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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Jan 2013 11:58:48 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/12/t13580101586ym95ml7zjj5ox5.htm/, Retrieved Sun, 28 Apr 2024 07:04:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205245, Retrieved Sun, 28 Apr 2024 07:04:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-12 16:58:48] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
33,7
34,59
35,1
35,87
37,15
37,61
37,97
38,94
39,18
39,49
39,86
40,02
40,2
40,85
41,45
41,7
41,92
41,97
42,31
42,61
42,82
43,07
43,51
43,57
43,86
44,49
45,99
48,22
49,46
50,39
50,4
50,59
51,32
51,86
52,47
52,73
52,73
53,59
54,11
54,8
55,72
56,06
56,66
57,05
57,31
57,89
58,32
58,72
59,02
59,54
61,49
62,26
63,49
64,36
65,93
66,82
68,85
71,27
72,27
73,4
73,58
74,84
75,74
77,81
78,74
79,06
79,48
81,19
85,11
86,64
88,48
89,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205245&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205245&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205245&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.199739945378135
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.199739945378135 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205245&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]0.199739945378135[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205245&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205245&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
beta0.199739945378135
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
335.135.48-0.380000000000003
435.8735.9140988207563-0.0440988207563109
537.1536.67529052470720.474709475292798
637.6138.0501089693727-0.440108969372666
737.9738.4222016278697-0.452201627869748
838.9438.69187889941910.24812110058086
939.1839.7114385944963-0.531438594496322
1039.4939.8452890786598-0.355289078659794
1139.8640.0843236574948-0.224323657494843
1240.0240.4095172623998-0.389517262399792
1340.240.4917151056842-0.291715105684219
1440.8540.61344794640890.236552053591119
1541.4541.31069684067230.139303159327746
1641.741.9385212461074-0.238521246107382
1741.9242.1408790254384-0.220879025438371
1841.9742.3167606609621-0.346760660962133
1942.3142.29749870548230.0125012945177332
2042.6142.6399957133664-0.0299957133664037
2142.8242.934004371217-0.114004371217014
2243.0743.1212331443373-0.0512331443372602
2343.5143.36099983888580.149000161114209
2443.5743.8307611229281-0.260761122928066
2543.8643.83867671047770.0213232895223214
2644.4944.13293582316210.357064176837852
2745.9944.83425580234021.15574419765977
2848.2246.56510408525191.65489591474811
2949.4649.12565290487020.334347095129829
3050.3950.4324353753887-0.0424353753887416
3150.451.3539593358265-0.953959335826497
3250.5951.1734155501955-0.583415550195546
3351.3251.24688416006670.0731158399332585
3451.8651.9914883139413-0.131488313941283
3552.4752.5052248452968-0.0352248452967885
3652.7353.1081890366213-0.378189036621258
3752.7353.2926495791039-0.562649579103912
3853.5953.18026598290670.409734017093335
3954.1154.1221062331005-0.0121062331004609
4054.854.63968813476220.160311865237766
4155.7255.36170881796830.358291182031707
4256.0656.3532738790968-0.293273879096773
4356.6656.63469537050520.0253046294948405
4457.0557.2397497158183-0.189749715818266
4557.3157.5918491179452-0.2818491179452
4657.8957.7955525905220.0944474094780432
4758.3258.3944175109322-0.0744175109322072
4858.7258.8095533613634-0.0895533613634356
4959.0259.1916659778563-0.171665977856264
5059.5459.4573774248160.0826225751840184
5161.4959.99388045347021.49611954652977
5262.2662.24271528997320.0172847100267504
5363.4963.01616773700990.473832262990136
5464.3664.34081096733790.0191890326620836
5565.9365.21464378367370.715356216326313
5666.8266.9275289952486-0.107528995248643
5768.8567.79605115961111.0539488403889
5871.2770.03656684342171.23343315657827
5972.2772.7029327147443-0.432932714744254
6073.473.6164587579488-0.216458757948814
6173.5874.7032232974595-1.12322329745952
6274.8474.65887073737750.181129262622505
6375.7475.9550494864001-0.215049486400105
6477.8176.81209551373290.997904486267061
6578.7479.0814169013125-0.341416901312527
6679.0679.9432223080932-0.883222308093181
6779.4880.0868075325179-0.606807532517905
6881.1980.38560382911770.804396170882256
6985.1182.25627387635212.85372612364786
7086.6486.7462769764137-0.106276976413724
7188.4888.25504921894990.224950781050111
7289.290.1399808756696-0.939980875669605

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 35.1 & 35.48 & -0.380000000000003 \tabularnewline
4 & 35.87 & 35.9140988207563 & -0.0440988207563109 \tabularnewline
5 & 37.15 & 36.6752905247072 & 0.474709475292798 \tabularnewline
6 & 37.61 & 38.0501089693727 & -0.440108969372666 \tabularnewline
7 & 37.97 & 38.4222016278697 & -0.452201627869748 \tabularnewline
8 & 38.94 & 38.6918788994191 & 0.24812110058086 \tabularnewline
9 & 39.18 & 39.7114385944963 & -0.531438594496322 \tabularnewline
10 & 39.49 & 39.8452890786598 & -0.355289078659794 \tabularnewline
11 & 39.86 & 40.0843236574948 & -0.224323657494843 \tabularnewline
12 & 40.02 & 40.4095172623998 & -0.389517262399792 \tabularnewline
13 & 40.2 & 40.4917151056842 & -0.291715105684219 \tabularnewline
14 & 40.85 & 40.6134479464089 & 0.236552053591119 \tabularnewline
15 & 41.45 & 41.3106968406723 & 0.139303159327746 \tabularnewline
16 & 41.7 & 41.9385212461074 & -0.238521246107382 \tabularnewline
17 & 41.92 & 42.1408790254384 & -0.220879025438371 \tabularnewline
18 & 41.97 & 42.3167606609621 & -0.346760660962133 \tabularnewline
19 & 42.31 & 42.2974987054823 & 0.0125012945177332 \tabularnewline
20 & 42.61 & 42.6399957133664 & -0.0299957133664037 \tabularnewline
21 & 42.82 & 42.934004371217 & -0.114004371217014 \tabularnewline
22 & 43.07 & 43.1212331443373 & -0.0512331443372602 \tabularnewline
23 & 43.51 & 43.3609998388858 & 0.149000161114209 \tabularnewline
24 & 43.57 & 43.8307611229281 & -0.260761122928066 \tabularnewline
25 & 43.86 & 43.8386767104777 & 0.0213232895223214 \tabularnewline
26 & 44.49 & 44.1329358231621 & 0.357064176837852 \tabularnewline
27 & 45.99 & 44.8342558023402 & 1.15574419765977 \tabularnewline
28 & 48.22 & 46.5651040852519 & 1.65489591474811 \tabularnewline
29 & 49.46 & 49.1256529048702 & 0.334347095129829 \tabularnewline
30 & 50.39 & 50.4324353753887 & -0.0424353753887416 \tabularnewline
31 & 50.4 & 51.3539593358265 & -0.953959335826497 \tabularnewline
32 & 50.59 & 51.1734155501955 & -0.583415550195546 \tabularnewline
33 & 51.32 & 51.2468841600667 & 0.0731158399332585 \tabularnewline
34 & 51.86 & 51.9914883139413 & -0.131488313941283 \tabularnewline
35 & 52.47 & 52.5052248452968 & -0.0352248452967885 \tabularnewline
36 & 52.73 & 53.1081890366213 & -0.378189036621258 \tabularnewline
37 & 52.73 & 53.2926495791039 & -0.562649579103912 \tabularnewline
38 & 53.59 & 53.1802659829067 & 0.409734017093335 \tabularnewline
39 & 54.11 & 54.1221062331005 & -0.0121062331004609 \tabularnewline
40 & 54.8 & 54.6396881347622 & 0.160311865237766 \tabularnewline
41 & 55.72 & 55.3617088179683 & 0.358291182031707 \tabularnewline
42 & 56.06 & 56.3532738790968 & -0.293273879096773 \tabularnewline
43 & 56.66 & 56.6346953705052 & 0.0253046294948405 \tabularnewline
44 & 57.05 & 57.2397497158183 & -0.189749715818266 \tabularnewline
45 & 57.31 & 57.5918491179452 & -0.2818491179452 \tabularnewline
46 & 57.89 & 57.795552590522 & 0.0944474094780432 \tabularnewline
47 & 58.32 & 58.3944175109322 & -0.0744175109322072 \tabularnewline
48 & 58.72 & 58.8095533613634 & -0.0895533613634356 \tabularnewline
49 & 59.02 & 59.1916659778563 & -0.171665977856264 \tabularnewline
50 & 59.54 & 59.457377424816 & 0.0826225751840184 \tabularnewline
51 & 61.49 & 59.9938804534702 & 1.49611954652977 \tabularnewline
52 & 62.26 & 62.2427152899732 & 0.0172847100267504 \tabularnewline
53 & 63.49 & 63.0161677370099 & 0.473832262990136 \tabularnewline
54 & 64.36 & 64.3408109673379 & 0.0191890326620836 \tabularnewline
55 & 65.93 & 65.2146437836737 & 0.715356216326313 \tabularnewline
56 & 66.82 & 66.9275289952486 & -0.107528995248643 \tabularnewline
57 & 68.85 & 67.7960511596111 & 1.0539488403889 \tabularnewline
58 & 71.27 & 70.0365668434217 & 1.23343315657827 \tabularnewline
59 & 72.27 & 72.7029327147443 & -0.432932714744254 \tabularnewline
60 & 73.4 & 73.6164587579488 & -0.216458757948814 \tabularnewline
61 & 73.58 & 74.7032232974595 & -1.12322329745952 \tabularnewline
62 & 74.84 & 74.6588707373775 & 0.181129262622505 \tabularnewline
63 & 75.74 & 75.9550494864001 & -0.215049486400105 \tabularnewline
64 & 77.81 & 76.8120955137329 & 0.997904486267061 \tabularnewline
65 & 78.74 & 79.0814169013125 & -0.341416901312527 \tabularnewline
66 & 79.06 & 79.9432223080932 & -0.883222308093181 \tabularnewline
67 & 79.48 & 80.0868075325179 & -0.606807532517905 \tabularnewline
68 & 81.19 & 80.3856038291177 & 0.804396170882256 \tabularnewline
69 & 85.11 & 82.2562738763521 & 2.85372612364786 \tabularnewline
70 & 86.64 & 86.7462769764137 & -0.106276976413724 \tabularnewline
71 & 88.48 & 88.2550492189499 & 0.224950781050111 \tabularnewline
72 & 89.2 & 90.1399808756696 & -0.939980875669605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205245&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]3[/C][C]35.1[/C][C]35.48[/C][C]-0.380000000000003[/C][/ROW]
[ROW][C]4[/C][C]35.87[/C][C]35.9140988207563[/C][C]-0.0440988207563109[/C][/ROW]
[ROW][C]5[/C][C]37.15[/C][C]36.6752905247072[/C][C]0.474709475292798[/C][/ROW]
[ROW][C]6[/C][C]37.61[/C][C]38.0501089693727[/C][C]-0.440108969372666[/C][/ROW]
[ROW][C]7[/C][C]37.97[/C][C]38.4222016278697[/C][C]-0.452201627869748[/C][/ROW]
[ROW][C]8[/C][C]38.94[/C][C]38.6918788994191[/C][C]0.24812110058086[/C][/ROW]
[ROW][C]9[/C][C]39.18[/C][C]39.7114385944963[/C][C]-0.531438594496322[/C][/ROW]
[ROW][C]10[/C][C]39.49[/C][C]39.8452890786598[/C][C]-0.355289078659794[/C][/ROW]
[ROW][C]11[/C][C]39.86[/C][C]40.0843236574948[/C][C]-0.224323657494843[/C][/ROW]
[ROW][C]12[/C][C]40.02[/C][C]40.4095172623998[/C][C]-0.389517262399792[/C][/ROW]
[ROW][C]13[/C][C]40.2[/C][C]40.4917151056842[/C][C]-0.291715105684219[/C][/ROW]
[ROW][C]14[/C][C]40.85[/C][C]40.6134479464089[/C][C]0.236552053591119[/C][/ROW]
[ROW][C]15[/C][C]41.45[/C][C]41.3106968406723[/C][C]0.139303159327746[/C][/ROW]
[ROW][C]16[/C][C]41.7[/C][C]41.9385212461074[/C][C]-0.238521246107382[/C][/ROW]
[ROW][C]17[/C][C]41.92[/C][C]42.1408790254384[/C][C]-0.220879025438371[/C][/ROW]
[ROW][C]18[/C][C]41.97[/C][C]42.3167606609621[/C][C]-0.346760660962133[/C][/ROW]
[ROW][C]19[/C][C]42.31[/C][C]42.2974987054823[/C][C]0.0125012945177332[/C][/ROW]
[ROW][C]20[/C][C]42.61[/C][C]42.6399957133664[/C][C]-0.0299957133664037[/C][/ROW]
[ROW][C]21[/C][C]42.82[/C][C]42.934004371217[/C][C]-0.114004371217014[/C][/ROW]
[ROW][C]22[/C][C]43.07[/C][C]43.1212331443373[/C][C]-0.0512331443372602[/C][/ROW]
[ROW][C]23[/C][C]43.51[/C][C]43.3609998388858[/C][C]0.149000161114209[/C][/ROW]
[ROW][C]24[/C][C]43.57[/C][C]43.8307611229281[/C][C]-0.260761122928066[/C][/ROW]
[ROW][C]25[/C][C]43.86[/C][C]43.8386767104777[/C][C]0.0213232895223214[/C][/ROW]
[ROW][C]26[/C][C]44.49[/C][C]44.1329358231621[/C][C]0.357064176837852[/C][/ROW]
[ROW][C]27[/C][C]45.99[/C][C]44.8342558023402[/C][C]1.15574419765977[/C][/ROW]
[ROW][C]28[/C][C]48.22[/C][C]46.5651040852519[/C][C]1.65489591474811[/C][/ROW]
[ROW][C]29[/C][C]49.46[/C][C]49.1256529048702[/C][C]0.334347095129829[/C][/ROW]
[ROW][C]30[/C][C]50.39[/C][C]50.4324353753887[/C][C]-0.0424353753887416[/C][/ROW]
[ROW][C]31[/C][C]50.4[/C][C]51.3539593358265[/C][C]-0.953959335826497[/C][/ROW]
[ROW][C]32[/C][C]50.59[/C][C]51.1734155501955[/C][C]-0.583415550195546[/C][/ROW]
[ROW][C]33[/C][C]51.32[/C][C]51.2468841600667[/C][C]0.0731158399332585[/C][/ROW]
[ROW][C]34[/C][C]51.86[/C][C]51.9914883139413[/C][C]-0.131488313941283[/C][/ROW]
[ROW][C]35[/C][C]52.47[/C][C]52.5052248452968[/C][C]-0.0352248452967885[/C][/ROW]
[ROW][C]36[/C][C]52.73[/C][C]53.1081890366213[/C][C]-0.378189036621258[/C][/ROW]
[ROW][C]37[/C][C]52.73[/C][C]53.2926495791039[/C][C]-0.562649579103912[/C][/ROW]
[ROW][C]38[/C][C]53.59[/C][C]53.1802659829067[/C][C]0.409734017093335[/C][/ROW]
[ROW][C]39[/C][C]54.11[/C][C]54.1221062331005[/C][C]-0.0121062331004609[/C][/ROW]
[ROW][C]40[/C][C]54.8[/C][C]54.6396881347622[/C][C]0.160311865237766[/C][/ROW]
[ROW][C]41[/C][C]55.72[/C][C]55.3617088179683[/C][C]0.358291182031707[/C][/ROW]
[ROW][C]42[/C][C]56.06[/C][C]56.3532738790968[/C][C]-0.293273879096773[/C][/ROW]
[ROW][C]43[/C][C]56.66[/C][C]56.6346953705052[/C][C]0.0253046294948405[/C][/ROW]
[ROW][C]44[/C][C]57.05[/C][C]57.2397497158183[/C][C]-0.189749715818266[/C][/ROW]
[ROW][C]45[/C][C]57.31[/C][C]57.5918491179452[/C][C]-0.2818491179452[/C][/ROW]
[ROW][C]46[/C][C]57.89[/C][C]57.795552590522[/C][C]0.0944474094780432[/C][/ROW]
[ROW][C]47[/C][C]58.32[/C][C]58.3944175109322[/C][C]-0.0744175109322072[/C][/ROW]
[ROW][C]48[/C][C]58.72[/C][C]58.8095533613634[/C][C]-0.0895533613634356[/C][/ROW]
[ROW][C]49[/C][C]59.02[/C][C]59.1916659778563[/C][C]-0.171665977856264[/C][/ROW]
[ROW][C]50[/C][C]59.54[/C][C]59.457377424816[/C][C]0.0826225751840184[/C][/ROW]
[ROW][C]51[/C][C]61.49[/C][C]59.9938804534702[/C][C]1.49611954652977[/C][/ROW]
[ROW][C]52[/C][C]62.26[/C][C]62.2427152899732[/C][C]0.0172847100267504[/C][/ROW]
[ROW][C]53[/C][C]63.49[/C][C]63.0161677370099[/C][C]0.473832262990136[/C][/ROW]
[ROW][C]54[/C][C]64.36[/C][C]64.3408109673379[/C][C]0.0191890326620836[/C][/ROW]
[ROW][C]55[/C][C]65.93[/C][C]65.2146437836737[/C][C]0.715356216326313[/C][/ROW]
[ROW][C]56[/C][C]66.82[/C][C]66.9275289952486[/C][C]-0.107528995248643[/C][/ROW]
[ROW][C]57[/C][C]68.85[/C][C]67.7960511596111[/C][C]1.0539488403889[/C][/ROW]
[ROW][C]58[/C][C]71.27[/C][C]70.0365668434217[/C][C]1.23343315657827[/C][/ROW]
[ROW][C]59[/C][C]72.27[/C][C]72.7029327147443[/C][C]-0.432932714744254[/C][/ROW]
[ROW][C]60[/C][C]73.4[/C][C]73.6164587579488[/C][C]-0.216458757948814[/C][/ROW]
[ROW][C]61[/C][C]73.58[/C][C]74.7032232974595[/C][C]-1.12322329745952[/C][/ROW]
[ROW][C]62[/C][C]74.84[/C][C]74.6588707373775[/C][C]0.181129262622505[/C][/ROW]
[ROW][C]63[/C][C]75.74[/C][C]75.9550494864001[/C][C]-0.215049486400105[/C][/ROW]
[ROW][C]64[/C][C]77.81[/C][C]76.8120955137329[/C][C]0.997904486267061[/C][/ROW]
[ROW][C]65[/C][C]78.74[/C][C]79.0814169013125[/C][C]-0.341416901312527[/C][/ROW]
[ROW][C]66[/C][C]79.06[/C][C]79.9432223080932[/C][C]-0.883222308093181[/C][/ROW]
[ROW][C]67[/C][C]79.48[/C][C]80.0868075325179[/C][C]-0.606807532517905[/C][/ROW]
[ROW][C]68[/C][C]81.19[/C][C]80.3856038291177[/C][C]0.804396170882256[/C][/ROW]
[ROW][C]69[/C][C]85.11[/C][C]82.2562738763521[/C][C]2.85372612364786[/C][/ROW]
[ROW][C]70[/C][C]86.64[/C][C]86.7462769764137[/C][C]-0.106276976413724[/C][/ROW]
[ROW][C]71[/C][C]88.48[/C][C]88.2550492189499[/C][C]0.224950781050111[/C][/ROW]
[ROW][C]72[/C][C]89.2[/C][C]90.1399808756696[/C][C]-0.939980875669605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205245&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205245&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
335.135.48-0.380000000000003
435.8735.9140988207563-0.0440988207563109
537.1536.67529052470720.474709475292798
637.6138.0501089693727-0.440108969372666
737.9738.4222016278697-0.452201627869748
838.9438.69187889941910.24812110058086
939.1839.7114385944963-0.531438594496322
1039.4939.8452890786598-0.355289078659794
1139.8640.0843236574948-0.224323657494843
1240.0240.4095172623998-0.389517262399792
1340.240.4917151056842-0.291715105684219
1440.8540.61344794640890.236552053591119
1541.4541.31069684067230.139303159327746
1641.741.9385212461074-0.238521246107382
1741.9242.1408790254384-0.220879025438371
1841.9742.3167606609621-0.346760660962133
1942.3142.29749870548230.0125012945177332
2042.6142.6399957133664-0.0299957133664037
2142.8242.934004371217-0.114004371217014
2243.0743.1212331443373-0.0512331443372602
2343.5143.36099983888580.149000161114209
2443.5743.8307611229281-0.260761122928066
2543.8643.83867671047770.0213232895223214
2644.4944.13293582316210.357064176837852
2745.9944.83425580234021.15574419765977
2848.2246.56510408525191.65489591474811
2949.4649.12565290487020.334347095129829
3050.3950.4324353753887-0.0424353753887416
3150.451.3539593358265-0.953959335826497
3250.5951.1734155501955-0.583415550195546
3351.3251.24688416006670.0731158399332585
3451.8651.9914883139413-0.131488313941283
3552.4752.5052248452968-0.0352248452967885
3652.7353.1081890366213-0.378189036621258
3752.7353.2926495791039-0.562649579103912
3853.5953.18026598290670.409734017093335
3954.1154.1221062331005-0.0121062331004609
4054.854.63968813476220.160311865237766
4155.7255.36170881796830.358291182031707
4256.0656.3532738790968-0.293273879096773
4356.6656.63469537050520.0253046294948405
4457.0557.2397497158183-0.189749715818266
4557.3157.5918491179452-0.2818491179452
4657.8957.7955525905220.0944474094780432
4758.3258.3944175109322-0.0744175109322072
4858.7258.8095533613634-0.0895533613634356
4959.0259.1916659778563-0.171665977856264
5059.5459.4573774248160.0826225751840184
5161.4959.99388045347021.49611954652977
5262.2662.24271528997320.0172847100267504
5363.4963.01616773700990.473832262990136
5464.3664.34081096733790.0191890326620836
5565.9365.21464378367370.715356216326313
5666.8266.9275289952486-0.107528995248643
5768.8567.79605115961111.0539488403889
5871.2770.03656684342171.23343315657827
5972.2772.7029327147443-0.432932714744254
6073.473.6164587579488-0.216458757948814
6173.5874.7032232974595-1.12322329745952
6274.8474.65887073737750.181129262622505
6375.7475.9550494864001-0.215049486400105
6477.8176.81209551373290.997904486267061
6578.7479.0814169013125-0.341416901312527
6679.0679.9432223080932-0.883222308093181
6779.4880.0868075325179-0.606807532517905
6881.1980.38560382911770.804396170882256
6985.1182.25627387635212.85372612364786
7086.6486.7462769764137-0.106276976413724
7188.4888.25504921894990.224950781050111
7289.290.1399808756696-0.939980875669605







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7390.672229146906989.431791157603891.9126671362099
7492.144458293813790.207080016094394.0818365715332
7593.616687440720691.015337874908396.2180370065329
7695.088916587627591.817492382551498.3603407927035
7796.561145734534392.6011204952803100.521170973788
7898.033374881441293.3612720071456102.705477755737
7999.505604028348194.095869519751104.915338536945
80100.97783317525594.8041291445634107.151537205946
81102.45006232216295.4859039171751109.414220727149
82103.92229146906996.141376037479111.703206900658
83105.39452061597696.770900468003114.018140763948
84106.86674976288297.3749208661319116.358578659633

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 90.6722291469069 & 89.4317911576038 & 91.9126671362099 \tabularnewline
74 & 92.1444582938137 & 90.2070800160943 & 94.0818365715332 \tabularnewline
75 & 93.6166874407206 & 91.0153378749083 & 96.2180370065329 \tabularnewline
76 & 95.0889165876275 & 91.8174923825514 & 98.3603407927035 \tabularnewline
77 & 96.5611457345343 & 92.6011204952803 & 100.521170973788 \tabularnewline
78 & 98.0333748814412 & 93.3612720071456 & 102.705477755737 \tabularnewline
79 & 99.5056040283481 & 94.095869519751 & 104.915338536945 \tabularnewline
80 & 100.977833175255 & 94.8041291445634 & 107.151537205946 \tabularnewline
81 & 102.450062322162 & 95.4859039171751 & 109.414220727149 \tabularnewline
82 & 103.922291469069 & 96.141376037479 & 111.703206900658 \tabularnewline
83 & 105.394520615976 & 96.770900468003 & 114.018140763948 \tabularnewline
84 & 106.866749762882 & 97.3749208661319 & 116.358578659633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205245&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]90.6722291469069[/C][C]89.4317911576038[/C][C]91.9126671362099[/C][/ROW]
[ROW][C]74[/C][C]92.1444582938137[/C][C]90.2070800160943[/C][C]94.0818365715332[/C][/ROW]
[ROW][C]75[/C][C]93.6166874407206[/C][C]91.0153378749083[/C][C]96.2180370065329[/C][/ROW]
[ROW][C]76[/C][C]95.0889165876275[/C][C]91.8174923825514[/C][C]98.3603407927035[/C][/ROW]
[ROW][C]77[/C][C]96.5611457345343[/C][C]92.6011204952803[/C][C]100.521170973788[/C][/ROW]
[ROW][C]78[/C][C]98.0333748814412[/C][C]93.3612720071456[/C][C]102.705477755737[/C][/ROW]
[ROW][C]79[/C][C]99.5056040283481[/C][C]94.095869519751[/C][C]104.915338536945[/C][/ROW]
[ROW][C]80[/C][C]100.977833175255[/C][C]94.8041291445634[/C][C]107.151537205946[/C][/ROW]
[ROW][C]81[/C][C]102.450062322162[/C][C]95.4859039171751[/C][C]109.414220727149[/C][/ROW]
[ROW][C]82[/C][C]103.922291469069[/C][C]96.141376037479[/C][C]111.703206900658[/C][/ROW]
[ROW][C]83[/C][C]105.394520615976[/C][C]96.770900468003[/C][C]114.018140763948[/C][/ROW]
[ROW][C]84[/C][C]106.866749762882[/C][C]97.3749208661319[/C][C]116.358578659633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205245&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205245&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
7390.672229146906989.431791157603891.9126671362099
7492.144458293813790.207080016094394.0818365715332
7593.616687440720691.015337874908396.2180370065329
7695.088916587627591.817492382551498.3603407927035
7796.561145734534392.6011204952803100.521170973788
7898.033374881441293.3612720071456102.705477755737
7999.505604028348194.095869519751104.915338536945
80100.97783317525594.8041291445634107.151537205946
81102.45006232216295.4859039171751109.414220727149
82103.92229146906996.141376037479111.703206900658
83105.39452061597696.770900468003114.018140763948
84106.86674976288297.3749208661319116.358578659633



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