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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 Nov 2015 20:35:27 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/24/t1448397399whxcp7amjropaxb.htm/, Retrieved Tue, 14 May 2024 01:41:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284062, Retrieved Tue, 14 May 2024 01:41:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 9 - 10 exp...] [2015-11-24 20:35:27] [c4e632f9a17048eeb9519d4e8ae83546] [Current]
- R P     [Exponential Smoothing] [oefening 10 kaas ...] [2015-12-14 19:30:35] [1625b1453ed47b256ce4b6eedb089cd5]
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Dataseries X:
79.58
80.08
80.41
80.34
80.32
80.39
81.01
81.54
82.48
84.68
88.26
90.6
92.46
93.31
93.58
93.92
93.92
93.67
93.76
93.95
93.89
94.07
93.93
93.35
93.58
93.55
93.44
93.38
93.17
92.95
93.37
94.13
94.07
94
94.47
94.81
94.18
94.14
93.96
93.23
93.13
92.51
92.49
92.73
92.75
92.83
92.85
93.27
93.98
94.34
94.57
94.62
94.82
95.07
95.72
96.06
96.54
96.38
96.8
97.02
97.29
97.45
97.95
97.69
97.63
97.35
97.38
98.06
98.34
98.53
98.79
98.77
99.2
99.76
99.84
99.83
99.88
99.48
99.66
99.58
99.89
100.7
101.19
100.99
101.52
101.75
101.56
102.57
102.66
102.62
102.76
102.73
102.26
101.72
101.48
100.93




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284062&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284062&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284062&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.980012676633916
beta0.795100345628685
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.980012676633916 \tabularnewline
beta & 0.795100345628685 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284062&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]0.980012676633916[/C][/ROW]
[ROW][C]beta[/C][C]0.795100345628685[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284062&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284062&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
alpha0.980012676633916
beta0.795100345628685
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392.4685.69873737846316.76126262153686
1493.3198.3810671858659-5.07106718586594
1593.5894.9819998749932-1.40199987499325
1693.9294.283340790946-0.363340790945955
1793.9294.2202746233055-0.300274623305512
1893.6794.0117320432311-0.341732043231104
1993.7691.6984694358312.06153056416899
2093.9595.1150386968585-1.16503869685855
2193.8994.9232492626437-1.03324926264372
2294.0795.4631715841306-1.39317158413058
2393.9395.9901064240372-2.06010642403719
2493.3592.78899472842060.561005271579361
2593.5892.2042922936571.37570770634299
2693.5592.12449579983981.42550420016022
2793.4493.00024834040770.439751659592346
2893.3893.4035992321237-0.0235992321236864
2993.1793.2216621512657-0.0516621512657309
3092.9592.9994144988734-0.0494144988734462
3193.3791.00504444071952.36495555928046
3294.1394.8589009826208-0.728900982620758
3394.0795.637023214252-1.56702321425205
349495.7749928261552-1.77499282615516
3594.4795.7357047862063-1.26570478620631
3694.8193.8211037860830.988896213916973
3794.1894.4745315661777-0.29453156617771
3894.1492.24494529802791.89505470197207
3993.9693.41317542805350.546824571946502
4093.2393.8492025930162-0.61920259301624
4193.1392.56323480282840.566765197171634
4292.5192.9088633218889-0.398863321888939
4392.4990.32644951035322.16355048964678
4492.7393.4706861148903-0.740686114890281
4592.7593.7563301465512-1.00633014655116
4692.8394.3917960868779-1.56179608687795
4792.8594.6781633574189-1.8281633574189
4893.2791.93083110321761.33916889678244
4993.9892.8560749025131.12392509748697
5094.3493.13019883527591.20980116472413
5194.5794.12943562842110.44056437157893
5294.6294.879834953718-0.259834953717998
5394.8294.68135429235140.138645707648593
5495.0794.96140928953150.108590710468533
5595.7293.62645834401172.09354165598835
5696.0697.3169121492627-1.25691214926267
5796.5497.3823305198403-0.842330519840317
5896.3898.647300071542-2.26730007154202
5996.898.2160410816152-1.41604108161523
6097.0296.19652835408470.823471645915262
6197.2996.44352838351520.846471616484791
6297.4596.01396466567281.43603533432722
6397.9596.95498327206150.995016727938548
6497.6998.4049327230073-0.714932723007294
6597.6397.58560054254420.0443994574557678
6697.3597.5191075748831-0.169107574883085
6797.3895.45628333927731.92371666072273
6898.0698.3296739533057-0.269673953305684
6998.3499.5675694256707-1.22756942567074
7098.53100.347517629397-1.81751762939747
7198.79100.69214181498-1.90214181497981
7298.7798.14711240842190.622887591578134
7399.297.92962043460741.2703795653926
7499.7697.96379901222471.79620098777534
7599.8499.55370680565860.286293194341411
7699.83100.034816340001-0.204816340001344
7799.8899.8855868893065-0.00558688930647122
7899.4899.8793938227143-0.399393822714273
7999.6697.53281750317882.12718249682116
8099.58100.647530172221-1.06753017222148
8199.89100.567674796702-0.677674796701822
82100.7101.807623028354-1.10762302835427
83101.19103.388483769753-2.19848376975318
84100.99100.8954089166020.0945910833980008
85101.52100.0331952052981.48680479470183
86101.75100.2868574110591.46314258894131
87101.56101.2534366218480.306563378151949
88102.57101.5001827496411.06981725035946
89102.66103.342441710597-0.682441710596919
90102.62102.872420619458-0.252420619458363
91102.76100.9813403644771.77865963552284
92102.73103.71925575172-0.989255751719597
93102.26103.838942678205-1.57894267820487
94101.72103.628243675533-1.9082436755335
95101.48103.18429146557-1.70429146557045
96100.93100.3489271891810.581072810818512

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 92.46 & 85.6987373784631 & 6.76126262153686 \tabularnewline
14 & 93.31 & 98.3810671858659 & -5.07106718586594 \tabularnewline
15 & 93.58 & 94.9819998749932 & -1.40199987499325 \tabularnewline
16 & 93.92 & 94.283340790946 & -0.363340790945955 \tabularnewline
17 & 93.92 & 94.2202746233055 & -0.300274623305512 \tabularnewline
18 & 93.67 & 94.0117320432311 & -0.341732043231104 \tabularnewline
19 & 93.76 & 91.698469435831 & 2.06153056416899 \tabularnewline
20 & 93.95 & 95.1150386968585 & -1.16503869685855 \tabularnewline
21 & 93.89 & 94.9232492626437 & -1.03324926264372 \tabularnewline
22 & 94.07 & 95.4631715841306 & -1.39317158413058 \tabularnewline
23 & 93.93 & 95.9901064240372 & -2.06010642403719 \tabularnewline
24 & 93.35 & 92.7889947284206 & 0.561005271579361 \tabularnewline
25 & 93.58 & 92.204292293657 & 1.37570770634299 \tabularnewline
26 & 93.55 & 92.1244957998398 & 1.42550420016022 \tabularnewline
27 & 93.44 & 93.0002483404077 & 0.439751659592346 \tabularnewline
28 & 93.38 & 93.4035992321237 & -0.0235992321236864 \tabularnewline
29 & 93.17 & 93.2216621512657 & -0.0516621512657309 \tabularnewline
30 & 92.95 & 92.9994144988734 & -0.0494144988734462 \tabularnewline
31 & 93.37 & 91.0050444407195 & 2.36495555928046 \tabularnewline
32 & 94.13 & 94.8589009826208 & -0.728900982620758 \tabularnewline
33 & 94.07 & 95.637023214252 & -1.56702321425205 \tabularnewline
34 & 94 & 95.7749928261552 & -1.77499282615516 \tabularnewline
35 & 94.47 & 95.7357047862063 & -1.26570478620631 \tabularnewline
36 & 94.81 & 93.821103786083 & 0.988896213916973 \tabularnewline
37 & 94.18 & 94.4745315661777 & -0.29453156617771 \tabularnewline
38 & 94.14 & 92.2449452980279 & 1.89505470197207 \tabularnewline
39 & 93.96 & 93.4131754280535 & 0.546824571946502 \tabularnewline
40 & 93.23 & 93.8492025930162 & -0.61920259301624 \tabularnewline
41 & 93.13 & 92.5632348028284 & 0.566765197171634 \tabularnewline
42 & 92.51 & 92.9088633218889 & -0.398863321888939 \tabularnewline
43 & 92.49 & 90.3264495103532 & 2.16355048964678 \tabularnewline
44 & 92.73 & 93.4706861148903 & -0.740686114890281 \tabularnewline
45 & 92.75 & 93.7563301465512 & -1.00633014655116 \tabularnewline
46 & 92.83 & 94.3917960868779 & -1.56179608687795 \tabularnewline
47 & 92.85 & 94.6781633574189 & -1.8281633574189 \tabularnewline
48 & 93.27 & 91.9308311032176 & 1.33916889678244 \tabularnewline
49 & 93.98 & 92.856074902513 & 1.12392509748697 \tabularnewline
50 & 94.34 & 93.1301988352759 & 1.20980116472413 \tabularnewline
51 & 94.57 & 94.1294356284211 & 0.44056437157893 \tabularnewline
52 & 94.62 & 94.879834953718 & -0.259834953717998 \tabularnewline
53 & 94.82 & 94.6813542923514 & 0.138645707648593 \tabularnewline
54 & 95.07 & 94.9614092895315 & 0.108590710468533 \tabularnewline
55 & 95.72 & 93.6264583440117 & 2.09354165598835 \tabularnewline
56 & 96.06 & 97.3169121492627 & -1.25691214926267 \tabularnewline
57 & 96.54 & 97.3823305198403 & -0.842330519840317 \tabularnewline
58 & 96.38 & 98.647300071542 & -2.26730007154202 \tabularnewline
59 & 96.8 & 98.2160410816152 & -1.41604108161523 \tabularnewline
60 & 97.02 & 96.1965283540847 & 0.823471645915262 \tabularnewline
61 & 97.29 & 96.4435283835152 & 0.846471616484791 \tabularnewline
62 & 97.45 & 96.0139646656728 & 1.43603533432722 \tabularnewline
63 & 97.95 & 96.9549832720615 & 0.995016727938548 \tabularnewline
64 & 97.69 & 98.4049327230073 & -0.714932723007294 \tabularnewline
65 & 97.63 & 97.5856005425442 & 0.0443994574557678 \tabularnewline
66 & 97.35 & 97.5191075748831 & -0.169107574883085 \tabularnewline
67 & 97.38 & 95.4562833392773 & 1.92371666072273 \tabularnewline
68 & 98.06 & 98.3296739533057 & -0.269673953305684 \tabularnewline
69 & 98.34 & 99.5675694256707 & -1.22756942567074 \tabularnewline
70 & 98.53 & 100.347517629397 & -1.81751762939747 \tabularnewline
71 & 98.79 & 100.69214181498 & -1.90214181497981 \tabularnewline
72 & 98.77 & 98.1471124084219 & 0.622887591578134 \tabularnewline
73 & 99.2 & 97.9296204346074 & 1.2703795653926 \tabularnewline
74 & 99.76 & 97.9637990122247 & 1.79620098777534 \tabularnewline
75 & 99.84 & 99.5537068056586 & 0.286293194341411 \tabularnewline
76 & 99.83 & 100.034816340001 & -0.204816340001344 \tabularnewline
77 & 99.88 & 99.8855868893065 & -0.00558688930647122 \tabularnewline
78 & 99.48 & 99.8793938227143 & -0.399393822714273 \tabularnewline
79 & 99.66 & 97.5328175031788 & 2.12718249682116 \tabularnewline
80 & 99.58 & 100.647530172221 & -1.06753017222148 \tabularnewline
81 & 99.89 & 100.567674796702 & -0.677674796701822 \tabularnewline
82 & 100.7 & 101.807623028354 & -1.10762302835427 \tabularnewline
83 & 101.19 & 103.388483769753 & -2.19848376975318 \tabularnewline
84 & 100.99 & 100.895408916602 & 0.0945910833980008 \tabularnewline
85 & 101.52 & 100.033195205298 & 1.48680479470183 \tabularnewline
86 & 101.75 & 100.286857411059 & 1.46314258894131 \tabularnewline
87 & 101.56 & 101.253436621848 & 0.306563378151949 \tabularnewline
88 & 102.57 & 101.500182749641 & 1.06981725035946 \tabularnewline
89 & 102.66 & 103.342441710597 & -0.682441710596919 \tabularnewline
90 & 102.62 & 102.872420619458 & -0.252420619458363 \tabularnewline
91 & 102.76 & 100.981340364477 & 1.77865963552284 \tabularnewline
92 & 102.73 & 103.71925575172 & -0.989255751719597 \tabularnewline
93 & 102.26 & 103.838942678205 & -1.57894267820487 \tabularnewline
94 & 101.72 & 103.628243675533 & -1.9082436755335 \tabularnewline
95 & 101.48 & 103.18429146557 & -1.70429146557045 \tabularnewline
96 & 100.93 & 100.348927189181 & 0.581072810818512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284062&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]13[/C][C]92.46[/C][C]85.6987373784631[/C][C]6.76126262153686[/C][/ROW]
[ROW][C]14[/C][C]93.31[/C][C]98.3810671858659[/C][C]-5.07106718586594[/C][/ROW]
[ROW][C]15[/C][C]93.58[/C][C]94.9819998749932[/C][C]-1.40199987499325[/C][/ROW]
[ROW][C]16[/C][C]93.92[/C][C]94.283340790946[/C][C]-0.363340790945955[/C][/ROW]
[ROW][C]17[/C][C]93.92[/C][C]94.2202746233055[/C][C]-0.300274623305512[/C][/ROW]
[ROW][C]18[/C][C]93.67[/C][C]94.0117320432311[/C][C]-0.341732043231104[/C][/ROW]
[ROW][C]19[/C][C]93.76[/C][C]91.698469435831[/C][C]2.06153056416899[/C][/ROW]
[ROW][C]20[/C][C]93.95[/C][C]95.1150386968585[/C][C]-1.16503869685855[/C][/ROW]
[ROW][C]21[/C][C]93.89[/C][C]94.9232492626437[/C][C]-1.03324926264372[/C][/ROW]
[ROW][C]22[/C][C]94.07[/C][C]95.4631715841306[/C][C]-1.39317158413058[/C][/ROW]
[ROW][C]23[/C][C]93.93[/C][C]95.9901064240372[/C][C]-2.06010642403719[/C][/ROW]
[ROW][C]24[/C][C]93.35[/C][C]92.7889947284206[/C][C]0.561005271579361[/C][/ROW]
[ROW][C]25[/C][C]93.58[/C][C]92.204292293657[/C][C]1.37570770634299[/C][/ROW]
[ROW][C]26[/C][C]93.55[/C][C]92.1244957998398[/C][C]1.42550420016022[/C][/ROW]
[ROW][C]27[/C][C]93.44[/C][C]93.0002483404077[/C][C]0.439751659592346[/C][/ROW]
[ROW][C]28[/C][C]93.38[/C][C]93.4035992321237[/C][C]-0.0235992321236864[/C][/ROW]
[ROW][C]29[/C][C]93.17[/C][C]93.2216621512657[/C][C]-0.0516621512657309[/C][/ROW]
[ROW][C]30[/C][C]92.95[/C][C]92.9994144988734[/C][C]-0.0494144988734462[/C][/ROW]
[ROW][C]31[/C][C]93.37[/C][C]91.0050444407195[/C][C]2.36495555928046[/C][/ROW]
[ROW][C]32[/C][C]94.13[/C][C]94.8589009826208[/C][C]-0.728900982620758[/C][/ROW]
[ROW][C]33[/C][C]94.07[/C][C]95.637023214252[/C][C]-1.56702321425205[/C][/ROW]
[ROW][C]34[/C][C]94[/C][C]95.7749928261552[/C][C]-1.77499282615516[/C][/ROW]
[ROW][C]35[/C][C]94.47[/C][C]95.7357047862063[/C][C]-1.26570478620631[/C][/ROW]
[ROW][C]36[/C][C]94.81[/C][C]93.821103786083[/C][C]0.988896213916973[/C][/ROW]
[ROW][C]37[/C][C]94.18[/C][C]94.4745315661777[/C][C]-0.29453156617771[/C][/ROW]
[ROW][C]38[/C][C]94.14[/C][C]92.2449452980279[/C][C]1.89505470197207[/C][/ROW]
[ROW][C]39[/C][C]93.96[/C][C]93.4131754280535[/C][C]0.546824571946502[/C][/ROW]
[ROW][C]40[/C][C]93.23[/C][C]93.8492025930162[/C][C]-0.61920259301624[/C][/ROW]
[ROW][C]41[/C][C]93.13[/C][C]92.5632348028284[/C][C]0.566765197171634[/C][/ROW]
[ROW][C]42[/C][C]92.51[/C][C]92.9088633218889[/C][C]-0.398863321888939[/C][/ROW]
[ROW][C]43[/C][C]92.49[/C][C]90.3264495103532[/C][C]2.16355048964678[/C][/ROW]
[ROW][C]44[/C][C]92.73[/C][C]93.4706861148903[/C][C]-0.740686114890281[/C][/ROW]
[ROW][C]45[/C][C]92.75[/C][C]93.7563301465512[/C][C]-1.00633014655116[/C][/ROW]
[ROW][C]46[/C][C]92.83[/C][C]94.3917960868779[/C][C]-1.56179608687795[/C][/ROW]
[ROW][C]47[/C][C]92.85[/C][C]94.6781633574189[/C][C]-1.8281633574189[/C][/ROW]
[ROW][C]48[/C][C]93.27[/C][C]91.9308311032176[/C][C]1.33916889678244[/C][/ROW]
[ROW][C]49[/C][C]93.98[/C][C]92.856074902513[/C][C]1.12392509748697[/C][/ROW]
[ROW][C]50[/C][C]94.34[/C][C]93.1301988352759[/C][C]1.20980116472413[/C][/ROW]
[ROW][C]51[/C][C]94.57[/C][C]94.1294356284211[/C][C]0.44056437157893[/C][/ROW]
[ROW][C]52[/C][C]94.62[/C][C]94.879834953718[/C][C]-0.259834953717998[/C][/ROW]
[ROW][C]53[/C][C]94.82[/C][C]94.6813542923514[/C][C]0.138645707648593[/C][/ROW]
[ROW][C]54[/C][C]95.07[/C][C]94.9614092895315[/C][C]0.108590710468533[/C][/ROW]
[ROW][C]55[/C][C]95.72[/C][C]93.6264583440117[/C][C]2.09354165598835[/C][/ROW]
[ROW][C]56[/C][C]96.06[/C][C]97.3169121492627[/C][C]-1.25691214926267[/C][/ROW]
[ROW][C]57[/C][C]96.54[/C][C]97.3823305198403[/C][C]-0.842330519840317[/C][/ROW]
[ROW][C]58[/C][C]96.38[/C][C]98.647300071542[/C][C]-2.26730007154202[/C][/ROW]
[ROW][C]59[/C][C]96.8[/C][C]98.2160410816152[/C][C]-1.41604108161523[/C][/ROW]
[ROW][C]60[/C][C]97.02[/C][C]96.1965283540847[/C][C]0.823471645915262[/C][/ROW]
[ROW][C]61[/C][C]97.29[/C][C]96.4435283835152[/C][C]0.846471616484791[/C][/ROW]
[ROW][C]62[/C][C]97.45[/C][C]96.0139646656728[/C][C]1.43603533432722[/C][/ROW]
[ROW][C]63[/C][C]97.95[/C][C]96.9549832720615[/C][C]0.995016727938548[/C][/ROW]
[ROW][C]64[/C][C]97.69[/C][C]98.4049327230073[/C][C]-0.714932723007294[/C][/ROW]
[ROW][C]65[/C][C]97.63[/C][C]97.5856005425442[/C][C]0.0443994574557678[/C][/ROW]
[ROW][C]66[/C][C]97.35[/C][C]97.5191075748831[/C][C]-0.169107574883085[/C][/ROW]
[ROW][C]67[/C][C]97.38[/C][C]95.4562833392773[/C][C]1.92371666072273[/C][/ROW]
[ROW][C]68[/C][C]98.06[/C][C]98.3296739533057[/C][C]-0.269673953305684[/C][/ROW]
[ROW][C]69[/C][C]98.34[/C][C]99.5675694256707[/C][C]-1.22756942567074[/C][/ROW]
[ROW][C]70[/C][C]98.53[/C][C]100.347517629397[/C][C]-1.81751762939747[/C][/ROW]
[ROW][C]71[/C][C]98.79[/C][C]100.69214181498[/C][C]-1.90214181497981[/C][/ROW]
[ROW][C]72[/C][C]98.77[/C][C]98.1471124084219[/C][C]0.622887591578134[/C][/ROW]
[ROW][C]73[/C][C]99.2[/C][C]97.9296204346074[/C][C]1.2703795653926[/C][/ROW]
[ROW][C]74[/C][C]99.76[/C][C]97.9637990122247[/C][C]1.79620098777534[/C][/ROW]
[ROW][C]75[/C][C]99.84[/C][C]99.5537068056586[/C][C]0.286293194341411[/C][/ROW]
[ROW][C]76[/C][C]99.83[/C][C]100.034816340001[/C][C]-0.204816340001344[/C][/ROW]
[ROW][C]77[/C][C]99.88[/C][C]99.8855868893065[/C][C]-0.00558688930647122[/C][/ROW]
[ROW][C]78[/C][C]99.48[/C][C]99.8793938227143[/C][C]-0.399393822714273[/C][/ROW]
[ROW][C]79[/C][C]99.66[/C][C]97.5328175031788[/C][C]2.12718249682116[/C][/ROW]
[ROW][C]80[/C][C]99.58[/C][C]100.647530172221[/C][C]-1.06753017222148[/C][/ROW]
[ROW][C]81[/C][C]99.89[/C][C]100.567674796702[/C][C]-0.677674796701822[/C][/ROW]
[ROW][C]82[/C][C]100.7[/C][C]101.807623028354[/C][C]-1.10762302835427[/C][/ROW]
[ROW][C]83[/C][C]101.19[/C][C]103.388483769753[/C][C]-2.19848376975318[/C][/ROW]
[ROW][C]84[/C][C]100.99[/C][C]100.895408916602[/C][C]0.0945910833980008[/C][/ROW]
[ROW][C]85[/C][C]101.52[/C][C]100.033195205298[/C][C]1.48680479470183[/C][/ROW]
[ROW][C]86[/C][C]101.75[/C][C]100.286857411059[/C][C]1.46314258894131[/C][/ROW]
[ROW][C]87[/C][C]101.56[/C][C]101.253436621848[/C][C]0.306563378151949[/C][/ROW]
[ROW][C]88[/C][C]102.57[/C][C]101.500182749641[/C][C]1.06981725035946[/C][/ROW]
[ROW][C]89[/C][C]102.66[/C][C]103.342441710597[/C][C]-0.682441710596919[/C][/ROW]
[ROW][C]90[/C][C]102.62[/C][C]102.872420619458[/C][C]-0.252420619458363[/C][/ROW]
[ROW][C]91[/C][C]102.76[/C][C]100.981340364477[/C][C]1.77865963552284[/C][/ROW]
[ROW][C]92[/C][C]102.73[/C][C]103.71925575172[/C][C]-0.989255751719597[/C][/ROW]
[ROW][C]93[/C][C]102.26[/C][C]103.838942678205[/C][C]-1.57894267820487[/C][/ROW]
[ROW][C]94[/C][C]101.72[/C][C]103.628243675533[/C][C]-1.9082436755335[/C][/ROW]
[ROW][C]95[/C][C]101.48[/C][C]103.18429146557[/C][C]-1.70429146557045[/C][/ROW]
[ROW][C]96[/C][C]100.93[/C][C]100.348927189181[/C][C]0.581072810818512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284062&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284062&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
1392.4685.69873737846316.76126262153686
1493.3198.3810671858659-5.07106718586594
1593.5894.9819998749932-1.40199987499325
1693.9294.283340790946-0.363340790945955
1793.9294.2202746233055-0.300274623305512
1893.6794.0117320432311-0.341732043231104
1993.7691.6984694358312.06153056416899
2093.9595.1150386968585-1.16503869685855
2193.8994.9232492626437-1.03324926264372
2294.0795.4631715841306-1.39317158413058
2393.9395.9901064240372-2.06010642403719
2493.3592.78899472842060.561005271579361
2593.5892.2042922936571.37570770634299
2693.5592.12449579983981.42550420016022
2793.4493.00024834040770.439751659592346
2893.3893.4035992321237-0.0235992321236864
2993.1793.2216621512657-0.0516621512657309
3092.9592.9994144988734-0.0494144988734462
3193.3791.00504444071952.36495555928046
3294.1394.8589009826208-0.728900982620758
3394.0795.637023214252-1.56702321425205
349495.7749928261552-1.77499282615516
3594.4795.7357047862063-1.26570478620631
3694.8193.8211037860830.988896213916973
3794.1894.4745315661777-0.29453156617771
3894.1492.24494529802791.89505470197207
3993.9693.41317542805350.546824571946502
4093.2393.8492025930162-0.61920259301624
4193.1392.56323480282840.566765197171634
4292.5192.9088633218889-0.398863321888939
4392.4990.32644951035322.16355048964678
4492.7393.4706861148903-0.740686114890281
4592.7593.7563301465512-1.00633014655116
4692.8394.3917960868779-1.56179608687795
4792.8594.6781633574189-1.8281633574189
4893.2791.93083110321761.33916889678244
4993.9892.8560749025131.12392509748697
5094.3493.13019883527591.20980116472413
5194.5794.12943562842110.44056437157893
5294.6294.879834953718-0.259834953717998
5394.8294.68135429235140.138645707648593
5495.0794.96140928953150.108590710468533
5595.7293.62645834401172.09354165598835
5696.0697.3169121492627-1.25691214926267
5796.5497.3823305198403-0.842330519840317
5896.3898.647300071542-2.26730007154202
5996.898.2160410816152-1.41604108161523
6097.0296.19652835408470.823471645915262
6197.2996.44352838351520.846471616484791
6297.4596.01396466567281.43603533432722
6397.9596.95498327206150.995016727938548
6497.6998.4049327230073-0.714932723007294
6597.6397.58560054254420.0443994574557678
6697.3597.5191075748831-0.169107574883085
6797.3895.45628333927731.92371666072273
6898.0698.3296739533057-0.269673953305684
6998.3499.5675694256707-1.22756942567074
7098.53100.347517629397-1.81751762939747
7198.79100.69214181498-1.90214181497981
7298.7798.14711240842190.622887591578134
7399.297.92962043460741.2703795653926
7499.7697.96379901222471.79620098777534
7599.8499.55370680565860.286293194341411
7699.83100.034816340001-0.204816340001344
7799.8899.8855868893065-0.00558688930647122
7899.4899.8793938227143-0.399393822714273
7999.6697.53281750317882.12718249682116
8099.58100.647530172221-1.06753017222148
8199.89100.567674796702-0.677674796701822
82100.7101.807623028354-1.10762302835427
83101.19103.388483769753-2.19848376975318
84100.99100.8954089166020.0945910833980008
85101.52100.0331952052981.48680479470183
86101.75100.2868574110591.46314258894131
87101.56101.2534366218480.306563378151949
88102.57101.5001827496411.06981725035946
89102.66103.342441710597-0.682441710596919
90102.62102.872420619458-0.252420619458363
91102.76100.9813403644771.77865963552284
92102.73103.71925575172-0.989255751719597
93102.26103.838942678205-1.57894267820487
94101.72103.628243675533-1.9082436755335
95101.48103.18429146557-1.70429146557045
96100.93100.3489271891810.581072810818512







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9799.486426796961696.4804404980412102.492413095882
9896.635410623409390.5723340381474102.698487208671
9993.415949588267183.7576420596966103.074257116838
10090.436826517761776.6931990490108104.180453986513
10187.473996200238669.2332415105596105.714750889918
10284.535179907548661.4331911460359107.637168669061
10380.350979099370752.4975924288422108.204365769899
10477.20877155642644.0759398727755110.341603240076
10574.78882845313235.7985829697589113.779073936505
10673.427962363199527.6154427501885119.240481976211
10773.164068457125519.2015918755795127.126545038671
10872.01096175760539.91863302354977134.103290491661

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 99.4864267969616 & 96.4804404980412 & 102.492413095882 \tabularnewline
98 & 96.6354106234093 & 90.5723340381474 & 102.698487208671 \tabularnewline
99 & 93.4159495882671 & 83.7576420596966 & 103.074257116838 \tabularnewline
100 & 90.4368265177617 & 76.6931990490108 & 104.180453986513 \tabularnewline
101 & 87.4739962002386 & 69.2332415105596 & 105.714750889918 \tabularnewline
102 & 84.5351799075486 & 61.4331911460359 & 107.637168669061 \tabularnewline
103 & 80.3509790993707 & 52.4975924288422 & 108.204365769899 \tabularnewline
104 & 77.208771556426 & 44.0759398727755 & 110.341603240076 \tabularnewline
105 & 74.788828453132 & 35.7985829697589 & 113.779073936505 \tabularnewline
106 & 73.4279623631995 & 27.6154427501885 & 119.240481976211 \tabularnewline
107 & 73.1640684571255 & 19.2015918755795 & 127.126545038671 \tabularnewline
108 & 72.0109617576053 & 9.91863302354977 & 134.103290491661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284062&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]97[/C][C]99.4864267969616[/C][C]96.4804404980412[/C][C]102.492413095882[/C][/ROW]
[ROW][C]98[/C][C]96.6354106234093[/C][C]90.5723340381474[/C][C]102.698487208671[/C][/ROW]
[ROW][C]99[/C][C]93.4159495882671[/C][C]83.7576420596966[/C][C]103.074257116838[/C][/ROW]
[ROW][C]100[/C][C]90.4368265177617[/C][C]76.6931990490108[/C][C]104.180453986513[/C][/ROW]
[ROW][C]101[/C][C]87.4739962002386[/C][C]69.2332415105596[/C][C]105.714750889918[/C][/ROW]
[ROW][C]102[/C][C]84.5351799075486[/C][C]61.4331911460359[/C][C]107.637168669061[/C][/ROW]
[ROW][C]103[/C][C]80.3509790993707[/C][C]52.4975924288422[/C][C]108.204365769899[/C][/ROW]
[ROW][C]104[/C][C]77.208771556426[/C][C]44.0759398727755[/C][C]110.341603240076[/C][/ROW]
[ROW][C]105[/C][C]74.788828453132[/C][C]35.7985829697589[/C][C]113.779073936505[/C][/ROW]
[ROW][C]106[/C][C]73.4279623631995[/C][C]27.6154427501885[/C][C]119.240481976211[/C][/ROW]
[ROW][C]107[/C][C]73.1640684571255[/C][C]19.2015918755795[/C][C]127.126545038671[/C][/ROW]
[ROW][C]108[/C][C]72.0109617576053[/C][C]9.91863302354977[/C][C]134.103290491661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284062&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284062&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
9799.486426796961696.4804404980412102.492413095882
9896.635410623409390.5723340381474102.698487208671
9993.415949588267183.7576420596966103.074257116838
10090.436826517761776.6931990490108104.180453986513
10187.473996200238669.2332415105596105.714750889918
10284.535179907548661.4331911460359107.637168669061
10380.350979099370752.4975924288422108.204365769899
10477.20877155642644.0759398727755110.341603240076
10574.78882845313235.7985829697589113.779073936505
10673.427962363199527.6154427501885119.240481976211
10773.164068457125519.2015918755795127.126545038671
10872.01096175760539.91863302354977134.103290491661



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')