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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 04:12:49 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/28/t1211969619l78fnm5u2jqrz1p.htm/, Retrieved Tue, 14 May 2024 10:57:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13416, Retrieved Tue, 14 May 2024 10:57:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact215
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exonential smooth...] [2008-05-28 10:12:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
161,79
161,79
161,85
161,77
161,86
161,89
161,89
161,89
162,18
162,43
162,58
162,57
162,57
162,57
162,44
162,79
163,15
163,23
163,23
163,23
163,38
163,71
163,73
163,73
163,73
163,73
163,93
164,27
164,57
164,73
164,73
164,76
165,75
165,86
165,99
166,13
166,13
166,13
166,15
166,45
166,48
166,51
166,51
166,51
166,58
166,82
167,35
167,5
167,5
167,6
167,72
167,29
166,98
166,98
166,98
166,98
167,63
167,83
167,85
167,87
167,87
167,96
167,7
169,25
168,79
168,77
168,77
169
168,92
169,23
169,28
169,29




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13416&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13416&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.792088674339765
beta0.000643553350096742
gamma0.0036999903249905

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.792088674339765 \tabularnewline
beta & 0.000643553350096742 \tabularnewline
gamma & 0.0036999903249905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13416&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]0.792088674339765[/C][/ROW]
[ROW][C]beta[/C][C]0.000643553350096742[/C][/ROW]
[ROW][C]gamma[/C][C]0.0036999903249905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13416&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
alpha0.792088674339765
beta0.000643553350096742
gamma0.0036999903249905







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13162.57161.9174097222220.652590277777733
14162.57162.4359805533380.134019446662421
15162.44162.4196989522070.0203010477933674
16162.79162.795852643753-0.00585264375331462
17163.15163.163370642374-0.0133706423742410
18163.23163.249926903731-0.0199269037311751
19163.23163.250863200289-0.0208632002891704
20163.23163.251047231904-0.0210472319038786
21163.38163.387324765307-0.00732476530654935
22163.71163.7011346419430.00886535805713606
23163.73163.7206897177260.0093102822736455
24163.73163.7197686255380.0102313744619664
25163.73163.87008435355-0.140084353550151
26163.73163.760364348663-0.0303643486632552
27163.93163.6136816128500.316318387150346
28164.27164.2243309502720.045669049728474
29164.57164.632722961873-0.0627229618733338
30164.73164.6802276554190.049772344580731
31164.73164.736451635245-0.00645163524529835
32164.76164.748138527390.0118614726100077
33165.75164.9105977691110.839402230889476
34165.86165.895639124375-0.0356391243746543
35165.99165.8804565198230.109543480176541
36166.13165.9594942849500.170505715049615
37166.13166.237292137517-0.107292137516879
38166.13166.15429386368-0.0242938636800147
39166.15166.0133522611250.136647738874558
40166.45166.482052801465-0.0320528014645731
41166.48166.829333704375-0.349333704374885
42166.51166.650292585988-0.140292585987766
43166.51166.556216921551-0.0462169215512915
44166.51166.536691884141-0.0266918841414281
45166.58166.669502013826-0.0895020138255234
46166.82166.917874147183-0.0978741471831768
47167.35166.8532542989880.496745701011832
48167.5167.2389815596360.261018440363614
49167.5167.588250059571-0.0882500595710383
50167.6167.5203985990960.0796014009036128
51167.72167.4619279782260.258072021774154
52167.29168.026792349542-0.73679234954173
53166.98167.815368529448-0.835368529448488
54166.98167.251013348965-0.271013348965113
55166.98167.052908792308-0.0729087923084819
56166.98167.011684014241-0.0316840142409376
57167.63167.1399166393680.490083360631701
58167.83167.847085810724-0.0170858107236143
59167.85167.8466765614730.00332343852730332
60167.87167.8408984252740.0291015747259848
61167.87168.005591427698-0.135591427697506
62167.96167.8997383033430.0602616966572214
63167.7167.825444129975-0.125444129974937
64169.25168.0849268001161.16507319988364
65168.79169.380005206888-0.590005206887895
66168.77169.010690647766-0.240690647765604
67168.77168.837029183226-0.0670291832256567
68169168.8007687150910.199231284908791
69168.92169.112701247907-0.192701247906655
70169.23169.278699398062-0.0486993980623822
71169.28169.2532940536900.0267059463102157
72169.29169.2660976558360.0239023441644122

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 162.57 & 161.917409722222 & 0.652590277777733 \tabularnewline
14 & 162.57 & 162.435980553338 & 0.134019446662421 \tabularnewline
15 & 162.44 & 162.419698952207 & 0.0203010477933674 \tabularnewline
16 & 162.79 & 162.795852643753 & -0.00585264375331462 \tabularnewline
17 & 163.15 & 163.163370642374 & -0.0133706423742410 \tabularnewline
18 & 163.23 & 163.249926903731 & -0.0199269037311751 \tabularnewline
19 & 163.23 & 163.250863200289 & -0.0208632002891704 \tabularnewline
20 & 163.23 & 163.251047231904 & -0.0210472319038786 \tabularnewline
21 & 163.38 & 163.387324765307 & -0.00732476530654935 \tabularnewline
22 & 163.71 & 163.701134641943 & 0.00886535805713606 \tabularnewline
23 & 163.73 & 163.720689717726 & 0.0093102822736455 \tabularnewline
24 & 163.73 & 163.719768625538 & 0.0102313744619664 \tabularnewline
25 & 163.73 & 163.87008435355 & -0.140084353550151 \tabularnewline
26 & 163.73 & 163.760364348663 & -0.0303643486632552 \tabularnewline
27 & 163.93 & 163.613681612850 & 0.316318387150346 \tabularnewline
28 & 164.27 & 164.224330950272 & 0.045669049728474 \tabularnewline
29 & 164.57 & 164.632722961873 & -0.0627229618733338 \tabularnewline
30 & 164.73 & 164.680227655419 & 0.049772344580731 \tabularnewline
31 & 164.73 & 164.736451635245 & -0.00645163524529835 \tabularnewline
32 & 164.76 & 164.74813852739 & 0.0118614726100077 \tabularnewline
33 & 165.75 & 164.910597769111 & 0.839402230889476 \tabularnewline
34 & 165.86 & 165.895639124375 & -0.0356391243746543 \tabularnewline
35 & 165.99 & 165.880456519823 & 0.109543480176541 \tabularnewline
36 & 166.13 & 165.959494284950 & 0.170505715049615 \tabularnewline
37 & 166.13 & 166.237292137517 & -0.107292137516879 \tabularnewline
38 & 166.13 & 166.15429386368 & -0.0242938636800147 \tabularnewline
39 & 166.15 & 166.013352261125 & 0.136647738874558 \tabularnewline
40 & 166.45 & 166.482052801465 & -0.0320528014645731 \tabularnewline
41 & 166.48 & 166.829333704375 & -0.349333704374885 \tabularnewline
42 & 166.51 & 166.650292585988 & -0.140292585987766 \tabularnewline
43 & 166.51 & 166.556216921551 & -0.0462169215512915 \tabularnewline
44 & 166.51 & 166.536691884141 & -0.0266918841414281 \tabularnewline
45 & 166.58 & 166.669502013826 & -0.0895020138255234 \tabularnewline
46 & 166.82 & 166.917874147183 & -0.0978741471831768 \tabularnewline
47 & 167.35 & 166.853254298988 & 0.496745701011832 \tabularnewline
48 & 167.5 & 167.238981559636 & 0.261018440363614 \tabularnewline
49 & 167.5 & 167.588250059571 & -0.0882500595710383 \tabularnewline
50 & 167.6 & 167.520398599096 & 0.0796014009036128 \tabularnewline
51 & 167.72 & 167.461927978226 & 0.258072021774154 \tabularnewline
52 & 167.29 & 168.026792349542 & -0.73679234954173 \tabularnewline
53 & 166.98 & 167.815368529448 & -0.835368529448488 \tabularnewline
54 & 166.98 & 167.251013348965 & -0.271013348965113 \tabularnewline
55 & 166.98 & 167.052908792308 & -0.0729087923084819 \tabularnewline
56 & 166.98 & 167.011684014241 & -0.0316840142409376 \tabularnewline
57 & 167.63 & 167.139916639368 & 0.490083360631701 \tabularnewline
58 & 167.83 & 167.847085810724 & -0.0170858107236143 \tabularnewline
59 & 167.85 & 167.846676561473 & 0.00332343852730332 \tabularnewline
60 & 167.87 & 167.840898425274 & 0.0291015747259848 \tabularnewline
61 & 167.87 & 168.005591427698 & -0.135591427697506 \tabularnewline
62 & 167.96 & 167.899738303343 & 0.0602616966572214 \tabularnewline
63 & 167.7 & 167.825444129975 & -0.125444129974937 \tabularnewline
64 & 169.25 & 168.084926800116 & 1.16507319988364 \tabularnewline
65 & 168.79 & 169.380005206888 & -0.590005206887895 \tabularnewline
66 & 168.77 & 169.010690647766 & -0.240690647765604 \tabularnewline
67 & 168.77 & 168.837029183226 & -0.0670291832256567 \tabularnewline
68 & 169 & 168.800768715091 & 0.199231284908791 \tabularnewline
69 & 168.92 & 169.112701247907 & -0.192701247906655 \tabularnewline
70 & 169.23 & 169.278699398062 & -0.0486993980623822 \tabularnewline
71 & 169.28 & 169.253294053690 & 0.0267059463102157 \tabularnewline
72 & 169.29 & 169.266097655836 & 0.0239023441644122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13416&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]162.57[/C][C]161.917409722222[/C][C]0.652590277777733[/C][/ROW]
[ROW][C]14[/C][C]162.57[/C][C]162.435980553338[/C][C]0.134019446662421[/C][/ROW]
[ROW][C]15[/C][C]162.44[/C][C]162.419698952207[/C][C]0.0203010477933674[/C][/ROW]
[ROW][C]16[/C][C]162.79[/C][C]162.795852643753[/C][C]-0.00585264375331462[/C][/ROW]
[ROW][C]17[/C][C]163.15[/C][C]163.163370642374[/C][C]-0.0133706423742410[/C][/ROW]
[ROW][C]18[/C][C]163.23[/C][C]163.249926903731[/C][C]-0.0199269037311751[/C][/ROW]
[ROW][C]19[/C][C]163.23[/C][C]163.250863200289[/C][C]-0.0208632002891704[/C][/ROW]
[ROW][C]20[/C][C]163.23[/C][C]163.251047231904[/C][C]-0.0210472319038786[/C][/ROW]
[ROW][C]21[/C][C]163.38[/C][C]163.387324765307[/C][C]-0.00732476530654935[/C][/ROW]
[ROW][C]22[/C][C]163.71[/C][C]163.701134641943[/C][C]0.00886535805713606[/C][/ROW]
[ROW][C]23[/C][C]163.73[/C][C]163.720689717726[/C][C]0.0093102822736455[/C][/ROW]
[ROW][C]24[/C][C]163.73[/C][C]163.719768625538[/C][C]0.0102313744619664[/C][/ROW]
[ROW][C]25[/C][C]163.73[/C][C]163.87008435355[/C][C]-0.140084353550151[/C][/ROW]
[ROW][C]26[/C][C]163.73[/C][C]163.760364348663[/C][C]-0.0303643486632552[/C][/ROW]
[ROW][C]27[/C][C]163.93[/C][C]163.613681612850[/C][C]0.316318387150346[/C][/ROW]
[ROW][C]28[/C][C]164.27[/C][C]164.224330950272[/C][C]0.045669049728474[/C][/ROW]
[ROW][C]29[/C][C]164.57[/C][C]164.632722961873[/C][C]-0.0627229618733338[/C][/ROW]
[ROW][C]30[/C][C]164.73[/C][C]164.680227655419[/C][C]0.049772344580731[/C][/ROW]
[ROW][C]31[/C][C]164.73[/C][C]164.736451635245[/C][C]-0.00645163524529835[/C][/ROW]
[ROW][C]32[/C][C]164.76[/C][C]164.74813852739[/C][C]0.0118614726100077[/C][/ROW]
[ROW][C]33[/C][C]165.75[/C][C]164.910597769111[/C][C]0.839402230889476[/C][/ROW]
[ROW][C]34[/C][C]165.86[/C][C]165.895639124375[/C][C]-0.0356391243746543[/C][/ROW]
[ROW][C]35[/C][C]165.99[/C][C]165.880456519823[/C][C]0.109543480176541[/C][/ROW]
[ROW][C]36[/C][C]166.13[/C][C]165.959494284950[/C][C]0.170505715049615[/C][/ROW]
[ROW][C]37[/C][C]166.13[/C][C]166.237292137517[/C][C]-0.107292137516879[/C][/ROW]
[ROW][C]38[/C][C]166.13[/C][C]166.15429386368[/C][C]-0.0242938636800147[/C][/ROW]
[ROW][C]39[/C][C]166.15[/C][C]166.013352261125[/C][C]0.136647738874558[/C][/ROW]
[ROW][C]40[/C][C]166.45[/C][C]166.482052801465[/C][C]-0.0320528014645731[/C][/ROW]
[ROW][C]41[/C][C]166.48[/C][C]166.829333704375[/C][C]-0.349333704374885[/C][/ROW]
[ROW][C]42[/C][C]166.51[/C][C]166.650292585988[/C][C]-0.140292585987766[/C][/ROW]
[ROW][C]43[/C][C]166.51[/C][C]166.556216921551[/C][C]-0.0462169215512915[/C][/ROW]
[ROW][C]44[/C][C]166.51[/C][C]166.536691884141[/C][C]-0.0266918841414281[/C][/ROW]
[ROW][C]45[/C][C]166.58[/C][C]166.669502013826[/C][C]-0.0895020138255234[/C][/ROW]
[ROW][C]46[/C][C]166.82[/C][C]166.917874147183[/C][C]-0.0978741471831768[/C][/ROW]
[ROW][C]47[/C][C]167.35[/C][C]166.853254298988[/C][C]0.496745701011832[/C][/ROW]
[ROW][C]48[/C][C]167.5[/C][C]167.238981559636[/C][C]0.261018440363614[/C][/ROW]
[ROW][C]49[/C][C]167.5[/C][C]167.588250059571[/C][C]-0.0882500595710383[/C][/ROW]
[ROW][C]50[/C][C]167.6[/C][C]167.520398599096[/C][C]0.0796014009036128[/C][/ROW]
[ROW][C]51[/C][C]167.72[/C][C]167.461927978226[/C][C]0.258072021774154[/C][/ROW]
[ROW][C]52[/C][C]167.29[/C][C]168.026792349542[/C][C]-0.73679234954173[/C][/ROW]
[ROW][C]53[/C][C]166.98[/C][C]167.815368529448[/C][C]-0.835368529448488[/C][/ROW]
[ROW][C]54[/C][C]166.98[/C][C]167.251013348965[/C][C]-0.271013348965113[/C][/ROW]
[ROW][C]55[/C][C]166.98[/C][C]167.052908792308[/C][C]-0.0729087923084819[/C][/ROW]
[ROW][C]56[/C][C]166.98[/C][C]167.011684014241[/C][C]-0.0316840142409376[/C][/ROW]
[ROW][C]57[/C][C]167.63[/C][C]167.139916639368[/C][C]0.490083360631701[/C][/ROW]
[ROW][C]58[/C][C]167.83[/C][C]167.847085810724[/C][C]-0.0170858107236143[/C][/ROW]
[ROW][C]59[/C][C]167.85[/C][C]167.846676561473[/C][C]0.00332343852730332[/C][/ROW]
[ROW][C]60[/C][C]167.87[/C][C]167.840898425274[/C][C]0.0291015747259848[/C][/ROW]
[ROW][C]61[/C][C]167.87[/C][C]168.005591427698[/C][C]-0.135591427697506[/C][/ROW]
[ROW][C]62[/C][C]167.96[/C][C]167.899738303343[/C][C]0.0602616966572214[/C][/ROW]
[ROW][C]63[/C][C]167.7[/C][C]167.825444129975[/C][C]-0.125444129974937[/C][/ROW]
[ROW][C]64[/C][C]169.25[/C][C]168.084926800116[/C][C]1.16507319988364[/C][/ROW]
[ROW][C]65[/C][C]168.79[/C][C]169.380005206888[/C][C]-0.590005206887895[/C][/ROW]
[ROW][C]66[/C][C]168.77[/C][C]169.010690647766[/C][C]-0.240690647765604[/C][/ROW]
[ROW][C]67[/C][C]168.77[/C][C]168.837029183226[/C][C]-0.0670291832256567[/C][/ROW]
[ROW][C]68[/C][C]169[/C][C]168.800768715091[/C][C]0.199231284908791[/C][/ROW]
[ROW][C]69[/C][C]168.92[/C][C]169.112701247907[/C][C]-0.192701247906655[/C][/ROW]
[ROW][C]70[/C][C]169.23[/C][C]169.278699398062[/C][C]-0.0486993980623822[/C][/ROW]
[ROW][C]71[/C][C]169.28[/C][C]169.253294053690[/C][C]0.0267059463102157[/C][/ROW]
[ROW][C]72[/C][C]169.29[/C][C]169.266097655836[/C][C]0.0239023441644122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13416&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
13162.57161.9174097222220.652590277777733
14162.57162.4359805533380.134019446662421
15162.44162.4196989522070.0203010477933674
16162.79162.795852643753-0.00585264375331462
17163.15163.163370642374-0.0133706423742410
18163.23163.249926903731-0.0199269037311751
19163.23163.250863200289-0.0208632002891704
20163.23163.251047231904-0.0210472319038786
21163.38163.387324765307-0.00732476530654935
22163.71163.7011346419430.00886535805713606
23163.73163.7206897177260.0093102822736455
24163.73163.7197686255380.0102313744619664
25163.73163.87008435355-0.140084353550151
26163.73163.760364348663-0.0303643486632552
27163.93163.6136816128500.316318387150346
28164.27164.2243309502720.045669049728474
29164.57164.632722961873-0.0627229618733338
30164.73164.6802276554190.049772344580731
31164.73164.736451635245-0.00645163524529835
32164.76164.748138527390.0118614726100077
33165.75164.9105977691110.839402230889476
34165.86165.895639124375-0.0356391243746543
35165.99165.8804565198230.109543480176541
36166.13165.9594942849500.170505715049615
37166.13166.237292137517-0.107292137516879
38166.13166.15429386368-0.0242938636800147
39166.15166.0133522611250.136647738874558
40166.45166.482052801465-0.0320528014645731
41166.48166.829333704375-0.349333704374885
42166.51166.650292585988-0.140292585987766
43166.51166.556216921551-0.0462169215512915
44166.51166.536691884141-0.0266918841414281
45166.58166.669502013826-0.0895020138255234
46166.82166.917874147183-0.0978741471831768
47167.35166.8532542989880.496745701011832
48167.5167.2389815596360.261018440363614
49167.5167.588250059571-0.0882500595710383
50167.6167.5203985990960.0796014009036128
51167.72167.4619279782260.258072021774154
52167.29168.026792349542-0.73679234954173
53166.98167.815368529448-0.835368529448488
54166.98167.251013348965-0.271013348965113
55166.98167.052908792308-0.0729087923084819
56166.98167.011684014241-0.0316840142409376
57167.63167.1399166393680.490083360631701
58167.83167.847085810724-0.0170858107236143
59167.85167.8466765614730.00332343852730332
60167.87167.8408984252740.0291015747259848
61167.87168.005591427698-0.135591427697506
62167.96167.8997383033430.0602616966572214
63167.7167.825444129975-0.125444129974937
64169.25168.0849268001161.16507319988364
65168.79169.380005206888-0.590005206887895
66168.77169.010690647766-0.240690647765604
67168.77168.837029183226-0.0670291832256567
68169168.8007687150910.199231284908791
69168.92169.112701247907-0.192701247906655
70169.23169.278699398062-0.0486993980623822
71169.28169.2532940536900.0267059463102157
72169.29169.2660976558360.0239023441644122







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73169.426583951341168.83655114721170.016616755472
74169.428389281117168.675499038626170.181279523609
75169.306296279952168.419825676588170.192766883317
76169.666275163672168.663729338761170.668820988583
77170.036708840292168.930070733496171.143346947089
78170.134846881687168.932981824095171.336711939278
79170.151937479338168.861746228513171.442128730163
80170.168979196005168.796029953869171.541928438140
81170.322704125917168.871612029975171.773796221859
82170.641450501419169.116121162256172.166779840581
83170.654703203403169.058497148905172.250909257901
84170.646363355463168.982211626098172.310515084829

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 169.426583951341 & 168.83655114721 & 170.016616755472 \tabularnewline
74 & 169.428389281117 & 168.675499038626 & 170.181279523609 \tabularnewline
75 & 169.306296279952 & 168.419825676588 & 170.192766883317 \tabularnewline
76 & 169.666275163672 & 168.663729338761 & 170.668820988583 \tabularnewline
77 & 170.036708840292 & 168.930070733496 & 171.143346947089 \tabularnewline
78 & 170.134846881687 & 168.932981824095 & 171.336711939278 \tabularnewline
79 & 170.151937479338 & 168.861746228513 & 171.442128730163 \tabularnewline
80 & 170.168979196005 & 168.796029953869 & 171.541928438140 \tabularnewline
81 & 170.322704125917 & 168.871612029975 & 171.773796221859 \tabularnewline
82 & 170.641450501419 & 169.116121162256 & 172.166779840581 \tabularnewline
83 & 170.654703203403 & 169.058497148905 & 172.250909257901 \tabularnewline
84 & 170.646363355463 & 168.982211626098 & 172.310515084829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13416&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]169.426583951341[/C][C]168.83655114721[/C][C]170.016616755472[/C][/ROW]
[ROW][C]74[/C][C]169.428389281117[/C][C]168.675499038626[/C][C]170.181279523609[/C][/ROW]
[ROW][C]75[/C][C]169.306296279952[/C][C]168.419825676588[/C][C]170.192766883317[/C][/ROW]
[ROW][C]76[/C][C]169.666275163672[/C][C]168.663729338761[/C][C]170.668820988583[/C][/ROW]
[ROW][C]77[/C][C]170.036708840292[/C][C]168.930070733496[/C][C]171.143346947089[/C][/ROW]
[ROW][C]78[/C][C]170.134846881687[/C][C]168.932981824095[/C][C]171.336711939278[/C][/ROW]
[ROW][C]79[/C][C]170.151937479338[/C][C]168.861746228513[/C][C]171.442128730163[/C][/ROW]
[ROW][C]80[/C][C]170.168979196005[/C][C]168.796029953869[/C][C]171.541928438140[/C][/ROW]
[ROW][C]81[/C][C]170.322704125917[/C][C]168.871612029975[/C][C]171.773796221859[/C][/ROW]
[ROW][C]82[/C][C]170.641450501419[/C][C]169.116121162256[/C][C]172.166779840581[/C][/ROW]
[ROW][C]83[/C][C]170.654703203403[/C][C]169.058497148905[/C][C]172.250909257901[/C][/ROW]
[ROW][C]84[/C][C]170.646363355463[/C][C]168.982211626098[/C][C]172.310515084829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13416&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13416&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
73169.426583951341168.83655114721170.016616755472
74169.428389281117168.675499038626170.181279523609
75169.306296279952168.419825676588170.192766883317
76169.666275163672168.663729338761170.668820988583
77170.036708840292168.930070733496171.143346947089
78170.134846881687168.932981824095171.336711939278
79170.151937479338168.861746228513171.442128730163
80170.168979196005168.796029953869171.541928438140
81170.322704125917168.871612029975171.773796221859
82170.641450501419169.116121162256172.166779840581
83170.654703203403169.058497148905172.250909257901
84170.646363355463168.982211626098172.310515084829



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')