370631547459[/C][/ROW]
[ROW][C]55[/C][C]93.78[/C][C]100.091590596391[/C][C]-6.3115905963914[/C][/ROW]
[ROW][C]56[/C][C]88.96[/C][C]93.5381361483805[/C][C]-4.57813614838048[/C][/ROW]
[ROW][C]57[/C][C]83.77[/C][C]88.3747141709966[/C][C]-4.60471417099657[/C][/ROW]
[ROW][C]58[/C][C]89.46[/C][C]82.8392984833371[/C][C]6.62070151666285[/C][/ROW]
[ROW][C]59[/C][C]86.78[/C][C]89.0259404207608[/C][C]-2.24594042076079[/C][/ROW]
[ROW][C]60[/C][C]88.4[/C][C]86.1774645879359[/C][C]2.22253541206409[/C][/ROW]
[ROW][C]61[/C][C]87.19[/C][C]87.9641847293382[/C][C]-0.774184729338188[/C][/ROW]
[ROW][C]62[/C][C]92.23[/C][C]86.6961104296685[/C][C]5.53388957033152[/C][/ROW]
[ROW][C]63[/C][C]95.99[/C][C]92.1512268083152[/C][C]3.83877319168478[/C][/ROW]
[ROW][C]64[/C][C]104.75[/C][C]96.1991865887781[/C][C]8.55081341122194[/C][/ROW]
[ROW][C]65[/C][C]105.63[/C][C]105.600612958538[/C][C]0.0293870414619448[/C][/ROW]
[ROW][C]66[/C][C]108.71[/C][C]106.482817383125[/C][C]2.22718261687491[/C][/ROW]
[ROW][C]67[/C][C]96.4[/C][C]109.729886127586[/C][C]-13.3298861275862[/C][/ROW]
[ROW][C]68[/C][C]93.31[/C][C]96.4199648268933[/C][C]-3.10996482689333[/C][/ROW]
[ROW][C]69[/C][C]93.77[/C][C]93.0966755065607[/C][C]0.673324493439324[/C][/ROW]
[ROW][C]70[/C][C]98.7[/C][C]93.6071839277748[/C][C]5.09281607222523[/C][/ROW]
[ROW][C]71[/C][C]95.04[/C][C]98.9192138432885[/C][C]-3.8792138432885[/C][/ROW]
[ROW][C]72[/C][C]95.61[/C][C]94.9682204683474[/C][C]0.641779531652602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294998&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
390.6894.42-3.74000000000001
489.6494.1694495415192-4.52944954151918
5102.6292.78967971650889.83032028349125
6101.84106.507086364249-4.66708636424856
792.51105.376991920596-12.8669919205963
894.2995.0817939305983-0.791793930598303
994.6896.8023987032583-2.12239870325828
1096.9497.0331901660181-0.0931901660181182
1194.0399.2861996462849-5.25619964628488
1289.6595.9819137584154-6.33191375841537
1384.991.1269347990612-6.22693479906123
1489.0785.90983067798993.16016932201012
1589.890.3168860127939-0.516886012793876
1693.2291.00811258822932.21188741177073
1792.2394.5940339859513-2.36403398595125
1898.4193.42669954246924.98330045753079
1996.6399.980514309343-3.350514309343
2089.897.9491805324358-8.14918053243585
219090.5078820472439-0.507882047243882
2292.1390.66978404157321.46021595842682
2393.2792.90931993906450.360680060935465
2490.8194.0763758097759-3.26637580977585
2585.4291.3713535554969-5.95135355549689
2688.2885.53492174571722.74507825428283
2788.7388.60083965021040.129160349789572
2890.1889.06052841902091.11947158097914
2992.7490.59450389102622.14549610897379
3096.1393.31544504531532.81455495468465
3194.8596.9165746396887-2.06657463968868
3294.2595.4815536603706-1.23155366037062
3396.9494.78917052024752.15082947975255
34101.2297.64051174930063.57948825069944
3598.71102.189021661028-3.47902166102797
3695.5199.4180480989782-3.90804809897818
3793.9195.9248917658409-2.01489176584091
3898.1794.17374769934473.99625230065533
3997.5998.7335205376211-1.14352053762111
4099.6498.06774106940941.57225893059061
41107.88100.2356817014497.64431829855108
42108.49109.049108707714-0.559108707714117
43100.25109.61716801138-9.36716801137993
4499.27100.674504032701-1.40450403270091
45101.7399.58914728128052.14085271871953
46101.25102.209740118654-0.959740118653926
4797.09101.657746661352-4.56774666135156
4894.7497.1551040356654-2.41510403566537
4994.5394.6239386494395-0.0939386494394654
5093.4894.4068919833514-0.92689198335141
5196.0593.28736257936982.76263742063024
52106.2296.064597658239810.1554023417602
5398.33106.996389846218-8.66638984621792
5499.8698.45629368452541.40370631547459
5593.78100.091590596391-6.3115905963914
5688.9693.5381361483805-4.57813614838048
5783.7788.3747141709966-4.60471417099657
5889.4682.83929848333716.62070151666285
5986.7889.0259404207608-2.24594042076079
6088.486.17746458793592.22253541206409
6187.1987.9641847293382-0.774184729338188
6292.2386.69611042966855.53388957033152
6395.9992.15122680831523.83877319168478
64104.7596.19918658877818.55081341122194
65105.63105.6006129585380.0293870414619448
66108.71106.4828173831252.22718261687491
6796.4109.729886127586-13.3298861275862
6893.3196.4199648268933-3.10996482689333
6993.7793.09667550656070.673324493439324
7098.793.60718392777485.09281607222523
7195.0498.9192138432885-3.8792138432885
7295.6194.96822046834740.641779531652602







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7395.586362591836486.3885671423681104.784158041305
7495.562725183672782.0583879445591109.067062422786
7595.539087775509178.3852212851312112.692954265887
7695.515450367345474.9919136060165116.038987128674
7795.491812959181871.7389081411011119.244717777262
7895.468175551018168.5579172832756122.378433818761
7995.444538142854565.410354525343125.478721760366
8095.420900734690862.2723995611002128.569401908281
8195.397263326527259.1284486278169131.666078025238
8295.373625918363655.9678441026288134.779407734098
8395.349988510199952.7830837743299137.91689324607
8495.326351102036349.568770083622141.083932120451

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 95.5863625918364 & 86.3885671423681 & 104.784158041305 \tabularnewline
74 & 95.5627251836727 & 82.0583879445591 & 109.067062422786 \tabularnewline
75 & 95.5390877755091 & 78.3852212851312 & 112.692954265887 \tabularnewline
76 & 95.5154503673454 & 74.9919136060165 & 116.038987128674 \tabularnewline
77 & 95.4918129591818 & 71.7389081411011 & 119.244717777262 \tabularnewline
78 & 95.4681755510181 & 68.5579172832756 & 122.378433818761 \tabularnewline
79 & 95.4445381428545 & 65.410354525343 & 125.478721760366 \tabularnewline
80 & 95.4209007346908 & 62.2723995611002 & 128.569401908281 \tabularnewline
81 & 95.3972633265272 & 59.1284486278169 & 131.666078025238 \tabularnewline
82 & 95.3736259183636 & 55.9678441026288 & 134.779407734098 \tabularnewline
83 & 95.3499885101999 & 52.7830837743299 & 137.91689324607 \tabularnewline
84 & 95.3263511020363 & 49.568770083622 & 141.083932120451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294998&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]95.5863625918364[/C][C]86.3885671423681[/C][C]104.784158041305[/C][/ROW]
[ROW][C]74[/C][C]95.5627251836727[/C][C]82.0583879445591[/C][C]109.067062422786[/C][/ROW]
[ROW][C]75[/C][C]95.5390877755091[/C][C]78.3852212851312[/C][C]112.692954265887[/C][/ROW]
[ROW][C]76[/C][C]95.5154503673454[/C][C]74.9919136060165[/C][C]116.038987128674[/C][/ROW]
[ROW][C]77[/C][C]95.4918129591818[/C][C]71.7389081411011[/C][C]119.244717777262[/C][/ROW]
[ROW][C]78[/C][C]95.4681755510181[/C][C]68.5579172832756[/C][C]122.378433818761[/C][/ROW]
[ROW][C]79[/C][C]95.4445381428545[/C][C]65.410354525343[/C][C]125.478721760366[/C][/ROW]
[ROW][C]80[/C][C]95.4209007346908[/C][C]62.2723995611002[/C][C]128.569401908281[/C][/ROW]
[ROW][C]81[/C][C]95.3972633265272[/C][C]59.1284486278169[/C][C]131.666078025238[/C][/ROW]
[ROW][C]82[/C][C]95.3736259183636[/C][C]55.9678441026288[/C][C]134.779407734098[/C][/ROW]
[ROW][C]83[/C][C]95.3499885101999[/C][C]52.7830837743299[/C][C]137.91689324607[/C][/ROW]
[ROW][C]84[/C][C]95.3263511020363[/C][C]49.568770083622[/C][C]141.083932120451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294998&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
7395.586362591836486.3885671423681104.784158041305
7495.562725183672782.0583879445591109.067062422786
7595.539087775509178.3852212851312112.692954265887
7695.515450367345474.9919136060165116.038987128674
7795.491812959181871.7389081411011119.244717777262
7895.468175551018168.5579172832756122.378433818761
7995.444538142854565.410354525343125.478721760366
8095.420900734690862.2723995611002128.569401908281
8195.397263326527259.1284486278169131.666078025238
8295.373625918363655.9678441026288134.779407734098
8395.349988510199952.7830837743299137.91689324607
8495.326351102036349.568770083622141.083932120451



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')