Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 May 2015 12:07:59 +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/2015/May/25/t1432552142p00pyurkizqyecy.htm/, Retrieved Tue, 07 May 2024 14:13:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279335, Retrieved Tue, 07 May 2024 14:13:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsadditief model double eigen reeks valerie weyts karel de grote-hogeschool
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [exponential smoot...] [2015-04-02 20:24:11] [69304374246e9fd5f7a19a35f2b701e6]
- R PD    [Exponential Smoothing] [additief model do...] [2015-05-25 11:07:59] [ab73e159a571dceeee45078a19254ea4] [Current]
Feedback Forum

Post a new message
Dataseries X:
123.2
136.9
146.8
149.6
146.5
157
147.9
133.6
128.7
100.8
91.8
89.3
96.7
91.6
93.3
93.3
101
100.4
86.9
83.9
80.3
87.7
92.7
95.5
92
87.4
86.8
83.7
85
81.7
90.9
101.5
113.8
120.1
122.1
132.5
140
149.4
144.3
154.4
151.4
145.5
136.8
146.6
145.1
133.6
131.4
127.5
130.1
131.1
132.3
128.6
125.1
128.7
156.1
163.2
159.8
157.4
156.2
152.5
149.4
145.9
144.8
135.9
137.6
136
117.7
111.5
107.8
107.3
102.6
101




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279335&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]2 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=279335&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279335&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.389135269023801
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.389135269023801 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279335&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]0.389135269023801[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279335&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279335&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
beta0.389135269023801
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3146.8150.6-3.80000000000001
4149.6159.02128597771-9.42128597770957
5146.5158.155131324223-11.6551313242234
6157150.5197086608646.48029133913602
7147.9163.541418574471-15.6414185744713
8133.6148.354790949581-14.7547909495805
9128.7128.3131814040260.386818595974432
10100.8123.563706162433-22.7637061624335
1191.886.80554524093624.99445475906384
1289.379.74906373723179.55093626276833
1396.780.965669889273215.7343301107268
1491.694.4884526698202-2.88845266982018
1593.388.26445386308725.03554613691283
1693.391.92396246375651.37603753624349
1710192.45942720060958.54057279939053
18100.4103.482865294518-3.08286529451766
1986.9101.683213678771-14.7832136787714
2083.982.43054384684631.46945615315366
2180.380.00236106232250.297638937677519
2287.776.518182870407611.1818171295924
2392.788.26942228730654.43057771269352
2495.594.99351633746630.506483662533668
259297.9906069937425-5.99060699374253
2687.492.1594505296167-4.75945052961666
2786.885.70738046736881.09261953263118
2883.785.5325572631399-1.8325572631399
298581.71944459954643.28055540045355
3081.784.2960244078494-2.59602440784941
3190.979.985819751508610.9141802484914
32101.593.43291221867968.06708778132044
33113.8107.1721005927026.62789940729769
34120.1122.051250011624-1.95125001162378
35122.1127.591949813418-5.49194981341786
36132.5127.4548384453085.04516155469172
37140139.8180887441620.181911255838202
38149.4147.3888768296412.01112317035916
39144.3157.571475785579-13.2714757855786
40154.4147.3070764854157.09292351458541
41151.4160.167183185428-8.76718318542802
42145.5153.755562997986-8.25556299798555
43136.8144.643032269822-7.84303226982149
44146.6132.89103179754213.7089682024578
45145.1148.025674827044-2.92567482704433
46133.6145.387191566146-11.7871915661463
47131.4129.3003796050192.09962039498114
48127.5127.917415952268-0.417415952267717
49130.1123.8549846833876.24501531661281
50131.1128.8851403986752.21485960132492
51132.3130.7470203854871.55297961451342
52128.6132.551339525569-3.95133952556878
53125.1127.313733956282-2.21373395628217
54128.7122.9522919976575.7477080023428
55156.1128.78892789741927.3110721025809
56163.2166.816629287385-3.61662928738536
57159.8172.509271276679-12.7092712766793
58157.4164.163645579332-6.76364557933223
59156.2159.131672537237-2.93167253723715
60152.5156.79085535577-4.29085535576965
61149.4151.42113220256-2.02113220256001
62145.9147.534638379184-1.63463837918417
63144.8143.3985429337441.40145706625631
64135.9142.843899306247-6.94389930624666
65137.6131.2417831816366.35821681836381
66136135.4159895937620.584010406238178
67117.7134.043248640306-16.343248640306
68111.5109.3835141839382.11648581606234
69107.8104.0071134613563.79288653864386
70107.3101.7830593849485.51694061505192
71102.6103.429895555375-0.829895555374648
7210198.40695392517232.59304607482774

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 146.8 & 150.6 & -3.80000000000001 \tabularnewline
4 & 149.6 & 159.02128597771 & -9.42128597770957 \tabularnewline
5 & 146.5 & 158.155131324223 & -11.6551313242234 \tabularnewline
6 & 157 & 150.519708660864 & 6.48029133913602 \tabularnewline
7 & 147.9 & 163.541418574471 & -15.6414185744713 \tabularnewline
8 & 133.6 & 148.354790949581 & -14.7547909495805 \tabularnewline
9 & 128.7 & 128.313181404026 & 0.386818595974432 \tabularnewline
10 & 100.8 & 123.563706162433 & -22.7637061624335 \tabularnewline
11 & 91.8 & 86.8055452409362 & 4.99445475906384 \tabularnewline
12 & 89.3 & 79.7490637372317 & 9.55093626276833 \tabularnewline
13 & 96.7 & 80.9656698892732 & 15.7343301107268 \tabularnewline
14 & 91.6 & 94.4884526698202 & -2.88845266982018 \tabularnewline
15 & 93.3 & 88.2644538630872 & 5.03554613691283 \tabularnewline
16 & 93.3 & 91.9239624637565 & 1.37603753624349 \tabularnewline
17 & 101 & 92.4594272006095 & 8.54057279939053 \tabularnewline
18 & 100.4 & 103.482865294518 & -3.08286529451766 \tabularnewline
19 & 86.9 & 101.683213678771 & -14.7832136787714 \tabularnewline
20 & 83.9 & 82.4305438468463 & 1.46945615315366 \tabularnewline
21 & 80.3 & 80.0023610623225 & 0.297638937677519 \tabularnewline
22 & 87.7 & 76.5181828704076 & 11.1818171295924 \tabularnewline
23 & 92.7 & 88.2694222873065 & 4.43057771269352 \tabularnewline
24 & 95.5 & 94.9935163374663 & 0.506483662533668 \tabularnewline
25 & 92 & 97.9906069937425 & -5.99060699374253 \tabularnewline
26 & 87.4 & 92.1594505296167 & -4.75945052961666 \tabularnewline
27 & 86.8 & 85.7073804673688 & 1.09261953263118 \tabularnewline
28 & 83.7 & 85.5325572631399 & -1.8325572631399 \tabularnewline
29 & 85 & 81.7194445995464 & 3.28055540045355 \tabularnewline
30 & 81.7 & 84.2960244078494 & -2.59602440784941 \tabularnewline
31 & 90.9 & 79.9858197515086 & 10.9141802484914 \tabularnewline
32 & 101.5 & 93.4329122186796 & 8.06708778132044 \tabularnewline
33 & 113.8 & 107.172100592702 & 6.62789940729769 \tabularnewline
34 & 120.1 & 122.051250011624 & -1.95125001162378 \tabularnewline
35 & 122.1 & 127.591949813418 & -5.49194981341786 \tabularnewline
36 & 132.5 & 127.454838445308 & 5.04516155469172 \tabularnewline
37 & 140 & 139.818088744162 & 0.181911255838202 \tabularnewline
38 & 149.4 & 147.388876829641 & 2.01112317035916 \tabularnewline
39 & 144.3 & 157.571475785579 & -13.2714757855786 \tabularnewline
40 & 154.4 & 147.307076485415 & 7.09292351458541 \tabularnewline
41 & 151.4 & 160.167183185428 & -8.76718318542802 \tabularnewline
42 & 145.5 & 153.755562997986 & -8.25556299798555 \tabularnewline
43 & 136.8 & 144.643032269822 & -7.84303226982149 \tabularnewline
44 & 146.6 & 132.891031797542 & 13.7089682024578 \tabularnewline
45 & 145.1 & 148.025674827044 & -2.92567482704433 \tabularnewline
46 & 133.6 & 145.387191566146 & -11.7871915661463 \tabularnewline
47 & 131.4 & 129.300379605019 & 2.09962039498114 \tabularnewline
48 & 127.5 & 127.917415952268 & -0.417415952267717 \tabularnewline
49 & 130.1 & 123.854984683387 & 6.24501531661281 \tabularnewline
50 & 131.1 & 128.885140398675 & 2.21485960132492 \tabularnewline
51 & 132.3 & 130.747020385487 & 1.55297961451342 \tabularnewline
52 & 128.6 & 132.551339525569 & -3.95133952556878 \tabularnewline
53 & 125.1 & 127.313733956282 & -2.21373395628217 \tabularnewline
54 & 128.7 & 122.952291997657 & 5.7477080023428 \tabularnewline
55 & 156.1 & 128.788927897419 & 27.3110721025809 \tabularnewline
56 & 163.2 & 166.816629287385 & -3.61662928738536 \tabularnewline
57 & 159.8 & 172.509271276679 & -12.7092712766793 \tabularnewline
58 & 157.4 & 164.163645579332 & -6.76364557933223 \tabularnewline
59 & 156.2 & 159.131672537237 & -2.93167253723715 \tabularnewline
60 & 152.5 & 156.79085535577 & -4.29085535576965 \tabularnewline
61 & 149.4 & 151.42113220256 & -2.02113220256001 \tabularnewline
62 & 145.9 & 147.534638379184 & -1.63463837918417 \tabularnewline
63 & 144.8 & 143.398542933744 & 1.40145706625631 \tabularnewline
64 & 135.9 & 142.843899306247 & -6.94389930624666 \tabularnewline
65 & 137.6 & 131.241783181636 & 6.35821681836381 \tabularnewline
66 & 136 & 135.415989593762 & 0.584010406238178 \tabularnewline
67 & 117.7 & 134.043248640306 & -16.343248640306 \tabularnewline
68 & 111.5 & 109.383514183938 & 2.11648581606234 \tabularnewline
69 & 107.8 & 104.007113461356 & 3.79288653864386 \tabularnewline
70 & 107.3 & 101.783059384948 & 5.51694061505192 \tabularnewline
71 & 102.6 & 103.429895555375 & -0.829895555374648 \tabularnewline
72 & 101 & 98.4069539251723 & 2.59304607482774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279335&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]146.8[/C][C]150.6[/C][C]-3.80000000000001[/C][/ROW]
[ROW][C]4[/C][C]149.6[/C][C]159.02128597771[/C][C]-9.42128597770957[/C][/ROW]
[ROW][C]5[/C][C]146.5[/C][C]158.155131324223[/C][C]-11.6551313242234[/C][/ROW]
[ROW][C]6[/C][C]157[/C][C]150.519708660864[/C][C]6.48029133913602[/C][/ROW]
[ROW][C]7[/C][C]147.9[/C][C]163.541418574471[/C][C]-15.6414185744713[/C][/ROW]
[ROW][C]8[/C][C]133.6[/C][C]148.354790949581[/C][C]-14.7547909495805[/C][/ROW]
[ROW][C]9[/C][C]128.7[/C][C]128.313181404026[/C][C]0.386818595974432[/C][/ROW]
[ROW][C]10[/C][C]100.8[/C][C]123.563706162433[/C][C]-22.7637061624335[/C][/ROW]
[ROW][C]11[/C][C]91.8[/C][C]86.8055452409362[/C][C]4.99445475906384[/C][/ROW]
[ROW][C]12[/C][C]89.3[/C][C]79.7490637372317[/C][C]9.55093626276833[/C][/ROW]
[ROW][C]13[/C][C]96.7[/C][C]80.9656698892732[/C][C]15.7343301107268[/C][/ROW]
[ROW][C]14[/C][C]91.6[/C][C]94.4884526698202[/C][C]-2.88845266982018[/C][/ROW]
[ROW][C]15[/C][C]93.3[/C][C]88.2644538630872[/C][C]5.03554613691283[/C][/ROW]
[ROW][C]16[/C][C]93.3[/C][C]91.9239624637565[/C][C]1.37603753624349[/C][/ROW]
[ROW][C]17[/C][C]101[/C][C]92.4594272006095[/C][C]8.54057279939053[/C][/ROW]
[ROW][C]18[/C][C]100.4[/C][C]103.482865294518[/C][C]-3.08286529451766[/C][/ROW]
[ROW][C]19[/C][C]86.9[/C][C]101.683213678771[/C][C]-14.7832136787714[/C][/ROW]
[ROW][C]20[/C][C]83.9[/C][C]82.4305438468463[/C][C]1.46945615315366[/C][/ROW]
[ROW][C]21[/C][C]80.3[/C][C]80.0023610623225[/C][C]0.297638937677519[/C][/ROW]
[ROW][C]22[/C][C]87.7[/C][C]76.5181828704076[/C][C]11.1818171295924[/C][/ROW]
[ROW][C]23[/C][C]92.7[/C][C]88.2694222873065[/C][C]4.43057771269352[/C][/ROW]
[ROW][C]24[/C][C]95.5[/C][C]94.9935163374663[/C][C]0.506483662533668[/C][/ROW]
[ROW][C]25[/C][C]92[/C][C]97.9906069937425[/C][C]-5.99060699374253[/C][/ROW]
[ROW][C]26[/C][C]87.4[/C][C]92.1594505296167[/C][C]-4.75945052961666[/C][/ROW]
[ROW][C]27[/C][C]86.8[/C][C]85.7073804673688[/C][C]1.09261953263118[/C][/ROW]
[ROW][C]28[/C][C]83.7[/C][C]85.5325572631399[/C][C]-1.8325572631399[/C][/ROW]
[ROW][C]29[/C][C]85[/C][C]81.7194445995464[/C][C]3.28055540045355[/C][/ROW]
[ROW][C]30[/C][C]81.7[/C][C]84.2960244078494[/C][C]-2.59602440784941[/C][/ROW]
[ROW][C]31[/C][C]90.9[/C][C]79.9858197515086[/C][C]10.9141802484914[/C][/ROW]
[ROW][C]32[/C][C]101.5[/C][C]93.4329122186796[/C][C]8.06708778132044[/C][/ROW]
[ROW][C]33[/C][C]113.8[/C][C]107.172100592702[/C][C]6.62789940729769[/C][/ROW]
[ROW][C]34[/C][C]120.1[/C][C]122.051250011624[/C][C]-1.95125001162378[/C][/ROW]
[ROW][C]35[/C][C]122.1[/C][C]127.591949813418[/C][C]-5.49194981341786[/C][/ROW]
[ROW][C]36[/C][C]132.5[/C][C]127.454838445308[/C][C]5.04516155469172[/C][/ROW]
[ROW][C]37[/C][C]140[/C][C]139.818088744162[/C][C]0.181911255838202[/C][/ROW]
[ROW][C]38[/C][C]149.4[/C][C]147.388876829641[/C][C]2.01112317035916[/C][/ROW]
[ROW][C]39[/C][C]144.3[/C][C]157.571475785579[/C][C]-13.2714757855786[/C][/ROW]
[ROW][C]40[/C][C]154.4[/C][C]147.307076485415[/C][C]7.09292351458541[/C][/ROW]
[ROW][C]41[/C][C]151.4[/C][C]160.167183185428[/C][C]-8.76718318542802[/C][/ROW]
[ROW][C]42[/C][C]145.5[/C][C]153.755562997986[/C][C]-8.25556299798555[/C][/ROW]
[ROW][C]43[/C][C]136.8[/C][C]144.643032269822[/C][C]-7.84303226982149[/C][/ROW]
[ROW][C]44[/C][C]146.6[/C][C]132.891031797542[/C][C]13.7089682024578[/C][/ROW]
[ROW][C]45[/C][C]145.1[/C][C]148.025674827044[/C][C]-2.92567482704433[/C][/ROW]
[ROW][C]46[/C][C]133.6[/C][C]145.387191566146[/C][C]-11.7871915661463[/C][/ROW]
[ROW][C]47[/C][C]131.4[/C][C]129.300379605019[/C][C]2.09962039498114[/C][/ROW]
[ROW][C]48[/C][C]127.5[/C][C]127.917415952268[/C][C]-0.417415952267717[/C][/ROW]
[ROW][C]49[/C][C]130.1[/C][C]123.854984683387[/C][C]6.24501531661281[/C][/ROW]
[ROW][C]50[/C][C]131.1[/C][C]128.885140398675[/C][C]2.21485960132492[/C][/ROW]
[ROW][C]51[/C][C]132.3[/C][C]130.747020385487[/C][C]1.55297961451342[/C][/ROW]
[ROW][C]52[/C][C]128.6[/C][C]132.551339525569[/C][C]-3.95133952556878[/C][/ROW]
[ROW][C]53[/C][C]125.1[/C][C]127.313733956282[/C][C]-2.21373395628217[/C][/ROW]
[ROW][C]54[/C][C]128.7[/C][C]122.952291997657[/C][C]5.7477080023428[/C][/ROW]
[ROW][C]55[/C][C]156.1[/C][C]128.788927897419[/C][C]27.3110721025809[/C][/ROW]
[ROW][C]56[/C][C]163.2[/C][C]166.816629287385[/C][C]-3.61662928738536[/C][/ROW]
[ROW][C]57[/C][C]159.8[/C][C]172.509271276679[/C][C]-12.7092712766793[/C][/ROW]
[ROW][C]58[/C][C]157.4[/C][C]164.163645579332[/C][C]-6.76364557933223[/C][/ROW]
[ROW][C]59[/C][C]156.2[/C][C]159.131672537237[/C][C]-2.93167253723715[/C][/ROW]
[ROW][C]60[/C][C]152.5[/C][C]156.79085535577[/C][C]-4.29085535576965[/C][/ROW]
[ROW][C]61[/C][C]149.4[/C][C]151.42113220256[/C][C]-2.02113220256001[/C][/ROW]
[ROW][C]62[/C][C]145.9[/C][C]147.534638379184[/C][C]-1.63463837918417[/C][/ROW]
[ROW][C]63[/C][C]144.8[/C][C]143.398542933744[/C][C]1.40145706625631[/C][/ROW]
[ROW][C]64[/C][C]135.9[/C][C]142.843899306247[/C][C]-6.94389930624666[/C][/ROW]
[ROW][C]65[/C][C]137.6[/C][C]131.241783181636[/C][C]6.35821681836381[/C][/ROW]
[ROW][C]66[/C][C]136[/C][C]135.415989593762[/C][C]0.584010406238178[/C][/ROW]
[ROW][C]67[/C][C]117.7[/C][C]134.043248640306[/C][C]-16.343248640306[/C][/ROW]
[ROW][C]68[/C][C]111.5[/C][C]109.383514183938[/C][C]2.11648581606234[/C][/ROW]
[ROW][C]69[/C][C]107.8[/C][C]104.007113461356[/C][C]3.79288653864386[/C][/ROW]
[ROW][C]70[/C][C]107.3[/C][C]101.783059384948[/C][C]5.51694061505192[/C][/ROW]
[ROW][C]71[/C][C]102.6[/C][C]103.429895555375[/C][C]-0.829895555374648[/C][/ROW]
[ROW][C]72[/C][C]101[/C][C]98.4069539251723[/C][C]2.59304607482774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279335&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279335&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
3146.8150.6-3.80000000000001
4149.6159.02128597771-9.42128597770957
5146.5158.155131324223-11.6551313242234
6157150.5197086608646.48029133913602
7147.9163.541418574471-15.6414185744713
8133.6148.354790949581-14.7547909495805
9128.7128.3131814040260.386818595974432
10100.8123.563706162433-22.7637061624335
1191.886.80554524093624.99445475906384
1289.379.74906373723179.55093626276833
1396.780.965669889273215.7343301107268
1491.694.4884526698202-2.88845266982018
1593.388.26445386308725.03554613691283
1693.391.92396246375651.37603753624349
1710192.45942720060958.54057279939053
18100.4103.482865294518-3.08286529451766
1986.9101.683213678771-14.7832136787714
2083.982.43054384684631.46945615315366
2180.380.00236106232250.297638937677519
2287.776.518182870407611.1818171295924
2392.788.26942228730654.43057771269352
2495.594.99351633746630.506483662533668
259297.9906069937425-5.99060699374253
2687.492.1594505296167-4.75945052961666
2786.885.70738046736881.09261953263118
2883.785.5325572631399-1.8325572631399
298581.71944459954643.28055540045355
3081.784.2960244078494-2.59602440784941
3190.979.985819751508610.9141802484914
32101.593.43291221867968.06708778132044
33113.8107.1721005927026.62789940729769
34120.1122.051250011624-1.95125001162378
35122.1127.591949813418-5.49194981341786
36132.5127.4548384453085.04516155469172
37140139.8180887441620.181911255838202
38149.4147.3888768296412.01112317035916
39144.3157.571475785579-13.2714757855786
40154.4147.3070764854157.09292351458541
41151.4160.167183185428-8.76718318542802
42145.5153.755562997986-8.25556299798555
43136.8144.643032269822-7.84303226982149
44146.6132.89103179754213.7089682024578
45145.1148.025674827044-2.92567482704433
46133.6145.387191566146-11.7871915661463
47131.4129.3003796050192.09962039498114
48127.5127.917415952268-0.417415952267717
49130.1123.8549846833876.24501531661281
50131.1128.8851403986752.21485960132492
51132.3130.7470203854871.55297961451342
52128.6132.551339525569-3.95133952556878
53125.1127.313733956282-2.21373395628217
54128.7122.9522919976575.7477080023428
55156.1128.78892789741927.3110721025809
56163.2166.816629287385-3.61662928738536
57159.8172.509271276679-12.7092712766793
58157.4164.163645579332-6.76364557933223
59156.2159.131672537237-2.93167253723715
60152.5156.79085535577-4.29085535576965
61149.4151.42113220256-2.02113220256001
62145.9147.534638379184-1.63463837918417
63144.8143.3985429337441.40145706625631
64135.9142.843899306247-6.94389930624666
65137.6131.2417831816366.35821681836381
66136135.4159895937620.584010406238178
67117.7134.043248640306-16.343248640306
68111.5109.3835141839382.11648581606234
69107.8104.0071134613563.79288653864386
70107.3101.7830593849485.51694061505192
71102.6103.429895555375-0.829895555374648
7210198.40695392517232.59304607482774







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7397.815999607091581.5675381905462114.064461023637
7494.631999214182966.8205524595199122.443445968846
7591.447998821274451.3437712918388131.55222635071
7688.263998428365934.8918443306901141.636152526042
7785.079998035457417.4475596522923152.712436418622
7881.8959976425488-0.959210888947169164.751206174045
7978.7119972496403-20.2883070915409177.712301590822
8075.5279968567318-40.4992741074011191.555267820865
8172.3439964638233-61.5542651873138206.24225811496
8269.1599960709147-83.4187301862797221.738722328109
8365.9759956780062-106.061366995874238.013358351886
8462.7919952850977-129.45383866438255.037829234576

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 97.8159996070915 & 81.5675381905462 & 114.064461023637 \tabularnewline
74 & 94.6319992141829 & 66.8205524595199 & 122.443445968846 \tabularnewline
75 & 91.4479988212744 & 51.3437712918388 & 131.55222635071 \tabularnewline
76 & 88.2639984283659 & 34.8918443306901 & 141.636152526042 \tabularnewline
77 & 85.0799980354574 & 17.4475596522923 & 152.712436418622 \tabularnewline
78 & 81.8959976425488 & -0.959210888947169 & 164.751206174045 \tabularnewline
79 & 78.7119972496403 & -20.2883070915409 & 177.712301590822 \tabularnewline
80 & 75.5279968567318 & -40.4992741074011 & 191.555267820865 \tabularnewline
81 & 72.3439964638233 & -61.5542651873138 & 206.24225811496 \tabularnewline
82 & 69.1599960709147 & -83.4187301862797 & 221.738722328109 \tabularnewline
83 & 65.9759956780062 & -106.061366995874 & 238.013358351886 \tabularnewline
84 & 62.7919952850977 & -129.45383866438 & 255.037829234576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279335&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]97.8159996070915[/C][C]81.5675381905462[/C][C]114.064461023637[/C][/ROW]
[ROW][C]74[/C][C]94.6319992141829[/C][C]66.8205524595199[/C][C]122.443445968846[/C][/ROW]
[ROW][C]75[/C][C]91.4479988212744[/C][C]51.3437712918388[/C][C]131.55222635071[/C][/ROW]
[ROW][C]76[/C][C]88.2639984283659[/C][C]34.8918443306901[/C][C]141.636152526042[/C][/ROW]
[ROW][C]77[/C][C]85.0799980354574[/C][C]17.4475596522923[/C][C]152.712436418622[/C][/ROW]
[ROW][C]78[/C][C]81.8959976425488[/C][C]-0.959210888947169[/C][C]164.751206174045[/C][/ROW]
[ROW][C]79[/C][C]78.7119972496403[/C][C]-20.2883070915409[/C][C]177.712301590822[/C][/ROW]
[ROW][C]80[/C][C]75.5279968567318[/C][C]-40.4992741074011[/C][C]191.555267820865[/C][/ROW]
[ROW][C]81[/C][C]72.3439964638233[/C][C]-61.5542651873138[/C][C]206.24225811496[/C][/ROW]
[ROW][C]82[/C][C]69.1599960709147[/C][C]-83.4187301862797[/C][C]221.738722328109[/C][/ROW]
[ROW][C]83[/C][C]65.9759956780062[/C][C]-106.061366995874[/C][C]238.013358351886[/C][/ROW]
[ROW][C]84[/C][C]62.7919952850977[/C][C]-129.45383866438[/C][C]255.037829234576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279335&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279335&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
7397.815999607091581.5675381905462114.064461023637
7494.631999214182966.8205524595199122.443445968846
7591.447998821274451.3437712918388131.55222635071
7688.263998428365934.8918443306901141.636152526042
7785.079998035457417.4475596522923152.712436418622
7881.8959976425488-0.959210888947169164.751206174045
7978.7119972496403-20.2883070915409177.712301590822
8075.5279968567318-40.4992741074011191.555267820865
8172.3439964638233-61.5542651873138206.24225811496
8269.1599960709147-83.4187301862797221.738722328109
8365.9759956780062-106.061366995874238.013358351886
8462.7919952850977-129.45383866438255.037829234576



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')