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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Nov 2012 12:06:05 -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/2012/Nov/23/t1353690474l2omjwc6awne7mi.htm/, Retrieved Wed, 01 May 2024 16:45:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192218, Retrieved Wed, 01 May 2024 16:45:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Workshop 8] [2012-11-23 16:59:10] [498ff5d3288f0a3191251bab12f09e42]
- R P     [Exponential Smoothing] [Workshop 8] [2012-11-23 17:06:05] [88970af05b38e2e8b1d3faaed6004b57] [Current]
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Dataseries X:
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225
41126
42362
40740
40256
39804
41002
41702
42254
43605
43271




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192218&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192218&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192218&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0258617241640165
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0258617241640165 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192218&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]0.0258617241640165[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192218&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192218&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
beta0.0258617241640165
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31592817117-1189
41617116666.250409969-495.250409968983
51593716896.4423804743-959.442380474251
61571316637.6295462792-924.629546279157
71559416389.7170319994-795.717031999386
81568316250.1384176052-567.138417605209
91643816324.4712402863113.528759713714
101703217082.4072897547-50.4072897546866
111769617675.103670331220.8963296688053
121774518339.6440854451-594.644085445128
131939418373.26556413161020.73443586842
142014820048.663516556799.3364834432759
152010820805.232529291-697.232529290959
161858420747.2008939403-2163.20089394025
171844119167.2567891098-726.256789109819
181839119005.4745363576-614.474536357618
191917818939.5831653925238.416834607477
201807919732.7490358052-1653.7490358052
211848318590.9802344047-107.980234404698
221964418992.1876793674651.812320632642
231919520170.0446698103-975.044669810268
241965019695.828333512-45.8283335120395
252083020149.6431337919680.356866208145
262359521347.23833539882247.76166460117
272293724170.3693275552-1233.36932755519
282181423480.4722702136-1666.4722702136
292192822314.3744240344-386.374424034355
302177722418.3821152559-641.382115255947
312138322250.7948679075-867.794867907465
322146721834.3521964027-367.352196402691
332205221908.8518352283143.148164771719
342268022497.5538935802182.446106419808
352432023130.27226445921189.72773554078
362497724801.0406749861175.959325013944
372520425462.5912865137-258.591286513652
382573925682.903669990656.0963300093827
392643426219.3544178039214.645582196066
402752526919.9055226437605.094477356288
413069528026.55430911032668.44569088973
423243631265.56491551471170.43508448528
433016033036.8343848216-2876.83438482157
443023630686.4344874958-450.434487495753
453129330750.7854750262542.214524973824
463107731821.8080775088-744.808077508773
473222631586.5460564531639.453943546891
483386532752.08343795671112.91656204329
493281034419.8653791018-1609.86537910184
503224233323.2314847263-1081.23148472631
513270032727.2689743109-27.2689743108676
523281933184.563751619-365.563751619004
533394733294.1096427103652.890357289732
543414834438.9945130398-290.994513039841
553526134632.4688932104628.531106789633
563950635761.72379132273744.27620867734
574159140103.55722982541487.44277017463
583914842227.0250644574-3079.02506445738
594121639704.39616754631511.60383245371
604022541811.4888489065-1586.48884890648
614112640779.4595119068346.540488093226
624236241689.4216464215672.578353578494
634074042942.8156822804-2202.81568228044
644025641263.8470707211-1007.84707072113
653980440753.7824077786-949.782407778628
664100240277.2193971328724.780602867177
674170241493.9634731636208.036526836397
684225442199.343656436754.6563435633143
694360542752.7571637177852.242836282261
704327144125.7976328704-854.797632870424

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15928 & 17117 & -1189 \tabularnewline
4 & 16171 & 16666.250409969 & -495.250409968983 \tabularnewline
5 & 15937 & 16896.4423804743 & -959.442380474251 \tabularnewline
6 & 15713 & 16637.6295462792 & -924.629546279157 \tabularnewline
7 & 15594 & 16389.7170319994 & -795.717031999386 \tabularnewline
8 & 15683 & 16250.1384176052 & -567.138417605209 \tabularnewline
9 & 16438 & 16324.4712402863 & 113.528759713714 \tabularnewline
10 & 17032 & 17082.4072897547 & -50.4072897546866 \tabularnewline
11 & 17696 & 17675.1036703312 & 20.8963296688053 \tabularnewline
12 & 17745 & 18339.6440854451 & -594.644085445128 \tabularnewline
13 & 19394 & 18373.2655641316 & 1020.73443586842 \tabularnewline
14 & 20148 & 20048.6635165567 & 99.3364834432759 \tabularnewline
15 & 20108 & 20805.232529291 & -697.232529290959 \tabularnewline
16 & 18584 & 20747.2008939403 & -2163.20089394025 \tabularnewline
17 & 18441 & 19167.2567891098 & -726.256789109819 \tabularnewline
18 & 18391 & 19005.4745363576 & -614.474536357618 \tabularnewline
19 & 19178 & 18939.5831653925 & 238.416834607477 \tabularnewline
20 & 18079 & 19732.7490358052 & -1653.7490358052 \tabularnewline
21 & 18483 & 18590.9802344047 & -107.980234404698 \tabularnewline
22 & 19644 & 18992.1876793674 & 651.812320632642 \tabularnewline
23 & 19195 & 20170.0446698103 & -975.044669810268 \tabularnewline
24 & 19650 & 19695.828333512 & -45.8283335120395 \tabularnewline
25 & 20830 & 20149.6431337919 & 680.356866208145 \tabularnewline
26 & 23595 & 21347.2383353988 & 2247.76166460117 \tabularnewline
27 & 22937 & 24170.3693275552 & -1233.36932755519 \tabularnewline
28 & 21814 & 23480.4722702136 & -1666.4722702136 \tabularnewline
29 & 21928 & 22314.3744240344 & -386.374424034355 \tabularnewline
30 & 21777 & 22418.3821152559 & -641.382115255947 \tabularnewline
31 & 21383 & 22250.7948679075 & -867.794867907465 \tabularnewline
32 & 21467 & 21834.3521964027 & -367.352196402691 \tabularnewline
33 & 22052 & 21908.8518352283 & 143.148164771719 \tabularnewline
34 & 22680 & 22497.5538935802 & 182.446106419808 \tabularnewline
35 & 24320 & 23130.2722644592 & 1189.72773554078 \tabularnewline
36 & 24977 & 24801.0406749861 & 175.959325013944 \tabularnewline
37 & 25204 & 25462.5912865137 & -258.591286513652 \tabularnewline
38 & 25739 & 25682.9036699906 & 56.0963300093827 \tabularnewline
39 & 26434 & 26219.3544178039 & 214.645582196066 \tabularnewline
40 & 27525 & 26919.9055226437 & 605.094477356288 \tabularnewline
41 & 30695 & 28026.5543091103 & 2668.44569088973 \tabularnewline
42 & 32436 & 31265.5649155147 & 1170.43508448528 \tabularnewline
43 & 30160 & 33036.8343848216 & -2876.83438482157 \tabularnewline
44 & 30236 & 30686.4344874958 & -450.434487495753 \tabularnewline
45 & 31293 & 30750.7854750262 & 542.214524973824 \tabularnewline
46 & 31077 & 31821.8080775088 & -744.808077508773 \tabularnewline
47 & 32226 & 31586.5460564531 & 639.453943546891 \tabularnewline
48 & 33865 & 32752.0834379567 & 1112.91656204329 \tabularnewline
49 & 32810 & 34419.8653791018 & -1609.86537910184 \tabularnewline
50 & 32242 & 33323.2314847263 & -1081.23148472631 \tabularnewline
51 & 32700 & 32727.2689743109 & -27.2689743108676 \tabularnewline
52 & 32819 & 33184.563751619 & -365.563751619004 \tabularnewline
53 & 33947 & 33294.1096427103 & 652.890357289732 \tabularnewline
54 & 34148 & 34438.9945130398 & -290.994513039841 \tabularnewline
55 & 35261 & 34632.4688932104 & 628.531106789633 \tabularnewline
56 & 39506 & 35761.7237913227 & 3744.27620867734 \tabularnewline
57 & 41591 & 40103.5572298254 & 1487.44277017463 \tabularnewline
58 & 39148 & 42227.0250644574 & -3079.02506445738 \tabularnewline
59 & 41216 & 39704.3961675463 & 1511.60383245371 \tabularnewline
60 & 40225 & 41811.4888489065 & -1586.48884890648 \tabularnewline
61 & 41126 & 40779.4595119068 & 346.540488093226 \tabularnewline
62 & 42362 & 41689.4216464215 & 672.578353578494 \tabularnewline
63 & 40740 & 42942.8156822804 & -2202.81568228044 \tabularnewline
64 & 40256 & 41263.8470707211 & -1007.84707072113 \tabularnewline
65 & 39804 & 40753.7824077786 & -949.782407778628 \tabularnewline
66 & 41002 & 40277.2193971328 & 724.780602867177 \tabularnewline
67 & 41702 & 41493.9634731636 & 208.036526836397 \tabularnewline
68 & 42254 & 42199.3436564367 & 54.6563435633143 \tabularnewline
69 & 43605 & 42752.7571637177 & 852.242836282261 \tabularnewline
70 & 43271 & 44125.7976328704 & -854.797632870424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192218&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]15928[/C][C]17117[/C][C]-1189[/C][/ROW]
[ROW][C]4[/C][C]16171[/C][C]16666.250409969[/C][C]-495.250409968983[/C][/ROW]
[ROW][C]5[/C][C]15937[/C][C]16896.4423804743[/C][C]-959.442380474251[/C][/ROW]
[ROW][C]6[/C][C]15713[/C][C]16637.6295462792[/C][C]-924.629546279157[/C][/ROW]
[ROW][C]7[/C][C]15594[/C][C]16389.7170319994[/C][C]-795.717031999386[/C][/ROW]
[ROW][C]8[/C][C]15683[/C][C]16250.1384176052[/C][C]-567.138417605209[/C][/ROW]
[ROW][C]9[/C][C]16438[/C][C]16324.4712402863[/C][C]113.528759713714[/C][/ROW]
[ROW][C]10[/C][C]17032[/C][C]17082.4072897547[/C][C]-50.4072897546866[/C][/ROW]
[ROW][C]11[/C][C]17696[/C][C]17675.1036703312[/C][C]20.8963296688053[/C][/ROW]
[ROW][C]12[/C][C]17745[/C][C]18339.6440854451[/C][C]-594.644085445128[/C][/ROW]
[ROW][C]13[/C][C]19394[/C][C]18373.2655641316[/C][C]1020.73443586842[/C][/ROW]
[ROW][C]14[/C][C]20148[/C][C]20048.6635165567[/C][C]99.3364834432759[/C][/ROW]
[ROW][C]15[/C][C]20108[/C][C]20805.232529291[/C][C]-697.232529290959[/C][/ROW]
[ROW][C]16[/C][C]18584[/C][C]20747.2008939403[/C][C]-2163.20089394025[/C][/ROW]
[ROW][C]17[/C][C]18441[/C][C]19167.2567891098[/C][C]-726.256789109819[/C][/ROW]
[ROW][C]18[/C][C]18391[/C][C]19005.4745363576[/C][C]-614.474536357618[/C][/ROW]
[ROW][C]19[/C][C]19178[/C][C]18939.5831653925[/C][C]238.416834607477[/C][/ROW]
[ROW][C]20[/C][C]18079[/C][C]19732.7490358052[/C][C]-1653.7490358052[/C][/ROW]
[ROW][C]21[/C][C]18483[/C][C]18590.9802344047[/C][C]-107.980234404698[/C][/ROW]
[ROW][C]22[/C][C]19644[/C][C]18992.1876793674[/C][C]651.812320632642[/C][/ROW]
[ROW][C]23[/C][C]19195[/C][C]20170.0446698103[/C][C]-975.044669810268[/C][/ROW]
[ROW][C]24[/C][C]19650[/C][C]19695.828333512[/C][C]-45.8283335120395[/C][/ROW]
[ROW][C]25[/C][C]20830[/C][C]20149.6431337919[/C][C]680.356866208145[/C][/ROW]
[ROW][C]26[/C][C]23595[/C][C]21347.2383353988[/C][C]2247.76166460117[/C][/ROW]
[ROW][C]27[/C][C]22937[/C][C]24170.3693275552[/C][C]-1233.36932755519[/C][/ROW]
[ROW][C]28[/C][C]21814[/C][C]23480.4722702136[/C][C]-1666.4722702136[/C][/ROW]
[ROW][C]29[/C][C]21928[/C][C]22314.3744240344[/C][C]-386.374424034355[/C][/ROW]
[ROW][C]30[/C][C]21777[/C][C]22418.3821152559[/C][C]-641.382115255947[/C][/ROW]
[ROW][C]31[/C][C]21383[/C][C]22250.7948679075[/C][C]-867.794867907465[/C][/ROW]
[ROW][C]32[/C][C]21467[/C][C]21834.3521964027[/C][C]-367.352196402691[/C][/ROW]
[ROW][C]33[/C][C]22052[/C][C]21908.8518352283[/C][C]143.148164771719[/C][/ROW]
[ROW][C]34[/C][C]22680[/C][C]22497.5538935802[/C][C]182.446106419808[/C][/ROW]
[ROW][C]35[/C][C]24320[/C][C]23130.2722644592[/C][C]1189.72773554078[/C][/ROW]
[ROW][C]36[/C][C]24977[/C][C]24801.0406749861[/C][C]175.959325013944[/C][/ROW]
[ROW][C]37[/C][C]25204[/C][C]25462.5912865137[/C][C]-258.591286513652[/C][/ROW]
[ROW][C]38[/C][C]25739[/C][C]25682.9036699906[/C][C]56.0963300093827[/C][/ROW]
[ROW][C]39[/C][C]26434[/C][C]26219.3544178039[/C][C]214.645582196066[/C][/ROW]
[ROW][C]40[/C][C]27525[/C][C]26919.9055226437[/C][C]605.094477356288[/C][/ROW]
[ROW][C]41[/C][C]30695[/C][C]28026.5543091103[/C][C]2668.44569088973[/C][/ROW]
[ROW][C]42[/C][C]32436[/C][C]31265.5649155147[/C][C]1170.43508448528[/C][/ROW]
[ROW][C]43[/C][C]30160[/C][C]33036.8343848216[/C][C]-2876.83438482157[/C][/ROW]
[ROW][C]44[/C][C]30236[/C][C]30686.4344874958[/C][C]-450.434487495753[/C][/ROW]
[ROW][C]45[/C][C]31293[/C][C]30750.7854750262[/C][C]542.214524973824[/C][/ROW]
[ROW][C]46[/C][C]31077[/C][C]31821.8080775088[/C][C]-744.808077508773[/C][/ROW]
[ROW][C]47[/C][C]32226[/C][C]31586.5460564531[/C][C]639.453943546891[/C][/ROW]
[ROW][C]48[/C][C]33865[/C][C]32752.0834379567[/C][C]1112.91656204329[/C][/ROW]
[ROW][C]49[/C][C]32810[/C][C]34419.8653791018[/C][C]-1609.86537910184[/C][/ROW]
[ROW][C]50[/C][C]32242[/C][C]33323.2314847263[/C][C]-1081.23148472631[/C][/ROW]
[ROW][C]51[/C][C]32700[/C][C]32727.2689743109[/C][C]-27.2689743108676[/C][/ROW]
[ROW][C]52[/C][C]32819[/C][C]33184.563751619[/C][C]-365.563751619004[/C][/ROW]
[ROW][C]53[/C][C]33947[/C][C]33294.1096427103[/C][C]652.890357289732[/C][/ROW]
[ROW][C]54[/C][C]34148[/C][C]34438.9945130398[/C][C]-290.994513039841[/C][/ROW]
[ROW][C]55[/C][C]35261[/C][C]34632.4688932104[/C][C]628.531106789633[/C][/ROW]
[ROW][C]56[/C][C]39506[/C][C]35761.7237913227[/C][C]3744.27620867734[/C][/ROW]
[ROW][C]57[/C][C]41591[/C][C]40103.5572298254[/C][C]1487.44277017463[/C][/ROW]
[ROW][C]58[/C][C]39148[/C][C]42227.0250644574[/C][C]-3079.02506445738[/C][/ROW]
[ROW][C]59[/C][C]41216[/C][C]39704.3961675463[/C][C]1511.60383245371[/C][/ROW]
[ROW][C]60[/C][C]40225[/C][C]41811.4888489065[/C][C]-1586.48884890648[/C][/ROW]
[ROW][C]61[/C][C]41126[/C][C]40779.4595119068[/C][C]346.540488093226[/C][/ROW]
[ROW][C]62[/C][C]42362[/C][C]41689.4216464215[/C][C]672.578353578494[/C][/ROW]
[ROW][C]63[/C][C]40740[/C][C]42942.8156822804[/C][C]-2202.81568228044[/C][/ROW]
[ROW][C]64[/C][C]40256[/C][C]41263.8470707211[/C][C]-1007.84707072113[/C][/ROW]
[ROW][C]65[/C][C]39804[/C][C]40753.7824077786[/C][C]-949.782407778628[/C][/ROW]
[ROW][C]66[/C][C]41002[/C][C]40277.2193971328[/C][C]724.780602867177[/C][/ROW]
[ROW][C]67[/C][C]41702[/C][C]41493.9634731636[/C][C]208.036526836397[/C][/ROW]
[ROW][C]68[/C][C]42254[/C][C]42199.3436564367[/C][C]54.6563435633143[/C][/ROW]
[ROW][C]69[/C][C]43605[/C][C]42752.7571637177[/C][C]852.242836282261[/C][/ROW]
[ROW][C]70[/C][C]43271[/C][C]44125.7976328704[/C][C]-854.797632870424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192218&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192218&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
31592817117-1189
41617116666.250409969-495.250409968983
51593716896.4423804743-959.442380474251
61571316637.6295462792-924.629546279157
71559416389.7170319994-795.717031999386
81568316250.1384176052-567.138417605209
91643816324.4712402863113.528759713714
101703217082.4072897547-50.4072897546866
111769617675.103670331220.8963296688053
121774518339.6440854451-594.644085445128
131939418373.26556413161020.73443586842
142014820048.663516556799.3364834432759
152010820805.232529291-697.232529290959
161858420747.2008939403-2163.20089394025
171844119167.2567891098-726.256789109819
181839119005.4745363576-614.474536357618
191917818939.5831653925238.416834607477
201807919732.7490358052-1653.7490358052
211848318590.9802344047-107.980234404698
221964418992.1876793674651.812320632642
231919520170.0446698103-975.044669810268
241965019695.828333512-45.8283335120395
252083020149.6431337919680.356866208145
262359521347.23833539882247.76166460117
272293724170.3693275552-1233.36932755519
282181423480.4722702136-1666.4722702136
292192822314.3744240344-386.374424034355
302177722418.3821152559-641.382115255947
312138322250.7948679075-867.794867907465
322146721834.3521964027-367.352196402691
332205221908.8518352283143.148164771719
342268022497.5538935802182.446106419808
352432023130.27226445921189.72773554078
362497724801.0406749861175.959325013944
372520425462.5912865137-258.591286513652
382573925682.903669990656.0963300093827
392643426219.3544178039214.645582196066
402752526919.9055226437605.094477356288
413069528026.55430911032668.44569088973
423243631265.56491551471170.43508448528
433016033036.8343848216-2876.83438482157
443023630686.4344874958-450.434487495753
453129330750.7854750262542.214524973824
463107731821.8080775088-744.808077508773
473222631586.5460564531639.453943546891
483386532752.08343795671112.91656204329
493281034419.8653791018-1609.86537910184
503224233323.2314847263-1081.23148472631
513270032727.2689743109-27.2689743108676
523281933184.563751619-365.563751619004
533394733294.1096427103652.890357289732
543414834438.9945130398-290.994513039841
553526134632.4688932104628.531106789633
563950635761.72379132273744.27620867734
574159140103.55722982541487.44277017463
583914842227.0250644574-3079.02506445738
594121639704.39616754631511.60383245371
604022541811.4888489065-1586.48884890648
614112640779.4595119068346.540488093226
624236241689.4216464215672.578353578494
634074042942.8156822804-2202.81568228044
644025641263.8470707211-1007.84707072113
653980440753.7824077786-949.782407778628
664100240277.2193971328724.780602867177
674170241493.9634731636208.036526836397
684225442199.343656436754.6563435633143
694360542752.7571637177852.242836282261
704327144125.7976328704-854.797632870424







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7143769.691092273141474.826175012746064.5560095334
7244268.382184546240980.719043887347556.045325205
7344767.073276819240688.591149809848845.5554038287
7445265.764369092340496.140459751950035.3882784327
7545764.455461365440364.301676378751164.6092463521
7646263.146553638540273.312908067552252.9801992094
7746761.837645911540211.593720431853312.0815713913
7847260.528738184640171.701564883554349.3559114858
7947759.219830457740148.538035968455369.901624947
8048257.910922730840138.442948669356377.3788967922
8148756.602015003940138.692537998357374.5114920094
8249255.293107276940147.201499286758363.3847152672

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
71 & 43769.6910922731 & 41474.8261750127 & 46064.5560095334 \tabularnewline
72 & 44268.3821845462 & 40980.7190438873 & 47556.045325205 \tabularnewline
73 & 44767.0732768192 & 40688.5911498098 & 48845.5554038287 \tabularnewline
74 & 45265.7643690923 & 40496.1404597519 & 50035.3882784327 \tabularnewline
75 & 45764.4554613654 & 40364.3016763787 & 51164.6092463521 \tabularnewline
76 & 46263.1465536385 & 40273.3129080675 & 52252.9801992094 \tabularnewline
77 & 46761.8376459115 & 40211.5937204318 & 53312.0815713913 \tabularnewline
78 & 47260.5287381846 & 40171.7015648835 & 54349.3559114858 \tabularnewline
79 & 47759.2198304577 & 40148.5380359684 & 55369.901624947 \tabularnewline
80 & 48257.9109227308 & 40138.4429486693 & 56377.3788967922 \tabularnewline
81 & 48756.6020150039 & 40138.6925379983 & 57374.5114920094 \tabularnewline
82 & 49255.2931072769 & 40147.2014992867 & 58363.3847152672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192218&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]71[/C][C]43769.6910922731[/C][C]41474.8261750127[/C][C]46064.5560095334[/C][/ROW]
[ROW][C]72[/C][C]44268.3821845462[/C][C]40980.7190438873[/C][C]47556.045325205[/C][/ROW]
[ROW][C]73[/C][C]44767.0732768192[/C][C]40688.5911498098[/C][C]48845.5554038287[/C][/ROW]
[ROW][C]74[/C][C]45265.7643690923[/C][C]40496.1404597519[/C][C]50035.3882784327[/C][/ROW]
[ROW][C]75[/C][C]45764.4554613654[/C][C]40364.3016763787[/C][C]51164.6092463521[/C][/ROW]
[ROW][C]76[/C][C]46263.1465536385[/C][C]40273.3129080675[/C][C]52252.9801992094[/C][/ROW]
[ROW][C]77[/C][C]46761.8376459115[/C][C]40211.5937204318[/C][C]53312.0815713913[/C][/ROW]
[ROW][C]78[/C][C]47260.5287381846[/C][C]40171.7015648835[/C][C]54349.3559114858[/C][/ROW]
[ROW][C]79[/C][C]47759.2198304577[/C][C]40148.5380359684[/C][C]55369.901624947[/C][/ROW]
[ROW][C]80[/C][C]48257.9109227308[/C][C]40138.4429486693[/C][C]56377.3788967922[/C][/ROW]
[ROW][C]81[/C][C]48756.6020150039[/C][C]40138.6925379983[/C][C]57374.5114920094[/C][/ROW]
[ROW][C]82[/C][C]49255.2931072769[/C][C]40147.2014992867[/C][C]58363.3847152672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192218&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192218&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
7143769.691092273141474.826175012746064.5560095334
7244268.382184546240980.719043887347556.045325205
7344767.073276819240688.591149809848845.5554038287
7445265.764369092340496.140459751950035.3882784327
7545764.455461365440364.301676378751164.6092463521
7646263.146553638540273.312908067552252.9801992094
7746761.837645911540211.593720431853312.0815713913
7847260.528738184640171.701564883554349.3559114858
7947759.219830457740148.538035968455369.901624947
8048257.910922730840138.442948669356377.3788967922
8148756.602015003940138.692537998357374.5114920094
8249255.293107276940147.201499286758363.3847152672



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')