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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Dec 2011 13:07:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324577271a22w1cogkydfhkf.htm/, Retrieved Fri, 03 May 2024 07:55:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159801, Retrieved Fri, 03 May 2024 07:55:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD    [Exponential Smoothing] [] [2011-12-22 18:07:32] [aedc5b8e4f26bdca34b1a0cf88d6dfa2] [Current]
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Dataseries X:
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.249
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.202
1.2271
1.277
1.265
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227
1.4684
1.457
1.4718
1.4748
1.5527
1.575
1.5557
1.5553
1.577
1.4975
1.437
1.3322
1.2732
1.3449
1.3239
1.2785
1.305
1.319
1.365
1.4016
1.4088
1.4268
1.4562
1.4816
1.4914
1.4614
1.4272
1.3686
1.3569
1.3406
1.2565
1.2208
1.277
1.2894
1.3067
1.3898
1.3661
1.322
1.336
1.3649
1.3999
1.4442
1.4349
1.4388
1.4264
1.4343
1.377
1.3706
1.3556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159801&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159801&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0.119119104612608

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.119119104612608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159801&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[/C][/ROW]
[ROW][C]gamma[/C][C]0.119119104612608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159801&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159801&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
gamma0.119119104612608







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.31191.286672783119660.0252272168803418
141.30141.30306959498835-0.00166959498834518
151.32011.32065709498834-0.000557094988344886
161.29381.29681959498834-0.00301959498834492
171.26941.27759876165501-0.0081987616550121
181.21651.22918626165501-0.0126862616550116
191.20371.23359876165501-0.0298987616550117
201.22921.192257094988350.0369429050116548
211.22561.22915292832168-0.00355292832167819
221.20151.24611542832168-0.0446154283216784
231.17861.24596542832168-0.0673654283216785
241.18561.21852376165501-0.032923761655012
251.21031.158740428321680.0515595716783215
261.19381.20146959498834-0.00766959498834496
271.2021.21305709498835-0.0110570949883451
281.22711.178719594988340.0483804050116552
291.2771.210898761655010.0661012383449877
301.2651.236786261655010.0282137383449885
311.26841.28209876165501-0.0136987616550117
321.28111.256957094988350.0241429050116546
331.27271.28105292832168-0.00835292832167811
341.26111.29321542832168-0.0321154283216782
351.28811.30556542832168-0.0174654283216786
361.32131.32802376165501-0.00672376165501198
371.29991.294440428321680.00545957167832167
381.30741.291069594988350.0163304050116548
391.32421.32665709498834-0.0024570949883449
401.35161.300919594988340.0506804050116549
411.35111.335398761655010.0157012383449879
421.34191.310886261655010.0310137383449887
431.37161.358998761655010.0126012383449881
441.36221.360157094988350.00204290501165483
451.38961.362152928321680.0274470716783217
461.42271.410115428321680.0125845716783217
471.46841.467165428321680.00123457167832131
481.4571.50832376165501-0.0513237616550117
491.47181.430140428321680.0416595716783215
501.47481.462969594988350.0118304050116551
511.55271.494057094988350.0586429050116548
521.5751.529419594988340.0455804050116551
531.55571.55879876165501-0.00309876165501199
541.55531.515486261655010.0398137383449884
551.5771.572398761655010.00460123834498827
561.49751.56555709498835-0.0680570949883452
571.4371.49745292832168-0.0604529283216781
581.33221.45751542832168-0.125315428321678
591.27321.37666542832168-0.103465428321678
601.34491.313123761655010.031776238344988
611.32391.318040428321680.00585957167832163
621.27851.31506959498835-0.0365695949883451
631.3051.297757094988350.00724290501165492
641.3191.281719594988340.0372804050116551
651.3651.302798761655010.0622012383449879
661.40161.324786261655010.0768137383449885
671.40881.41869876165501-0.00989876165501169
681.42681.397357094988350.0294429050116547
691.45621.426752928321680.0294470716783217
701.48161.476715428321680.00488457167832168
711.49141.52606542832168-0.0346654283216785
721.46141.53132376165501-0.0699237616550119
731.42721.43454042832168-0.00734042832167847
741.36861.41836959498835-0.049769594988345
751.35691.38785709498835-0.0309570949883451
761.34061.333619594988340.00698040501165509
771.25651.32439876165501-0.0678987616550122
781.22081.216286261655010.00451373834498869
791.2771.237898761655010.039101238344988
801.28941.265557094988350.0238429050116549
811.30671.289352928321680.0173470716783217
821.38981.327215428321680.0625845716783215
831.36611.43426542832168-0.0681654283216784
841.3221.40602376165501-0.0840237616550119
851.3361.295140428321680.0408595716783215
861.36491.327169594988350.0377304050116549
871.39991.384157094988350.0157429050116549
881.44421.376619594988340.0675804050116551
891.43491.427998761655010.00690123834498801
901.43881.394686261655010.0441137383449886
911.42641.45589876165501-0.029498761655012
921.43431.414957094988350.0193429050116547
931.3771.43425292832168-0.0572529283216781
941.37061.39751542832168-0.0269154283216784
951.35561.41506542832168-0.0594654283216787

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.3119 & 1.28667278311966 & 0.0252272168803418 \tabularnewline
14 & 1.3014 & 1.30306959498835 & -0.00166959498834518 \tabularnewline
15 & 1.3201 & 1.32065709498834 & -0.000557094988344886 \tabularnewline
16 & 1.2938 & 1.29681959498834 & -0.00301959498834492 \tabularnewline
17 & 1.2694 & 1.27759876165501 & -0.0081987616550121 \tabularnewline
18 & 1.2165 & 1.22918626165501 & -0.0126862616550116 \tabularnewline
19 & 1.2037 & 1.23359876165501 & -0.0298987616550117 \tabularnewline
20 & 1.2292 & 1.19225709498835 & 0.0369429050116548 \tabularnewline
21 & 1.2256 & 1.22915292832168 & -0.00355292832167819 \tabularnewline
22 & 1.2015 & 1.24611542832168 & -0.0446154283216784 \tabularnewline
23 & 1.1786 & 1.24596542832168 & -0.0673654283216785 \tabularnewline
24 & 1.1856 & 1.21852376165501 & -0.032923761655012 \tabularnewline
25 & 1.2103 & 1.15874042832168 & 0.0515595716783215 \tabularnewline
26 & 1.1938 & 1.20146959498834 & -0.00766959498834496 \tabularnewline
27 & 1.202 & 1.21305709498835 & -0.0110570949883451 \tabularnewline
28 & 1.2271 & 1.17871959498834 & 0.0483804050116552 \tabularnewline
29 & 1.277 & 1.21089876165501 & 0.0661012383449877 \tabularnewline
30 & 1.265 & 1.23678626165501 & 0.0282137383449885 \tabularnewline
31 & 1.2684 & 1.28209876165501 & -0.0136987616550117 \tabularnewline
32 & 1.2811 & 1.25695709498835 & 0.0241429050116546 \tabularnewline
33 & 1.2727 & 1.28105292832168 & -0.00835292832167811 \tabularnewline
34 & 1.2611 & 1.29321542832168 & -0.0321154283216782 \tabularnewline
35 & 1.2881 & 1.30556542832168 & -0.0174654283216786 \tabularnewline
36 & 1.3213 & 1.32802376165501 & -0.00672376165501198 \tabularnewline
37 & 1.2999 & 1.29444042832168 & 0.00545957167832167 \tabularnewline
38 & 1.3074 & 1.29106959498835 & 0.0163304050116548 \tabularnewline
39 & 1.3242 & 1.32665709498834 & -0.0024570949883449 \tabularnewline
40 & 1.3516 & 1.30091959498834 & 0.0506804050116549 \tabularnewline
41 & 1.3511 & 1.33539876165501 & 0.0157012383449879 \tabularnewline
42 & 1.3419 & 1.31088626165501 & 0.0310137383449887 \tabularnewline
43 & 1.3716 & 1.35899876165501 & 0.0126012383449881 \tabularnewline
44 & 1.3622 & 1.36015709498835 & 0.00204290501165483 \tabularnewline
45 & 1.3896 & 1.36215292832168 & 0.0274470716783217 \tabularnewline
46 & 1.4227 & 1.41011542832168 & 0.0125845716783217 \tabularnewline
47 & 1.4684 & 1.46716542832168 & 0.00123457167832131 \tabularnewline
48 & 1.457 & 1.50832376165501 & -0.0513237616550117 \tabularnewline
49 & 1.4718 & 1.43014042832168 & 0.0416595716783215 \tabularnewline
50 & 1.4748 & 1.46296959498835 & 0.0118304050116551 \tabularnewline
51 & 1.5527 & 1.49405709498835 & 0.0586429050116548 \tabularnewline
52 & 1.575 & 1.52941959498834 & 0.0455804050116551 \tabularnewline
53 & 1.5557 & 1.55879876165501 & -0.00309876165501199 \tabularnewline
54 & 1.5553 & 1.51548626165501 & 0.0398137383449884 \tabularnewline
55 & 1.577 & 1.57239876165501 & 0.00460123834498827 \tabularnewline
56 & 1.4975 & 1.56555709498835 & -0.0680570949883452 \tabularnewline
57 & 1.437 & 1.49745292832168 & -0.0604529283216781 \tabularnewline
58 & 1.3322 & 1.45751542832168 & -0.125315428321678 \tabularnewline
59 & 1.2732 & 1.37666542832168 & -0.103465428321678 \tabularnewline
60 & 1.3449 & 1.31312376165501 & 0.031776238344988 \tabularnewline
61 & 1.3239 & 1.31804042832168 & 0.00585957167832163 \tabularnewline
62 & 1.2785 & 1.31506959498835 & -0.0365695949883451 \tabularnewline
63 & 1.305 & 1.29775709498835 & 0.00724290501165492 \tabularnewline
64 & 1.319 & 1.28171959498834 & 0.0372804050116551 \tabularnewline
65 & 1.365 & 1.30279876165501 & 0.0622012383449879 \tabularnewline
66 & 1.4016 & 1.32478626165501 & 0.0768137383449885 \tabularnewline
67 & 1.4088 & 1.41869876165501 & -0.00989876165501169 \tabularnewline
68 & 1.4268 & 1.39735709498835 & 0.0294429050116547 \tabularnewline
69 & 1.4562 & 1.42675292832168 & 0.0294470716783217 \tabularnewline
70 & 1.4816 & 1.47671542832168 & 0.00488457167832168 \tabularnewline
71 & 1.4914 & 1.52606542832168 & -0.0346654283216785 \tabularnewline
72 & 1.4614 & 1.53132376165501 & -0.0699237616550119 \tabularnewline
73 & 1.4272 & 1.43454042832168 & -0.00734042832167847 \tabularnewline
74 & 1.3686 & 1.41836959498835 & -0.049769594988345 \tabularnewline
75 & 1.3569 & 1.38785709498835 & -0.0309570949883451 \tabularnewline
76 & 1.3406 & 1.33361959498834 & 0.00698040501165509 \tabularnewline
77 & 1.2565 & 1.32439876165501 & -0.0678987616550122 \tabularnewline
78 & 1.2208 & 1.21628626165501 & 0.00451373834498869 \tabularnewline
79 & 1.277 & 1.23789876165501 & 0.039101238344988 \tabularnewline
80 & 1.2894 & 1.26555709498835 & 0.0238429050116549 \tabularnewline
81 & 1.3067 & 1.28935292832168 & 0.0173470716783217 \tabularnewline
82 & 1.3898 & 1.32721542832168 & 0.0625845716783215 \tabularnewline
83 & 1.3661 & 1.43426542832168 & -0.0681654283216784 \tabularnewline
84 & 1.322 & 1.40602376165501 & -0.0840237616550119 \tabularnewline
85 & 1.336 & 1.29514042832168 & 0.0408595716783215 \tabularnewline
86 & 1.3649 & 1.32716959498835 & 0.0377304050116549 \tabularnewline
87 & 1.3999 & 1.38415709498835 & 0.0157429050116549 \tabularnewline
88 & 1.4442 & 1.37661959498834 & 0.0675804050116551 \tabularnewline
89 & 1.4349 & 1.42799876165501 & 0.00690123834498801 \tabularnewline
90 & 1.4388 & 1.39468626165501 & 0.0441137383449886 \tabularnewline
91 & 1.4264 & 1.45589876165501 & -0.029498761655012 \tabularnewline
92 & 1.4343 & 1.41495709498835 & 0.0193429050116547 \tabularnewline
93 & 1.377 & 1.43425292832168 & -0.0572529283216781 \tabularnewline
94 & 1.3706 & 1.39751542832168 & -0.0269154283216784 \tabularnewline
95 & 1.3556 & 1.41506542832168 & -0.0594654283216787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159801&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]1.3119[/C][C]1.28667278311966[/C][C]0.0252272168803418[/C][/ROW]
[ROW][C]14[/C][C]1.3014[/C][C]1.30306959498835[/C][C]-0.00166959498834518[/C][/ROW]
[ROW][C]15[/C][C]1.3201[/C][C]1.32065709498834[/C][C]-0.000557094988344886[/C][/ROW]
[ROW][C]16[/C][C]1.2938[/C][C]1.29681959498834[/C][C]-0.00301959498834492[/C][/ROW]
[ROW][C]17[/C][C]1.2694[/C][C]1.27759876165501[/C][C]-0.0081987616550121[/C][/ROW]
[ROW][C]18[/C][C]1.2165[/C][C]1.22918626165501[/C][C]-0.0126862616550116[/C][/ROW]
[ROW][C]19[/C][C]1.2037[/C][C]1.23359876165501[/C][C]-0.0298987616550117[/C][/ROW]
[ROW][C]20[/C][C]1.2292[/C][C]1.19225709498835[/C][C]0.0369429050116548[/C][/ROW]
[ROW][C]21[/C][C]1.2256[/C][C]1.22915292832168[/C][C]-0.00355292832167819[/C][/ROW]
[ROW][C]22[/C][C]1.2015[/C][C]1.24611542832168[/C][C]-0.0446154283216784[/C][/ROW]
[ROW][C]23[/C][C]1.1786[/C][C]1.24596542832168[/C][C]-0.0673654283216785[/C][/ROW]
[ROW][C]24[/C][C]1.1856[/C][C]1.21852376165501[/C][C]-0.032923761655012[/C][/ROW]
[ROW][C]25[/C][C]1.2103[/C][C]1.15874042832168[/C][C]0.0515595716783215[/C][/ROW]
[ROW][C]26[/C][C]1.1938[/C][C]1.20146959498834[/C][C]-0.00766959498834496[/C][/ROW]
[ROW][C]27[/C][C]1.202[/C][C]1.21305709498835[/C][C]-0.0110570949883451[/C][/ROW]
[ROW][C]28[/C][C]1.2271[/C][C]1.17871959498834[/C][C]0.0483804050116552[/C][/ROW]
[ROW][C]29[/C][C]1.277[/C][C]1.21089876165501[/C][C]0.0661012383449877[/C][/ROW]
[ROW][C]30[/C][C]1.265[/C][C]1.23678626165501[/C][C]0.0282137383449885[/C][/ROW]
[ROW][C]31[/C][C]1.2684[/C][C]1.28209876165501[/C][C]-0.0136987616550117[/C][/ROW]
[ROW][C]32[/C][C]1.2811[/C][C]1.25695709498835[/C][C]0.0241429050116546[/C][/ROW]
[ROW][C]33[/C][C]1.2727[/C][C]1.28105292832168[/C][C]-0.00835292832167811[/C][/ROW]
[ROW][C]34[/C][C]1.2611[/C][C]1.29321542832168[/C][C]-0.0321154283216782[/C][/ROW]
[ROW][C]35[/C][C]1.2881[/C][C]1.30556542832168[/C][C]-0.0174654283216786[/C][/ROW]
[ROW][C]36[/C][C]1.3213[/C][C]1.32802376165501[/C][C]-0.00672376165501198[/C][/ROW]
[ROW][C]37[/C][C]1.2999[/C][C]1.29444042832168[/C][C]0.00545957167832167[/C][/ROW]
[ROW][C]38[/C][C]1.3074[/C][C]1.29106959498835[/C][C]0.0163304050116548[/C][/ROW]
[ROW][C]39[/C][C]1.3242[/C][C]1.32665709498834[/C][C]-0.0024570949883449[/C][/ROW]
[ROW][C]40[/C][C]1.3516[/C][C]1.30091959498834[/C][C]0.0506804050116549[/C][/ROW]
[ROW][C]41[/C][C]1.3511[/C][C]1.33539876165501[/C][C]0.0157012383449879[/C][/ROW]
[ROW][C]42[/C][C]1.3419[/C][C]1.31088626165501[/C][C]0.0310137383449887[/C][/ROW]
[ROW][C]43[/C][C]1.3716[/C][C]1.35899876165501[/C][C]0.0126012383449881[/C][/ROW]
[ROW][C]44[/C][C]1.3622[/C][C]1.36015709498835[/C][C]0.00204290501165483[/C][/ROW]
[ROW][C]45[/C][C]1.3896[/C][C]1.36215292832168[/C][C]0.0274470716783217[/C][/ROW]
[ROW][C]46[/C][C]1.4227[/C][C]1.41011542832168[/C][C]0.0125845716783217[/C][/ROW]
[ROW][C]47[/C][C]1.4684[/C][C]1.46716542832168[/C][C]0.00123457167832131[/C][/ROW]
[ROW][C]48[/C][C]1.457[/C][C]1.50832376165501[/C][C]-0.0513237616550117[/C][/ROW]
[ROW][C]49[/C][C]1.4718[/C][C]1.43014042832168[/C][C]0.0416595716783215[/C][/ROW]
[ROW][C]50[/C][C]1.4748[/C][C]1.46296959498835[/C][C]0.0118304050116551[/C][/ROW]
[ROW][C]51[/C][C]1.5527[/C][C]1.49405709498835[/C][C]0.0586429050116548[/C][/ROW]
[ROW][C]52[/C][C]1.575[/C][C]1.52941959498834[/C][C]0.0455804050116551[/C][/ROW]
[ROW][C]53[/C][C]1.5557[/C][C]1.55879876165501[/C][C]-0.00309876165501199[/C][/ROW]
[ROW][C]54[/C][C]1.5553[/C][C]1.51548626165501[/C][C]0.0398137383449884[/C][/ROW]
[ROW][C]55[/C][C]1.577[/C][C]1.57239876165501[/C][C]0.00460123834498827[/C][/ROW]
[ROW][C]56[/C][C]1.4975[/C][C]1.56555709498835[/C][C]-0.0680570949883452[/C][/ROW]
[ROW][C]57[/C][C]1.437[/C][C]1.49745292832168[/C][C]-0.0604529283216781[/C][/ROW]
[ROW][C]58[/C][C]1.3322[/C][C]1.45751542832168[/C][C]-0.125315428321678[/C][/ROW]
[ROW][C]59[/C][C]1.2732[/C][C]1.37666542832168[/C][C]-0.103465428321678[/C][/ROW]
[ROW][C]60[/C][C]1.3449[/C][C]1.31312376165501[/C][C]0.031776238344988[/C][/ROW]
[ROW][C]61[/C][C]1.3239[/C][C]1.31804042832168[/C][C]0.00585957167832163[/C][/ROW]
[ROW][C]62[/C][C]1.2785[/C][C]1.31506959498835[/C][C]-0.0365695949883451[/C][/ROW]
[ROW][C]63[/C][C]1.305[/C][C]1.29775709498835[/C][C]0.00724290501165492[/C][/ROW]
[ROW][C]64[/C][C]1.319[/C][C]1.28171959498834[/C][C]0.0372804050116551[/C][/ROW]
[ROW][C]65[/C][C]1.365[/C][C]1.30279876165501[/C][C]0.0622012383449879[/C][/ROW]
[ROW][C]66[/C][C]1.4016[/C][C]1.32478626165501[/C][C]0.0768137383449885[/C][/ROW]
[ROW][C]67[/C][C]1.4088[/C][C]1.41869876165501[/C][C]-0.00989876165501169[/C][/ROW]
[ROW][C]68[/C][C]1.4268[/C][C]1.39735709498835[/C][C]0.0294429050116547[/C][/ROW]
[ROW][C]69[/C][C]1.4562[/C][C]1.42675292832168[/C][C]0.0294470716783217[/C][/ROW]
[ROW][C]70[/C][C]1.4816[/C][C]1.47671542832168[/C][C]0.00488457167832168[/C][/ROW]
[ROW][C]71[/C][C]1.4914[/C][C]1.52606542832168[/C][C]-0.0346654283216785[/C][/ROW]
[ROW][C]72[/C][C]1.4614[/C][C]1.53132376165501[/C][C]-0.0699237616550119[/C][/ROW]
[ROW][C]73[/C][C]1.4272[/C][C]1.43454042832168[/C][C]-0.00734042832167847[/C][/ROW]
[ROW][C]74[/C][C]1.3686[/C][C]1.41836959498835[/C][C]-0.049769594988345[/C][/ROW]
[ROW][C]75[/C][C]1.3569[/C][C]1.38785709498835[/C][C]-0.0309570949883451[/C][/ROW]
[ROW][C]76[/C][C]1.3406[/C][C]1.33361959498834[/C][C]0.00698040501165509[/C][/ROW]
[ROW][C]77[/C][C]1.2565[/C][C]1.32439876165501[/C][C]-0.0678987616550122[/C][/ROW]
[ROW][C]78[/C][C]1.2208[/C][C]1.21628626165501[/C][C]0.00451373834498869[/C][/ROW]
[ROW][C]79[/C][C]1.277[/C][C]1.23789876165501[/C][C]0.039101238344988[/C][/ROW]
[ROW][C]80[/C][C]1.2894[/C][C]1.26555709498835[/C][C]0.0238429050116549[/C][/ROW]
[ROW][C]81[/C][C]1.3067[/C][C]1.28935292832168[/C][C]0.0173470716783217[/C][/ROW]
[ROW][C]82[/C][C]1.3898[/C][C]1.32721542832168[/C][C]0.0625845716783215[/C][/ROW]
[ROW][C]83[/C][C]1.3661[/C][C]1.43426542832168[/C][C]-0.0681654283216784[/C][/ROW]
[ROW][C]84[/C][C]1.322[/C][C]1.40602376165501[/C][C]-0.0840237616550119[/C][/ROW]
[ROW][C]85[/C][C]1.336[/C][C]1.29514042832168[/C][C]0.0408595716783215[/C][/ROW]
[ROW][C]86[/C][C]1.3649[/C][C]1.32716959498835[/C][C]0.0377304050116549[/C][/ROW]
[ROW][C]87[/C][C]1.3999[/C][C]1.38415709498835[/C][C]0.0157429050116549[/C][/ROW]
[ROW][C]88[/C][C]1.4442[/C][C]1.37661959498834[/C][C]0.0675804050116551[/C][/ROW]
[ROW][C]89[/C][C]1.4349[/C][C]1.42799876165501[/C][C]0.00690123834498801[/C][/ROW]
[ROW][C]90[/C][C]1.4388[/C][C]1.39468626165501[/C][C]0.0441137383449886[/C][/ROW]
[ROW][C]91[/C][C]1.4264[/C][C]1.45589876165501[/C][C]-0.029498761655012[/C][/ROW]
[ROW][C]92[/C][C]1.4343[/C][C]1.41495709498835[/C][C]0.0193429050116547[/C][/ROW]
[ROW][C]93[/C][C]1.377[/C][C]1.43425292832168[/C][C]-0.0572529283216781[/C][/ROW]
[ROW][C]94[/C][C]1.3706[/C][C]1.39751542832168[/C][C]-0.0269154283216784[/C][/ROW]
[ROW][C]95[/C][C]1.3556[/C][C]1.41506542832168[/C][C]-0.0594654283216787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159801&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159801&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
131.31191.286672783119660.0252272168803418
141.30141.30306959498835-0.00166959498834518
151.32011.32065709498834-0.000557094988344886
161.29381.29681959498834-0.00301959498834492
171.26941.27759876165501-0.0081987616550121
181.21651.22918626165501-0.0126862616550116
191.20371.23359876165501-0.0298987616550117
201.22921.192257094988350.0369429050116548
211.22561.22915292832168-0.00355292832167819
221.20151.24611542832168-0.0446154283216784
231.17861.24596542832168-0.0673654283216785
241.18561.21852376165501-0.032923761655012
251.21031.158740428321680.0515595716783215
261.19381.20146959498834-0.00766959498834496
271.2021.21305709498835-0.0110570949883451
281.22711.178719594988340.0483804050116552
291.2771.210898761655010.0661012383449877
301.2651.236786261655010.0282137383449885
311.26841.28209876165501-0.0136987616550117
321.28111.256957094988350.0241429050116546
331.27271.28105292832168-0.00835292832167811
341.26111.29321542832168-0.0321154283216782
351.28811.30556542832168-0.0174654283216786
361.32131.32802376165501-0.00672376165501198
371.29991.294440428321680.00545957167832167
381.30741.291069594988350.0163304050116548
391.32421.32665709498834-0.0024570949883449
401.35161.300919594988340.0506804050116549
411.35111.335398761655010.0157012383449879
421.34191.310886261655010.0310137383449887
431.37161.358998761655010.0126012383449881
441.36221.360157094988350.00204290501165483
451.38961.362152928321680.0274470716783217
461.42271.410115428321680.0125845716783217
471.46841.467165428321680.00123457167832131
481.4571.50832376165501-0.0513237616550117
491.47181.430140428321680.0416595716783215
501.47481.462969594988350.0118304050116551
511.55271.494057094988350.0586429050116548
521.5751.529419594988340.0455804050116551
531.55571.55879876165501-0.00309876165501199
541.55531.515486261655010.0398137383449884
551.5771.572398761655010.00460123834498827
561.49751.56555709498835-0.0680570949883452
571.4371.49745292832168-0.0604529283216781
581.33221.45751542832168-0.125315428321678
591.27321.37666542832168-0.103465428321678
601.34491.313123761655010.031776238344988
611.32391.318040428321680.00585957167832163
621.27851.31506959498835-0.0365695949883451
631.3051.297757094988350.00724290501165492
641.3191.281719594988340.0372804050116551
651.3651.302798761655010.0622012383449879
661.40161.324786261655010.0768137383449885
671.40881.41869876165501-0.00989876165501169
681.42681.397357094988350.0294429050116547
691.45621.426752928321680.0294470716783217
701.48161.476715428321680.00488457167832168
711.49141.52606542832168-0.0346654283216785
721.46141.53132376165501-0.0699237616550119
731.42721.43454042832168-0.00734042832167847
741.36861.41836959498835-0.049769594988345
751.35691.38785709498835-0.0309570949883451
761.34061.333619594988340.00698040501165509
771.25651.32439876165501-0.0678987616550122
781.22081.216286261655010.00451373834498869
791.2771.237898761655010.039101238344988
801.28941.265557094988350.0238429050116549
811.30671.289352928321680.0173470716783217
821.38981.327215428321680.0625845716783215
831.36611.43426542832168-0.0681654283216784
841.3221.40602376165501-0.0840237616550119
851.3361.295140428321680.0408595716783215
861.36491.327169594988350.0377304050116549
871.39991.384157094988350.0157429050116549
881.44421.376619594988340.0675804050116551
891.43491.427998761655010.00690123834498801
901.43881.394686261655010.0441137383449886
911.42641.45589876165501-0.029498761655012
921.43431.414957094988350.0193429050116547
931.3771.43425292832168-0.0572529283216781
941.37061.39751542832168-0.0269154283216784
951.35561.41506542832168-0.0594654283216787







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
961.395523761655011.314183179632861.47686434367717
971.368664189976691.253631235709641.48369714424374
981.359833784965041.218947764185441.50071980574463
991.379090879953381.216409715909071.54177204399769
1001.355810474941721.173927404210791.53769354567266
1011.339609236596741.140366315261451.53885215793202
1021.299395498251751.084188546723871.51460244977962
1031.316494259906761.086428351372651.54656016844087
1041.305051354895111.061029608828641.54907310096157
1051.305004283216781.047782777823031.56222578861054
1061.325519711538461.055743520741841.59529590233508
1071.369985139860141.088213098300951.65175718141933

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
96 & 1.39552376165501 & 1.31418317963286 & 1.47686434367717 \tabularnewline
97 & 1.36866418997669 & 1.25363123570964 & 1.48369714424374 \tabularnewline
98 & 1.35983378496504 & 1.21894776418544 & 1.50071980574463 \tabularnewline
99 & 1.37909087995338 & 1.21640971590907 & 1.54177204399769 \tabularnewline
100 & 1.35581047494172 & 1.17392740421079 & 1.53769354567266 \tabularnewline
101 & 1.33960923659674 & 1.14036631526145 & 1.53885215793202 \tabularnewline
102 & 1.29939549825175 & 1.08418854672387 & 1.51460244977962 \tabularnewline
103 & 1.31649425990676 & 1.08642835137265 & 1.54656016844087 \tabularnewline
104 & 1.30505135489511 & 1.06102960882864 & 1.54907310096157 \tabularnewline
105 & 1.30500428321678 & 1.04778277782303 & 1.56222578861054 \tabularnewline
106 & 1.32551971153846 & 1.05574352074184 & 1.59529590233508 \tabularnewline
107 & 1.36998513986014 & 1.08821309830095 & 1.65175718141933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159801&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]96[/C][C]1.39552376165501[/C][C]1.31418317963286[/C][C]1.47686434367717[/C][/ROW]
[ROW][C]97[/C][C]1.36866418997669[/C][C]1.25363123570964[/C][C]1.48369714424374[/C][/ROW]
[ROW][C]98[/C][C]1.35983378496504[/C][C]1.21894776418544[/C][C]1.50071980574463[/C][/ROW]
[ROW][C]99[/C][C]1.37909087995338[/C][C]1.21640971590907[/C][C]1.54177204399769[/C][/ROW]
[ROW][C]100[/C][C]1.35581047494172[/C][C]1.17392740421079[/C][C]1.53769354567266[/C][/ROW]
[ROW][C]101[/C][C]1.33960923659674[/C][C]1.14036631526145[/C][C]1.53885215793202[/C][/ROW]
[ROW][C]102[/C][C]1.29939549825175[/C][C]1.08418854672387[/C][C]1.51460244977962[/C][/ROW]
[ROW][C]103[/C][C]1.31649425990676[/C][C]1.08642835137265[/C][C]1.54656016844087[/C][/ROW]
[ROW][C]104[/C][C]1.30505135489511[/C][C]1.06102960882864[/C][C]1.54907310096157[/C][/ROW]
[ROW][C]105[/C][C]1.30500428321678[/C][C]1.04778277782303[/C][C]1.56222578861054[/C][/ROW]
[ROW][C]106[/C][C]1.32551971153846[/C][C]1.05574352074184[/C][C]1.59529590233508[/C][/ROW]
[ROW][C]107[/C][C]1.36998513986014[/C][C]1.08821309830095[/C][C]1.65175718141933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159801&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159801&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
961.395523761655011.314183179632861.47686434367717
971.368664189976691.253631235709641.48369714424374
981.359833784965041.218947764185441.50071980574463
991.379090879953381.216409715909071.54177204399769
1001.355810474941721.173927404210791.53769354567266
1011.339609236596741.140366315261451.53885215793202
1021.299395498251751.084188546723871.51460244977962
1031.316494259906761.086428351372651.54656016844087
1041.305051354895111.061029608828641.54907310096157
1051.305004283216781.047782777823031.56222578861054
1061.325519711538461.055743520741841.59529590233508
1071.369985139860141.088213098300951.65175718141933



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