Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Dec 2013 13:26:01 -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/17/t1387304849uljfbethysf7zqv.htm/, Retrieved Thu, 25 Apr 2024 04:44:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232415, Retrieved Thu, 25 Apr 2024 04:44:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-17 18:26:01] [d7aee701571668449ffc3c4d70a8a545] [Current]
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Dataseries X:
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1
-2
-4
-1
1
1
-2
1
1
3
3
1
1
0
2
2
-1
1
0
1
1
3
2
0
0
3
-2
0
1
-1
-2
-1
-1
1
-2
-5
-5
-6
-4
-3
-3
-1
-2
-3
-3
-3
-5
-5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232415&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232415&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.518370486514584
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.518370486514584 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232415&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]0.518370486514584[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232415&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
alpha0.518370486514584
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2660
356-1
455.48162951348542-0.481629513485417
535.2319669882602-2.2319669882602
654.074981174671270.92501882532873
754.554483633192070.445516366807928
854.785426169004510.214573830995493
934.89665491017094-1.89665491017094
1063.913484981635362.08651501836464
1164.995072786825021.00492721317498
1245.51599739523028-1.51599739523028
1364.730149087909921.26985091209008
1455.38840232301104-0.388402323011041
1545.18706602186841-1.18706602186841
1654.571726030587550.428273969412447
1754.793730616473410.206269383526585
1844.90065457716515-0.900654577165154
1934.43378182581847-1.43378182581847
2023.69055164321318-1.69055164321318
2132.814219565442740.185780434557265
2222.91052265968908-0.910522659689075
23-12.4385345856035-3.4385345856035
2400.65609973956699-0.65609973956699
25-20.315996998365558-2.31599699836556
261-0.8845474924435111.88454749244351
27-20.09234630807427-2.09234630807427
28-2-0.992264265599182-1.00773573440082
29-2-1.51464472851867-0.485355271481335
30-6-1.76623857672886-4.23376142327114
31-4-3.9608955454966-0.0391044545034025
32-2-3.981166140602411.98116614060241
330-2.954188084432122.95418808443212
34-5-1.42282416984946-3.57717583015054
35-4-3.2771265452728-0.722873454727197
36-5-3.65184280968822-1.34815719031178
37-1-4.350687708328273.35068770832827
38-2-2.613790090803710.61379009080371
39-4-2.29561942281596-1.70438057718404
40-1-3.179120011816862.17912001181686
411-2.049528511117693.04952851111769
421-0.4687429331695191.46874293316952
43-20.292610055662421-2.29261005566242
441-0.8958113342795351.89581133427953
4510.08692130941080950.913078690589191
4630.5602343544776272.43976564552237
4731.824936859128631.17506314087137
4812.43405491114747-1.43405491114747
4911.69068316916733-0.690683169167331
5001.33265339873863-1.33265339873863
5120.6418452080791721.35815479192083
5221.345872568329280.654127431670716
53-11.68495292332697-2.68495292332697
5410.2931525701932150.706847429806785
5500.659561416273741-0.659561416273741
5610.3176642440336740.682335755966326
5710.6713669618202350.328633038179765
5830.8417206297062452.15827937029375
5921.960508956919810.0394910430801922
6001.98097994813426-1.98097994813426
6100.954098408644267-0.954098408644267
6230.4595219523725482.54047804762745
63-21.77643079390081-3.77643079390081
640-0.1811594740222080.181159474022208
651-0.08725174933658991.08725174933659
66-10.47634746893085-1.47634746893085
67-2-0.288947486803409-1.71105251319659
68-1-1.175906610521130.175906610521126
69-1-1.084721815244160.0847218152441587
701-1.040804526657652.04080452665765
71-20.0170883087070425-2.01708830870704
72-5-1.02851073922031-3.97148926077969
73-5-3.08721355951812-1.91278644048188
74-6-4.07874559726921-1.92125440273079
75-4-5.074667176731061.07466717673106
76-3-4.517591429487721.51759142948772
77-3-3.730916821853810.73091682185381
78-1-3.352031113307762.35203111330776
79-2-2.132807600804980.132807600804978
80-3-2.06396406016287-0.936035939837133
81-3-2.54917746569138-0.450822534308623
82-3-2.78287056213268-0.217129437867325
83-5-2.8954240544766-2.1045759455234
84-5-3.98637411126445-1.01362588873555

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6 & 6 & 0 \tabularnewline
3 & 5 & 6 & -1 \tabularnewline
4 & 5 & 5.48162951348542 & -0.481629513485417 \tabularnewline
5 & 3 & 5.2319669882602 & -2.2319669882602 \tabularnewline
6 & 5 & 4.07498117467127 & 0.92501882532873 \tabularnewline
7 & 5 & 4.55448363319207 & 0.445516366807928 \tabularnewline
8 & 5 & 4.78542616900451 & 0.214573830995493 \tabularnewline
9 & 3 & 4.89665491017094 & -1.89665491017094 \tabularnewline
10 & 6 & 3.91348498163536 & 2.08651501836464 \tabularnewline
11 & 6 & 4.99507278682502 & 1.00492721317498 \tabularnewline
12 & 4 & 5.51599739523028 & -1.51599739523028 \tabularnewline
13 & 6 & 4.73014908790992 & 1.26985091209008 \tabularnewline
14 & 5 & 5.38840232301104 & -0.388402323011041 \tabularnewline
15 & 4 & 5.18706602186841 & -1.18706602186841 \tabularnewline
16 & 5 & 4.57172603058755 & 0.428273969412447 \tabularnewline
17 & 5 & 4.79373061647341 & 0.206269383526585 \tabularnewline
18 & 4 & 4.90065457716515 & -0.900654577165154 \tabularnewline
19 & 3 & 4.43378182581847 & -1.43378182581847 \tabularnewline
20 & 2 & 3.69055164321318 & -1.69055164321318 \tabularnewline
21 & 3 & 2.81421956544274 & 0.185780434557265 \tabularnewline
22 & 2 & 2.91052265968908 & -0.910522659689075 \tabularnewline
23 & -1 & 2.4385345856035 & -3.4385345856035 \tabularnewline
24 & 0 & 0.65609973956699 & -0.65609973956699 \tabularnewline
25 & -2 & 0.315996998365558 & -2.31599699836556 \tabularnewline
26 & 1 & -0.884547492443511 & 1.88454749244351 \tabularnewline
27 & -2 & 0.09234630807427 & -2.09234630807427 \tabularnewline
28 & -2 & -0.992264265599182 & -1.00773573440082 \tabularnewline
29 & -2 & -1.51464472851867 & -0.485355271481335 \tabularnewline
30 & -6 & -1.76623857672886 & -4.23376142327114 \tabularnewline
31 & -4 & -3.9608955454966 & -0.0391044545034025 \tabularnewline
32 & -2 & -3.98116614060241 & 1.98116614060241 \tabularnewline
33 & 0 & -2.95418808443212 & 2.95418808443212 \tabularnewline
34 & -5 & -1.42282416984946 & -3.57717583015054 \tabularnewline
35 & -4 & -3.2771265452728 & -0.722873454727197 \tabularnewline
36 & -5 & -3.65184280968822 & -1.34815719031178 \tabularnewline
37 & -1 & -4.35068770832827 & 3.35068770832827 \tabularnewline
38 & -2 & -2.61379009080371 & 0.61379009080371 \tabularnewline
39 & -4 & -2.29561942281596 & -1.70438057718404 \tabularnewline
40 & -1 & -3.17912001181686 & 2.17912001181686 \tabularnewline
41 & 1 & -2.04952851111769 & 3.04952851111769 \tabularnewline
42 & 1 & -0.468742933169519 & 1.46874293316952 \tabularnewline
43 & -2 & 0.292610055662421 & -2.29261005566242 \tabularnewline
44 & 1 & -0.895811334279535 & 1.89581133427953 \tabularnewline
45 & 1 & 0.0869213094108095 & 0.913078690589191 \tabularnewline
46 & 3 & 0.560234354477627 & 2.43976564552237 \tabularnewline
47 & 3 & 1.82493685912863 & 1.17506314087137 \tabularnewline
48 & 1 & 2.43405491114747 & -1.43405491114747 \tabularnewline
49 & 1 & 1.69068316916733 & -0.690683169167331 \tabularnewline
50 & 0 & 1.33265339873863 & -1.33265339873863 \tabularnewline
51 & 2 & 0.641845208079172 & 1.35815479192083 \tabularnewline
52 & 2 & 1.34587256832928 & 0.654127431670716 \tabularnewline
53 & -1 & 1.68495292332697 & -2.68495292332697 \tabularnewline
54 & 1 & 0.293152570193215 & 0.706847429806785 \tabularnewline
55 & 0 & 0.659561416273741 & -0.659561416273741 \tabularnewline
56 & 1 & 0.317664244033674 & 0.682335755966326 \tabularnewline
57 & 1 & 0.671366961820235 & 0.328633038179765 \tabularnewline
58 & 3 & 0.841720629706245 & 2.15827937029375 \tabularnewline
59 & 2 & 1.96050895691981 & 0.0394910430801922 \tabularnewline
60 & 0 & 1.98097994813426 & -1.98097994813426 \tabularnewline
61 & 0 & 0.954098408644267 & -0.954098408644267 \tabularnewline
62 & 3 & 0.459521952372548 & 2.54047804762745 \tabularnewline
63 & -2 & 1.77643079390081 & -3.77643079390081 \tabularnewline
64 & 0 & -0.181159474022208 & 0.181159474022208 \tabularnewline
65 & 1 & -0.0872517493365899 & 1.08725174933659 \tabularnewline
66 & -1 & 0.47634746893085 & -1.47634746893085 \tabularnewline
67 & -2 & -0.288947486803409 & -1.71105251319659 \tabularnewline
68 & -1 & -1.17590661052113 & 0.175906610521126 \tabularnewline
69 & -1 & -1.08472181524416 & 0.0847218152441587 \tabularnewline
70 & 1 & -1.04080452665765 & 2.04080452665765 \tabularnewline
71 & -2 & 0.0170883087070425 & -2.01708830870704 \tabularnewline
72 & -5 & -1.02851073922031 & -3.97148926077969 \tabularnewline
73 & -5 & -3.08721355951812 & -1.91278644048188 \tabularnewline
74 & -6 & -4.07874559726921 & -1.92125440273079 \tabularnewline
75 & -4 & -5.07466717673106 & 1.07466717673106 \tabularnewline
76 & -3 & -4.51759142948772 & 1.51759142948772 \tabularnewline
77 & -3 & -3.73091682185381 & 0.73091682185381 \tabularnewline
78 & -1 & -3.35203111330776 & 2.35203111330776 \tabularnewline
79 & -2 & -2.13280760080498 & 0.132807600804978 \tabularnewline
80 & -3 & -2.06396406016287 & -0.936035939837133 \tabularnewline
81 & -3 & -2.54917746569138 & -0.450822534308623 \tabularnewline
82 & -3 & -2.78287056213268 & -0.217129437867325 \tabularnewline
83 & -5 & -2.8954240544766 & -2.1045759455234 \tabularnewline
84 & -5 & -3.98637411126445 & -1.01362588873555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232415&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]2[/C][C]6[/C][C]6[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]5[/C][C]6[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]5[/C][C]5.48162951348542[/C][C]-0.481629513485417[/C][/ROW]
[ROW][C]5[/C][C]3[/C][C]5.2319669882602[/C][C]-2.2319669882602[/C][/ROW]
[ROW][C]6[/C][C]5[/C][C]4.07498117467127[/C][C]0.92501882532873[/C][/ROW]
[ROW][C]7[/C][C]5[/C][C]4.55448363319207[/C][C]0.445516366807928[/C][/ROW]
[ROW][C]8[/C][C]5[/C][C]4.78542616900451[/C][C]0.214573830995493[/C][/ROW]
[ROW][C]9[/C][C]3[/C][C]4.89665491017094[/C][C]-1.89665491017094[/C][/ROW]
[ROW][C]10[/C][C]6[/C][C]3.91348498163536[/C][C]2.08651501836464[/C][/ROW]
[ROW][C]11[/C][C]6[/C][C]4.99507278682502[/C][C]1.00492721317498[/C][/ROW]
[ROW][C]12[/C][C]4[/C][C]5.51599739523028[/C][C]-1.51599739523028[/C][/ROW]
[ROW][C]13[/C][C]6[/C][C]4.73014908790992[/C][C]1.26985091209008[/C][/ROW]
[ROW][C]14[/C][C]5[/C][C]5.38840232301104[/C][C]-0.388402323011041[/C][/ROW]
[ROW][C]15[/C][C]4[/C][C]5.18706602186841[/C][C]-1.18706602186841[/C][/ROW]
[ROW][C]16[/C][C]5[/C][C]4.57172603058755[/C][C]0.428273969412447[/C][/ROW]
[ROW][C]17[/C][C]5[/C][C]4.79373061647341[/C][C]0.206269383526585[/C][/ROW]
[ROW][C]18[/C][C]4[/C][C]4.90065457716515[/C][C]-0.900654577165154[/C][/ROW]
[ROW][C]19[/C][C]3[/C][C]4.43378182581847[/C][C]-1.43378182581847[/C][/ROW]
[ROW][C]20[/C][C]2[/C][C]3.69055164321318[/C][C]-1.69055164321318[/C][/ROW]
[ROW][C]21[/C][C]3[/C][C]2.81421956544274[/C][C]0.185780434557265[/C][/ROW]
[ROW][C]22[/C][C]2[/C][C]2.91052265968908[/C][C]-0.910522659689075[/C][/ROW]
[ROW][C]23[/C][C]-1[/C][C]2.4385345856035[/C][C]-3.4385345856035[/C][/ROW]
[ROW][C]24[/C][C]0[/C][C]0.65609973956699[/C][C]-0.65609973956699[/C][/ROW]
[ROW][C]25[/C][C]-2[/C][C]0.315996998365558[/C][C]-2.31599699836556[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]-0.884547492443511[/C][C]1.88454749244351[/C][/ROW]
[ROW][C]27[/C][C]-2[/C][C]0.09234630807427[/C][C]-2.09234630807427[/C][/ROW]
[ROW][C]28[/C][C]-2[/C][C]-0.992264265599182[/C][C]-1.00773573440082[/C][/ROW]
[ROW][C]29[/C][C]-2[/C][C]-1.51464472851867[/C][C]-0.485355271481335[/C][/ROW]
[ROW][C]30[/C][C]-6[/C][C]-1.76623857672886[/C][C]-4.23376142327114[/C][/ROW]
[ROW][C]31[/C][C]-4[/C][C]-3.9608955454966[/C][C]-0.0391044545034025[/C][/ROW]
[ROW][C]32[/C][C]-2[/C][C]-3.98116614060241[/C][C]1.98116614060241[/C][/ROW]
[ROW][C]33[/C][C]0[/C][C]-2.95418808443212[/C][C]2.95418808443212[/C][/ROW]
[ROW][C]34[/C][C]-5[/C][C]-1.42282416984946[/C][C]-3.57717583015054[/C][/ROW]
[ROW][C]35[/C][C]-4[/C][C]-3.2771265452728[/C][C]-0.722873454727197[/C][/ROW]
[ROW][C]36[/C][C]-5[/C][C]-3.65184280968822[/C][C]-1.34815719031178[/C][/ROW]
[ROW][C]37[/C][C]-1[/C][C]-4.35068770832827[/C][C]3.35068770832827[/C][/ROW]
[ROW][C]38[/C][C]-2[/C][C]-2.61379009080371[/C][C]0.61379009080371[/C][/ROW]
[ROW][C]39[/C][C]-4[/C][C]-2.29561942281596[/C][C]-1.70438057718404[/C][/ROW]
[ROW][C]40[/C][C]-1[/C][C]-3.17912001181686[/C][C]2.17912001181686[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]-2.04952851111769[/C][C]3.04952851111769[/C][/ROW]
[ROW][C]42[/C][C]1[/C][C]-0.468742933169519[/C][C]1.46874293316952[/C][/ROW]
[ROW][C]43[/C][C]-2[/C][C]0.292610055662421[/C][C]-2.29261005566242[/C][/ROW]
[ROW][C]44[/C][C]1[/C][C]-0.895811334279535[/C][C]1.89581133427953[/C][/ROW]
[ROW][C]45[/C][C]1[/C][C]0.0869213094108095[/C][C]0.913078690589191[/C][/ROW]
[ROW][C]46[/C][C]3[/C][C]0.560234354477627[/C][C]2.43976564552237[/C][/ROW]
[ROW][C]47[/C][C]3[/C][C]1.82493685912863[/C][C]1.17506314087137[/C][/ROW]
[ROW][C]48[/C][C]1[/C][C]2.43405491114747[/C][C]-1.43405491114747[/C][/ROW]
[ROW][C]49[/C][C]1[/C][C]1.69068316916733[/C][C]-0.690683169167331[/C][/ROW]
[ROW][C]50[/C][C]0[/C][C]1.33265339873863[/C][C]-1.33265339873863[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]0.641845208079172[/C][C]1.35815479192083[/C][/ROW]
[ROW][C]52[/C][C]2[/C][C]1.34587256832928[/C][C]0.654127431670716[/C][/ROW]
[ROW][C]53[/C][C]-1[/C][C]1.68495292332697[/C][C]-2.68495292332697[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]0.293152570193215[/C][C]0.706847429806785[/C][/ROW]
[ROW][C]55[/C][C]0[/C][C]0.659561416273741[/C][C]-0.659561416273741[/C][/ROW]
[ROW][C]56[/C][C]1[/C][C]0.317664244033674[/C][C]0.682335755966326[/C][/ROW]
[ROW][C]57[/C][C]1[/C][C]0.671366961820235[/C][C]0.328633038179765[/C][/ROW]
[ROW][C]58[/C][C]3[/C][C]0.841720629706245[/C][C]2.15827937029375[/C][/ROW]
[ROW][C]59[/C][C]2[/C][C]1.96050895691981[/C][C]0.0394910430801922[/C][/ROW]
[ROW][C]60[/C][C]0[/C][C]1.98097994813426[/C][C]-1.98097994813426[/C][/ROW]
[ROW][C]61[/C][C]0[/C][C]0.954098408644267[/C][C]-0.954098408644267[/C][/ROW]
[ROW][C]62[/C][C]3[/C][C]0.459521952372548[/C][C]2.54047804762745[/C][/ROW]
[ROW][C]63[/C][C]-2[/C][C]1.77643079390081[/C][C]-3.77643079390081[/C][/ROW]
[ROW][C]64[/C][C]0[/C][C]-0.181159474022208[/C][C]0.181159474022208[/C][/ROW]
[ROW][C]65[/C][C]1[/C][C]-0.0872517493365899[/C][C]1.08725174933659[/C][/ROW]
[ROW][C]66[/C][C]-1[/C][C]0.47634746893085[/C][C]-1.47634746893085[/C][/ROW]
[ROW][C]67[/C][C]-2[/C][C]-0.288947486803409[/C][C]-1.71105251319659[/C][/ROW]
[ROW][C]68[/C][C]-1[/C][C]-1.17590661052113[/C][C]0.175906610521126[/C][/ROW]
[ROW][C]69[/C][C]-1[/C][C]-1.08472181524416[/C][C]0.0847218152441587[/C][/ROW]
[ROW][C]70[/C][C]1[/C][C]-1.04080452665765[/C][C]2.04080452665765[/C][/ROW]
[ROW][C]71[/C][C]-2[/C][C]0.0170883087070425[/C][C]-2.01708830870704[/C][/ROW]
[ROW][C]72[/C][C]-5[/C][C]-1.02851073922031[/C][C]-3.97148926077969[/C][/ROW]
[ROW][C]73[/C][C]-5[/C][C]-3.08721355951812[/C][C]-1.91278644048188[/C][/ROW]
[ROW][C]74[/C][C]-6[/C][C]-4.07874559726921[/C][C]-1.92125440273079[/C][/ROW]
[ROW][C]75[/C][C]-4[/C][C]-5.07466717673106[/C][C]1.07466717673106[/C][/ROW]
[ROW][C]76[/C][C]-3[/C][C]-4.51759142948772[/C][C]1.51759142948772[/C][/ROW]
[ROW][C]77[/C][C]-3[/C][C]-3.73091682185381[/C][C]0.73091682185381[/C][/ROW]
[ROW][C]78[/C][C]-1[/C][C]-3.35203111330776[/C][C]2.35203111330776[/C][/ROW]
[ROW][C]79[/C][C]-2[/C][C]-2.13280760080498[/C][C]0.132807600804978[/C][/ROW]
[ROW][C]80[/C][C]-3[/C][C]-2.06396406016287[/C][C]-0.936035939837133[/C][/ROW]
[ROW][C]81[/C][C]-3[/C][C]-2.54917746569138[/C][C]-0.450822534308623[/C][/ROW]
[ROW][C]82[/C][C]-3[/C][C]-2.78287056213268[/C][C]-0.217129437867325[/C][/ROW]
[ROW][C]83[/C][C]-5[/C][C]-2.8954240544766[/C][C]-2.1045759455234[/C][/ROW]
[ROW][C]84[/C][C]-5[/C][C]-3.98637411126445[/C][C]-1.01362588873555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232415&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232415&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
2660
356-1
455.48162951348542-0.481629513485417
535.2319669882602-2.2319669882602
654.074981174671270.92501882532873
754.554483633192070.445516366807928
854.785426169004510.214573830995493
934.89665491017094-1.89665491017094
1063.913484981635362.08651501836464
1164.995072786825021.00492721317498
1245.51599739523028-1.51599739523028
1364.730149087909921.26985091209008
1455.38840232301104-0.388402323011041
1545.18706602186841-1.18706602186841
1654.571726030587550.428273969412447
1754.793730616473410.206269383526585
1844.90065457716515-0.900654577165154
1934.43378182581847-1.43378182581847
2023.69055164321318-1.69055164321318
2132.814219565442740.185780434557265
2222.91052265968908-0.910522659689075
23-12.4385345856035-3.4385345856035
2400.65609973956699-0.65609973956699
25-20.315996998365558-2.31599699836556
261-0.8845474924435111.88454749244351
27-20.09234630807427-2.09234630807427
28-2-0.992264265599182-1.00773573440082
29-2-1.51464472851867-0.485355271481335
30-6-1.76623857672886-4.23376142327114
31-4-3.9608955454966-0.0391044545034025
32-2-3.981166140602411.98116614060241
330-2.954188084432122.95418808443212
34-5-1.42282416984946-3.57717583015054
35-4-3.2771265452728-0.722873454727197
36-5-3.65184280968822-1.34815719031178
37-1-4.350687708328273.35068770832827
38-2-2.613790090803710.61379009080371
39-4-2.29561942281596-1.70438057718404
40-1-3.179120011816862.17912001181686
411-2.049528511117693.04952851111769
421-0.4687429331695191.46874293316952
43-20.292610055662421-2.29261005566242
441-0.8958113342795351.89581133427953
4510.08692130941080950.913078690589191
4630.5602343544776272.43976564552237
4731.824936859128631.17506314087137
4812.43405491114747-1.43405491114747
4911.69068316916733-0.690683169167331
5001.33265339873863-1.33265339873863
5120.6418452080791721.35815479192083
5221.345872568329280.654127431670716
53-11.68495292332697-2.68495292332697
5410.2931525701932150.706847429806785
5500.659561416273741-0.659561416273741
5610.3176642440336740.682335755966326
5710.6713669618202350.328633038179765
5830.8417206297062452.15827937029375
5921.960508956919810.0394910430801922
6001.98097994813426-1.98097994813426
6100.954098408644267-0.954098408644267
6230.4595219523725482.54047804762745
63-21.77643079390081-3.77643079390081
640-0.1811594740222080.181159474022208
651-0.08725174933658991.08725174933659
66-10.47634746893085-1.47634746893085
67-2-0.288947486803409-1.71105251319659
68-1-1.175906610521130.175906610521126
69-1-1.084721815244160.0847218152441587
701-1.040804526657652.04080452665765
71-20.0170883087070425-2.01708830870704
72-5-1.02851073922031-3.97148926077969
73-5-3.08721355951812-1.91278644048188
74-6-4.07874559726921-1.92125440273079
75-4-5.074667176731061.07466717673106
76-3-4.517591429487721.51759142948772
77-3-3.730916821853810.73091682185381
78-1-3.352031113307762.35203111330776
79-2-2.132807600804980.132807600804978
80-3-2.06396406016287-0.936035939837133
81-3-2.54917746569138-0.450822534308623
82-3-2.78287056213268-0.217129437867325
83-5-2.8954240544766-2.1045759455234
84-5-3.98637411126445-1.01362588873555







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85-4.51180785635208-7.88719241766412-1.13642329504003
86-4.51180785635208-8.31373764360163-0.709878069102526
87-4.51180785635208-8.69703416774876-0.326581544955387
88-4.51180785635208-9.048058339740180.0244426270360334
89-4.51180785635208-9.373805143318670.350189430614523
90-4.51180785635208-9.679057297679860.655441584975708
91-4.51180785635208-9.967256138513130.943640425808979
92-4.51180785635208-10.24097578282851.21736007012431
93-4.51180785635208-10.50220135763371.47858564492958
94-4.51180785635208-10.75250200609451.72888629339034
95-4.51180785635208-10.99314357062121.96952785791708
96-4.51180785635208-11.22516482671292.20154911400877

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & -4.51180785635208 & -7.88719241766412 & -1.13642329504003 \tabularnewline
86 & -4.51180785635208 & -8.31373764360163 & -0.709878069102526 \tabularnewline
87 & -4.51180785635208 & -8.69703416774876 & -0.326581544955387 \tabularnewline
88 & -4.51180785635208 & -9.04805833974018 & 0.0244426270360334 \tabularnewline
89 & -4.51180785635208 & -9.37380514331867 & 0.350189430614523 \tabularnewline
90 & -4.51180785635208 & -9.67905729767986 & 0.655441584975708 \tabularnewline
91 & -4.51180785635208 & -9.96725613851313 & 0.943640425808979 \tabularnewline
92 & -4.51180785635208 & -10.2409757828285 & 1.21736007012431 \tabularnewline
93 & -4.51180785635208 & -10.5022013576337 & 1.47858564492958 \tabularnewline
94 & -4.51180785635208 & -10.7525020060945 & 1.72888629339034 \tabularnewline
95 & -4.51180785635208 & -10.9931435706212 & 1.96952785791708 \tabularnewline
96 & -4.51180785635208 & -11.2251648267129 & 2.20154911400877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232415&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]85[/C][C]-4.51180785635208[/C][C]-7.88719241766412[/C][C]-1.13642329504003[/C][/ROW]
[ROW][C]86[/C][C]-4.51180785635208[/C][C]-8.31373764360163[/C][C]-0.709878069102526[/C][/ROW]
[ROW][C]87[/C][C]-4.51180785635208[/C][C]-8.69703416774876[/C][C]-0.326581544955387[/C][/ROW]
[ROW][C]88[/C][C]-4.51180785635208[/C][C]-9.04805833974018[/C][C]0.0244426270360334[/C][/ROW]
[ROW][C]89[/C][C]-4.51180785635208[/C][C]-9.37380514331867[/C][C]0.350189430614523[/C][/ROW]
[ROW][C]90[/C][C]-4.51180785635208[/C][C]-9.67905729767986[/C][C]0.655441584975708[/C][/ROW]
[ROW][C]91[/C][C]-4.51180785635208[/C][C]-9.96725613851313[/C][C]0.943640425808979[/C][/ROW]
[ROW][C]92[/C][C]-4.51180785635208[/C][C]-10.2409757828285[/C][C]1.21736007012431[/C][/ROW]
[ROW][C]93[/C][C]-4.51180785635208[/C][C]-10.5022013576337[/C][C]1.47858564492958[/C][/ROW]
[ROW][C]94[/C][C]-4.51180785635208[/C][C]-10.7525020060945[/C][C]1.72888629339034[/C][/ROW]
[ROW][C]95[/C][C]-4.51180785635208[/C][C]-10.9931435706212[/C][C]1.96952785791708[/C][/ROW]
[ROW][C]96[/C][C]-4.51180785635208[/C][C]-11.2251648267129[/C][C]2.20154911400877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232415&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232415&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
85-4.51180785635208-7.88719241766412-1.13642329504003
86-4.51180785635208-8.31373764360163-0.709878069102526
87-4.51180785635208-8.69703416774876-0.326581544955387
88-4.51180785635208-9.048058339740180.0244426270360334
89-4.51180785635208-9.373805143318670.350189430614523
90-4.51180785635208-9.679057297679860.655441584975708
91-4.51180785635208-9.967256138513130.943640425808979
92-4.51180785635208-10.24097578282851.21736007012431
93-4.51180785635208-10.50220135763371.47858564492958
94-4.51180785635208-10.75250200609451.72888629339034
95-4.51180785635208-10.99314357062121.96952785791708
96-4.51180785635208-11.22516482671292.20154911400877



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')