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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 May 2016 18:39:17 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/May/24/t1464111573lj1bvlcxcgbu4pm.htm/, Retrieved Wed, 22 May 2024 03:30:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295577, Retrieved Wed, 22 May 2024 03:30:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2016-04-26 08:31:59] [9dd841f4e56c9b98fc9b2251347c7b43]
- RMP     [Exponential Smoothing] [] [2016-05-24 17:39:17] [e1772292a6a44abe5991636299c33e7e] [Current]
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Dataseries X:
92.8
92.9
93.06
93.28
93.41
93.49
93.49
93.5
93.56
94.12
94.3
94.36
94.36
94.5
94.85
95.16
95.73
95.76
95.76
95.81
96.09
96.48
96.71
96.69
96.69
96.66
96.73
96.84
97.87
98
97.98
98.03
98.11
98.18
98.32
98.34
98.28
98.52
98.56
99.6
100.16
100.46
100.46
100.68
100.83
100.64
100.9
100.92
100.75
100.96
101.05
101.33
101.38
101.44
101.51
101.4
101.26
100.83
100.75
100.81
100.82
100.85
100.79
100.84
101.04
101.11
101.15
101.11
101.28
101.62
102.07
102.14




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=295577&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=295577&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295577&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
alpha0.867413557325273
beta0.0644166182105862
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.867413557325273 \tabularnewline
beta & 0.0644166182105862 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295577&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]0.867413557325273[/C][/ROW]
[ROW][C]beta[/C][C]0.0644166182105862[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295577&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295577&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
alpha0.867413557325273
beta0.0644166182105862
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1394.3693.33543958358361.02456041641639
1494.594.41352957208730.0864704279126727
1594.8594.8819132042524-0.031913204252433
1695.1695.2038122515409-0.0438122515408708
1795.7395.7781234868811-0.0481234868810816
1895.7695.8071554862298-0.0471554862298404
1995.7695.7032531370380.0567468629619867
2095.8195.8663683583968-0.05636835839681
2196.0995.96950828226630.120491717733657
2296.4896.7344865755298-0.254486575529839
2396.7196.7470662083321-0.0370662083321349
2496.6996.8063683029746-0.116368302974607
2596.6996.8705282093255-0.180528209325544
2696.6696.7438485425607-0.0838485425607161
2796.7397.0115612269314-0.281561226931359
2896.8497.063150212608-0.22315021260799
2997.8797.42340386932060.446596130679396
309897.84117926041480.158820739585195
3197.9897.8978439405370.0821560594630171
3298.0398.0409616162462-0.0109616162462203
3398.1198.1842690716002-0.0742690716001988
3498.1898.7060115630777-0.526011563077716
3598.3298.465037869485-0.145037869485023
3698.3498.3642833623375-0.0242833623374992
3798.2898.4504493538835-0.17044935388347
3898.5298.29494284511970.22505715488029
3998.5698.7759905917255-0.215990591725543
4099.698.86758662563310.732413374366885
41100.16100.184822456068-0.0248224560679375
42100.46100.1509892931650.309010706835238
43100.46100.3290860917950.130913908204974
44100.68100.5097315278380.170268472162377
45100.83100.8215700894450.00842991055490927
46100.64101.38986918571-0.749869185709898
47100.9101.021189964712-0.121189964711917
48100.92100.968741137938-0.0487411379380944
49100.75101.025792925564-0.275792925564218
50100.96100.8361214398450.123878560155006
51101.05101.174334902255-0.124334902255256
52101.33101.483992868701-0.153992868700726
53101.38101.896138238616-0.516138238615838
54101.44101.4083132642450.031686735755315
55101.51101.2339957399180.276004260081862
56101.4101.46735572118-0.0673557211803768
57101.26101.460977572735-0.200977572735439
58100.83101.64556714418-0.81556714418015
59100.75101.197954688309-0.447954688308656
60100.81100.7478875232630.0621124767370986
61100.82100.7534746879180.0665253120815663
62100.85100.8152894540670.0347105459332369
63100.79100.939821440109-0.149821440108823
64100.84101.117770945681-0.277770945680871
65101.04101.260378526612-0.220378526611611
66101.11101.0062889532960.103711046704447
67101.15100.8363297982860.313670201714459
68101.11100.968449593920.141550406080299
69101.28101.0484360260830.231563973916636
70101.62101.4726307998230.147369200176982
71102.07101.9109004330590.159099566940839
72102.14102.0885953591340.0514046408656128

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 94.36 & 93.3354395835836 & 1.02456041641639 \tabularnewline
14 & 94.5 & 94.4135295720873 & 0.0864704279126727 \tabularnewline
15 & 94.85 & 94.8819132042524 & -0.031913204252433 \tabularnewline
16 & 95.16 & 95.2038122515409 & -0.0438122515408708 \tabularnewline
17 & 95.73 & 95.7781234868811 & -0.0481234868810816 \tabularnewline
18 & 95.76 & 95.8071554862298 & -0.0471554862298404 \tabularnewline
19 & 95.76 & 95.703253137038 & 0.0567468629619867 \tabularnewline
20 & 95.81 & 95.8663683583968 & -0.05636835839681 \tabularnewline
21 & 96.09 & 95.9695082822663 & 0.120491717733657 \tabularnewline
22 & 96.48 & 96.7344865755298 & -0.254486575529839 \tabularnewline
23 & 96.71 & 96.7470662083321 & -0.0370662083321349 \tabularnewline
24 & 96.69 & 96.8063683029746 & -0.116368302974607 \tabularnewline
25 & 96.69 & 96.8705282093255 & -0.180528209325544 \tabularnewline
26 & 96.66 & 96.7438485425607 & -0.0838485425607161 \tabularnewline
27 & 96.73 & 97.0115612269314 & -0.281561226931359 \tabularnewline
28 & 96.84 & 97.063150212608 & -0.22315021260799 \tabularnewline
29 & 97.87 & 97.4234038693206 & 0.446596130679396 \tabularnewline
30 & 98 & 97.8411792604148 & 0.158820739585195 \tabularnewline
31 & 97.98 & 97.897843940537 & 0.0821560594630171 \tabularnewline
32 & 98.03 & 98.0409616162462 & -0.0109616162462203 \tabularnewline
33 & 98.11 & 98.1842690716002 & -0.0742690716001988 \tabularnewline
34 & 98.18 & 98.7060115630777 & -0.526011563077716 \tabularnewline
35 & 98.32 & 98.465037869485 & -0.145037869485023 \tabularnewline
36 & 98.34 & 98.3642833623375 & -0.0242833623374992 \tabularnewline
37 & 98.28 & 98.4504493538835 & -0.17044935388347 \tabularnewline
38 & 98.52 & 98.2949428451197 & 0.22505715488029 \tabularnewline
39 & 98.56 & 98.7759905917255 & -0.215990591725543 \tabularnewline
40 & 99.6 & 98.8675866256331 & 0.732413374366885 \tabularnewline
41 & 100.16 & 100.184822456068 & -0.0248224560679375 \tabularnewline
42 & 100.46 & 100.150989293165 & 0.309010706835238 \tabularnewline
43 & 100.46 & 100.329086091795 & 0.130913908204974 \tabularnewline
44 & 100.68 & 100.509731527838 & 0.170268472162377 \tabularnewline
45 & 100.83 & 100.821570089445 & 0.00842991055490927 \tabularnewline
46 & 100.64 & 101.38986918571 & -0.749869185709898 \tabularnewline
47 & 100.9 & 101.021189964712 & -0.121189964711917 \tabularnewline
48 & 100.92 & 100.968741137938 & -0.0487411379380944 \tabularnewline
49 & 100.75 & 101.025792925564 & -0.275792925564218 \tabularnewline
50 & 100.96 & 100.836121439845 & 0.123878560155006 \tabularnewline
51 & 101.05 & 101.174334902255 & -0.124334902255256 \tabularnewline
52 & 101.33 & 101.483992868701 & -0.153992868700726 \tabularnewline
53 & 101.38 & 101.896138238616 & -0.516138238615838 \tabularnewline
54 & 101.44 & 101.408313264245 & 0.031686735755315 \tabularnewline
55 & 101.51 & 101.233995739918 & 0.276004260081862 \tabularnewline
56 & 101.4 & 101.46735572118 & -0.0673557211803768 \tabularnewline
57 & 101.26 & 101.460977572735 & -0.200977572735439 \tabularnewline
58 & 100.83 & 101.64556714418 & -0.81556714418015 \tabularnewline
59 & 100.75 & 101.197954688309 & -0.447954688308656 \tabularnewline
60 & 100.81 & 100.747887523263 & 0.0621124767370986 \tabularnewline
61 & 100.82 & 100.753474687918 & 0.0665253120815663 \tabularnewline
62 & 100.85 & 100.815289454067 & 0.0347105459332369 \tabularnewline
63 & 100.79 & 100.939821440109 & -0.149821440108823 \tabularnewline
64 & 100.84 & 101.117770945681 & -0.277770945680871 \tabularnewline
65 & 101.04 & 101.260378526612 & -0.220378526611611 \tabularnewline
66 & 101.11 & 101.006288953296 & 0.103711046704447 \tabularnewline
67 & 101.15 & 100.836329798286 & 0.313670201714459 \tabularnewline
68 & 101.11 & 100.96844959392 & 0.141550406080299 \tabularnewline
69 & 101.28 & 101.048436026083 & 0.231563973916636 \tabularnewline
70 & 101.62 & 101.472630799823 & 0.147369200176982 \tabularnewline
71 & 102.07 & 101.910900433059 & 0.159099566940839 \tabularnewline
72 & 102.14 & 102.088595359134 & 0.0514046408656128 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295577&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]94.36[/C][C]93.3354395835836[/C][C]1.02456041641639[/C][/ROW]
[ROW][C]14[/C][C]94.5[/C][C]94.4135295720873[/C][C]0.0864704279126727[/C][/ROW]
[ROW][C]15[/C][C]94.85[/C][C]94.8819132042524[/C][C]-0.031913204252433[/C][/ROW]
[ROW][C]16[/C][C]95.16[/C][C]95.2038122515409[/C][C]-0.0438122515408708[/C][/ROW]
[ROW][C]17[/C][C]95.73[/C][C]95.7781234868811[/C][C]-0.0481234868810816[/C][/ROW]
[ROW][C]18[/C][C]95.76[/C][C]95.8071554862298[/C][C]-0.0471554862298404[/C][/ROW]
[ROW][C]19[/C][C]95.76[/C][C]95.703253137038[/C][C]0.0567468629619867[/C][/ROW]
[ROW][C]20[/C][C]95.81[/C][C]95.8663683583968[/C][C]-0.05636835839681[/C][/ROW]
[ROW][C]21[/C][C]96.09[/C][C]95.9695082822663[/C][C]0.120491717733657[/C][/ROW]
[ROW][C]22[/C][C]96.48[/C][C]96.7344865755298[/C][C]-0.254486575529839[/C][/ROW]
[ROW][C]23[/C][C]96.71[/C][C]96.7470662083321[/C][C]-0.0370662083321349[/C][/ROW]
[ROW][C]24[/C][C]96.69[/C][C]96.8063683029746[/C][C]-0.116368302974607[/C][/ROW]
[ROW][C]25[/C][C]96.69[/C][C]96.8705282093255[/C][C]-0.180528209325544[/C][/ROW]
[ROW][C]26[/C][C]96.66[/C][C]96.7438485425607[/C][C]-0.0838485425607161[/C][/ROW]
[ROW][C]27[/C][C]96.73[/C][C]97.0115612269314[/C][C]-0.281561226931359[/C][/ROW]
[ROW][C]28[/C][C]96.84[/C][C]97.063150212608[/C][C]-0.22315021260799[/C][/ROW]
[ROW][C]29[/C][C]97.87[/C][C]97.4234038693206[/C][C]0.446596130679396[/C][/ROW]
[ROW][C]30[/C][C]98[/C][C]97.8411792604148[/C][C]0.158820739585195[/C][/ROW]
[ROW][C]31[/C][C]97.98[/C][C]97.897843940537[/C][C]0.0821560594630171[/C][/ROW]
[ROW][C]32[/C][C]98.03[/C][C]98.0409616162462[/C][C]-0.0109616162462203[/C][/ROW]
[ROW][C]33[/C][C]98.11[/C][C]98.1842690716002[/C][C]-0.0742690716001988[/C][/ROW]
[ROW][C]34[/C][C]98.18[/C][C]98.7060115630777[/C][C]-0.526011563077716[/C][/ROW]
[ROW][C]35[/C][C]98.32[/C][C]98.465037869485[/C][C]-0.145037869485023[/C][/ROW]
[ROW][C]36[/C][C]98.34[/C][C]98.3642833623375[/C][C]-0.0242833623374992[/C][/ROW]
[ROW][C]37[/C][C]98.28[/C][C]98.4504493538835[/C][C]-0.17044935388347[/C][/ROW]
[ROW][C]38[/C][C]98.52[/C][C]98.2949428451197[/C][C]0.22505715488029[/C][/ROW]
[ROW][C]39[/C][C]98.56[/C][C]98.7759905917255[/C][C]-0.215990591725543[/C][/ROW]
[ROW][C]40[/C][C]99.6[/C][C]98.8675866256331[/C][C]0.732413374366885[/C][/ROW]
[ROW][C]41[/C][C]100.16[/C][C]100.184822456068[/C][C]-0.0248224560679375[/C][/ROW]
[ROW][C]42[/C][C]100.46[/C][C]100.150989293165[/C][C]0.309010706835238[/C][/ROW]
[ROW][C]43[/C][C]100.46[/C][C]100.329086091795[/C][C]0.130913908204974[/C][/ROW]
[ROW][C]44[/C][C]100.68[/C][C]100.509731527838[/C][C]0.170268472162377[/C][/ROW]
[ROW][C]45[/C][C]100.83[/C][C]100.821570089445[/C][C]0.00842991055490927[/C][/ROW]
[ROW][C]46[/C][C]100.64[/C][C]101.38986918571[/C][C]-0.749869185709898[/C][/ROW]
[ROW][C]47[/C][C]100.9[/C][C]101.021189964712[/C][C]-0.121189964711917[/C][/ROW]
[ROW][C]48[/C][C]100.92[/C][C]100.968741137938[/C][C]-0.0487411379380944[/C][/ROW]
[ROW][C]49[/C][C]100.75[/C][C]101.025792925564[/C][C]-0.275792925564218[/C][/ROW]
[ROW][C]50[/C][C]100.96[/C][C]100.836121439845[/C][C]0.123878560155006[/C][/ROW]
[ROW][C]51[/C][C]101.05[/C][C]101.174334902255[/C][C]-0.124334902255256[/C][/ROW]
[ROW][C]52[/C][C]101.33[/C][C]101.483992868701[/C][C]-0.153992868700726[/C][/ROW]
[ROW][C]53[/C][C]101.38[/C][C]101.896138238616[/C][C]-0.516138238615838[/C][/ROW]
[ROW][C]54[/C][C]101.44[/C][C]101.408313264245[/C][C]0.031686735755315[/C][/ROW]
[ROW][C]55[/C][C]101.51[/C][C]101.233995739918[/C][C]0.276004260081862[/C][/ROW]
[ROW][C]56[/C][C]101.4[/C][C]101.46735572118[/C][C]-0.0673557211803768[/C][/ROW]
[ROW][C]57[/C][C]101.26[/C][C]101.460977572735[/C][C]-0.200977572735439[/C][/ROW]
[ROW][C]58[/C][C]100.83[/C][C]101.64556714418[/C][C]-0.81556714418015[/C][/ROW]
[ROW][C]59[/C][C]100.75[/C][C]101.197954688309[/C][C]-0.447954688308656[/C][/ROW]
[ROW][C]60[/C][C]100.81[/C][C]100.747887523263[/C][C]0.0621124767370986[/C][/ROW]
[ROW][C]61[/C][C]100.82[/C][C]100.753474687918[/C][C]0.0665253120815663[/C][/ROW]
[ROW][C]62[/C][C]100.85[/C][C]100.815289454067[/C][C]0.0347105459332369[/C][/ROW]
[ROW][C]63[/C][C]100.79[/C][C]100.939821440109[/C][C]-0.149821440108823[/C][/ROW]
[ROW][C]64[/C][C]100.84[/C][C]101.117770945681[/C][C]-0.277770945680871[/C][/ROW]
[ROW][C]65[/C][C]101.04[/C][C]101.260378526612[/C][C]-0.220378526611611[/C][/ROW]
[ROW][C]66[/C][C]101.11[/C][C]101.006288953296[/C][C]0.103711046704447[/C][/ROW]
[ROW][C]67[/C][C]101.15[/C][C]100.836329798286[/C][C]0.313670201714459[/C][/ROW]
[ROW][C]68[/C][C]101.11[/C][C]100.96844959392[/C][C]0.141550406080299[/C][/ROW]
[ROW][C]69[/C][C]101.28[/C][C]101.048436026083[/C][C]0.231563973916636[/C][/ROW]
[ROW][C]70[/C][C]101.62[/C][C]101.472630799823[/C][C]0.147369200176982[/C][/ROW]
[ROW][C]71[/C][C]102.07[/C][C]101.910900433059[/C][C]0.159099566940839[/C][/ROW]
[ROW][C]72[/C][C]102.14[/C][C]102.088595359134[/C][C]0.0514046408656128[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295577&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295577&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
1394.3693.33543958358361.02456041641639
1494.594.41352957208730.0864704279126727
1594.8594.8819132042524-0.031913204252433
1695.1695.2038122515409-0.0438122515408708
1795.7395.7781234868811-0.0481234868810816
1895.7695.8071554862298-0.0471554862298404
1995.7695.7032531370380.0567468629619867
2095.8195.8663683583968-0.05636835839681
2196.0995.96950828226630.120491717733657
2296.4896.7344865755298-0.254486575529839
2396.7196.7470662083321-0.0370662083321349
2496.6996.8063683029746-0.116368302974607
2596.6996.8705282093255-0.180528209325544
2696.6696.7438485425607-0.0838485425607161
2796.7397.0115612269314-0.281561226931359
2896.8497.063150212608-0.22315021260799
2997.8797.42340386932060.446596130679396
309897.84117926041480.158820739585195
3197.9897.8978439405370.0821560594630171
3298.0398.0409616162462-0.0109616162462203
3398.1198.1842690716002-0.0742690716001988
3498.1898.7060115630777-0.526011563077716
3598.3298.465037869485-0.145037869485023
3698.3498.3642833623375-0.0242833623374992
3798.2898.4504493538835-0.17044935388347
3898.5298.29494284511970.22505715488029
3998.5698.7759905917255-0.215990591725543
4099.698.86758662563310.732413374366885
41100.16100.184822456068-0.0248224560679375
42100.46100.1509892931650.309010706835238
43100.46100.3290860917950.130913908204974
44100.68100.5097315278380.170268472162377
45100.83100.8215700894450.00842991055490927
46100.64101.38986918571-0.749869185709898
47100.9101.021189964712-0.121189964711917
48100.92100.968741137938-0.0487411379380944
49100.75101.025792925564-0.275792925564218
50100.96100.8361214398450.123878560155006
51101.05101.174334902255-0.124334902255256
52101.33101.483992868701-0.153992868700726
53101.38101.896138238616-0.516138238615838
54101.44101.4083132642450.031686735755315
55101.51101.2339957399180.276004260081862
56101.4101.46735572118-0.0673557211803768
57101.26101.460977572735-0.200977572735439
58100.83101.64556714418-0.81556714418015
59100.75101.197954688309-0.447954688308656
60100.81100.7478875232630.0621124767370986
61100.82100.7534746879180.0665253120815663
62100.85100.8152894540670.0347105459332369
63100.79100.939821440109-0.149821440108823
64100.84101.117770945681-0.277770945680871
65101.04101.260378526612-0.220378526611611
66101.11101.0062889532960.103711046704447
67101.15100.8363297982860.313670201714459
68101.11100.968449593920.141550406080299
69101.28101.0484360260830.231563973916636
70101.62101.4726307998230.147369200176982
71102.07101.9109004330590.159099566940839
72102.14102.0885953591340.0514046408656128







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73102.117644331243101.547489122067102.687799540419
74102.146560593947101.370800655966102.922320531928
75102.244454418583101.288737705594103.200171131572
76102.575024756754101.449943320886103.700106192622
77103.024153159263101.734913510268104.313392808259
78103.067480111215101.622088379337104.512871843093
79102.888428188272101.292005387428104.484850989117
80102.762631001356101.015766734385104.509495268327
81102.762988727532100.8641411581104.661836296964
82102.997033645907100.941730294672105.052336997141
83103.323784341379101.109166725542105.538401957216
84103.35117234384297.2513738959586109.450970791725

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 102.117644331243 & 101.547489122067 & 102.687799540419 \tabularnewline
74 & 102.146560593947 & 101.370800655966 & 102.922320531928 \tabularnewline
75 & 102.244454418583 & 101.288737705594 & 103.200171131572 \tabularnewline
76 & 102.575024756754 & 101.449943320886 & 103.700106192622 \tabularnewline
77 & 103.024153159263 & 101.734913510268 & 104.313392808259 \tabularnewline
78 & 103.067480111215 & 101.622088379337 & 104.512871843093 \tabularnewline
79 & 102.888428188272 & 101.292005387428 & 104.484850989117 \tabularnewline
80 & 102.762631001356 & 101.015766734385 & 104.509495268327 \tabularnewline
81 & 102.762988727532 & 100.8641411581 & 104.661836296964 \tabularnewline
82 & 102.997033645907 & 100.941730294672 & 105.052336997141 \tabularnewline
83 & 103.323784341379 & 101.109166725542 & 105.538401957216 \tabularnewline
84 & 103.351172343842 & 97.2513738959586 & 109.450970791725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295577&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]102.117644331243[/C][C]101.547489122067[/C][C]102.687799540419[/C][/ROW]
[ROW][C]74[/C][C]102.146560593947[/C][C]101.370800655966[/C][C]102.922320531928[/C][/ROW]
[ROW][C]75[/C][C]102.244454418583[/C][C]101.288737705594[/C][C]103.200171131572[/C][/ROW]
[ROW][C]76[/C][C]102.575024756754[/C][C]101.449943320886[/C][C]103.700106192622[/C][/ROW]
[ROW][C]77[/C][C]103.024153159263[/C][C]101.734913510268[/C][C]104.313392808259[/C][/ROW]
[ROW][C]78[/C][C]103.067480111215[/C][C]101.622088379337[/C][C]104.512871843093[/C][/ROW]
[ROW][C]79[/C][C]102.888428188272[/C][C]101.292005387428[/C][C]104.484850989117[/C][/ROW]
[ROW][C]80[/C][C]102.762631001356[/C][C]101.015766734385[/C][C]104.509495268327[/C][/ROW]
[ROW][C]81[/C][C]102.762988727532[/C][C]100.8641411581[/C][C]104.661836296964[/C][/ROW]
[ROW][C]82[/C][C]102.997033645907[/C][C]100.941730294672[/C][C]105.052336997141[/C][/ROW]
[ROW][C]83[/C][C]103.323784341379[/C][C]101.109166725542[/C][C]105.538401957216[/C][/ROW]
[ROW][C]84[/C][C]103.351172343842[/C][C]97.2513738959586[/C][C]109.450970791725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295577&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295577&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
73102.117644331243101.547489122067102.687799540419
74102.146560593947101.370800655966102.922320531928
75102.244454418583101.288737705594103.200171131572
76102.575024756754101.449943320886103.700106192622
77103.024153159263101.734913510268104.313392808259
78103.067480111215101.622088379337104.512871843093
79102.888428188272101.292005387428104.484850989117
80102.762631001356101.015766734385104.509495268327
81102.762988727532100.8641411581104.661836296964
82102.997033645907100.941730294672105.052336997141
83103.323784341379101.109166725542105.538401957216
84103.35117234384297.2513738959586109.450970791725



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')