Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 12 Jan 2014 18:18:29 -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/2014/Jan/12/t13895687681gt2dp7u7fetgby.htm/, Retrieved Sun, 19 May 2024 06:08:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233087, Retrieved Sun, 19 May 2024 06:08:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-12 23:18:29] [354a1e9bb909abf3036d55f04d250334] [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
43221
41373




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233087&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]4 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=233087&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233087&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.030010761469554
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.030010761469554 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233087&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]0.030010761469554[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233087&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233087&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
beta0.030010761469554
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31592817117-1189
41617116661.3172046127-490.3172046127
51593716889.6024119407-952.60241194065
61571316627.0140881806-914.014088180578
71559416375.5838294004-781.583829400379
81568316233.1279035278-550.127903527782
91643816305.6181462373132.381853762736
101703217064.5910264734-32.5910264734339
111769617657.612944951938.3870550481079
121774518322.7649697045-577.764969704462
131939418354.42580301321039.5741969868
142014820034.6242162689113.375783731131
152010820792.0267098709-684.02670987085
161858420731.4985474421-2147.49854744211
171844119143.0504807786-702.050480778613
181839118978.9814112604-587.981411260378
191917818911.3356413785266.664358621489
201807919706.3384418375-1627.33844183753
211848318558.5007760293-75.500776029312
221964418960.2349402491683.765059750869
231919520141.7552503585-946.755250358528
241965019664.34240437-14.3424043699706
252083020118.9119778935711.088022106476
262359521320.25227090882274.74772909118
272293724153.51918241-1216.51918240998
282181423459.0105154035-1645.01051540354
292192822286.6424972109-358.642497210858
302177722389.8793627742-612.879362774216
312138322220.4863864084-837.486386408385
322146721801.3527822319-334.352782231887
332205221875.3186006376176.681399362358
342268022465.62094397214.379056029986
352432023100.05462268461219.9453773154
362497724776.6661124091200.333887590903
372520425439.6782849239-235.678284923855
382573925659.605400131579.3945998685485
392643426196.9880925301237.011907469921
402752526899.1010003506625.898999649398
413069528008.88470593312686.11529406689
423243631259.49707130311176.50292869693
433016033035.8048200644-2875.80482006443
443023630673.4997275765-437.49972757648
453129330736.3700276092556.629972390812
463107731810.0749169374-733.074916937414
473222631572.0747804659653.925219534107
483386532740.69957424831124.30042575174
493281034413.4406861456-1603.44068614561
503224233310.3202101831-1068.32021018311
513270032710.2591071822-10.2591071822062
523281933167.9512235637-348.951223563672
533394733276.4789316288670.521068371207
543414834424.601779472-276.601779471988
553526134617.3007494462643.6992505538
563950635749.61865411273756.3813458873
574159140107.35051867281483.64948132719
583914842236.8759693613-3088.87596936135
594121639701.17644943581514.82355056419
604022541814.6374576802-1589.63745768025
614112640775.9312271147350.068772885257
624236241687.4370575557674.56294244426
634074042943.6812051176-2203.68120511764
644025641255.5470541159-999.547054115908
653980440741.5498858972-937.549885897242
664100240261.4132999058740.586700094231
674170241481.6388707098220.361129290177
684225442188.252075998165.7479240018874
694360542742.2252212625862.774778737548
704327144119.1177493491-848.11774934909
714322143759.6650898753-538.665089875285
724137343693.4993403511-2320.49934035106

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15928 & 17117 & -1189 \tabularnewline
4 & 16171 & 16661.3172046127 & -490.3172046127 \tabularnewline
5 & 15937 & 16889.6024119407 & -952.60241194065 \tabularnewline
6 & 15713 & 16627.0140881806 & -914.014088180578 \tabularnewline
7 & 15594 & 16375.5838294004 & -781.583829400379 \tabularnewline
8 & 15683 & 16233.1279035278 & -550.127903527782 \tabularnewline
9 & 16438 & 16305.6181462373 & 132.381853762736 \tabularnewline
10 & 17032 & 17064.5910264734 & -32.5910264734339 \tabularnewline
11 & 17696 & 17657.6129449519 & 38.3870550481079 \tabularnewline
12 & 17745 & 18322.7649697045 & -577.764969704462 \tabularnewline
13 & 19394 & 18354.4258030132 & 1039.5741969868 \tabularnewline
14 & 20148 & 20034.6242162689 & 113.375783731131 \tabularnewline
15 & 20108 & 20792.0267098709 & -684.02670987085 \tabularnewline
16 & 18584 & 20731.4985474421 & -2147.49854744211 \tabularnewline
17 & 18441 & 19143.0504807786 & -702.050480778613 \tabularnewline
18 & 18391 & 18978.9814112604 & -587.981411260378 \tabularnewline
19 & 19178 & 18911.3356413785 & 266.664358621489 \tabularnewline
20 & 18079 & 19706.3384418375 & -1627.33844183753 \tabularnewline
21 & 18483 & 18558.5007760293 & -75.500776029312 \tabularnewline
22 & 19644 & 18960.2349402491 & 683.765059750869 \tabularnewline
23 & 19195 & 20141.7552503585 & -946.755250358528 \tabularnewline
24 & 19650 & 19664.34240437 & -14.3424043699706 \tabularnewline
25 & 20830 & 20118.9119778935 & 711.088022106476 \tabularnewline
26 & 23595 & 21320.2522709088 & 2274.74772909118 \tabularnewline
27 & 22937 & 24153.51918241 & -1216.51918240998 \tabularnewline
28 & 21814 & 23459.0105154035 & -1645.01051540354 \tabularnewline
29 & 21928 & 22286.6424972109 & -358.642497210858 \tabularnewline
30 & 21777 & 22389.8793627742 & -612.879362774216 \tabularnewline
31 & 21383 & 22220.4863864084 & -837.486386408385 \tabularnewline
32 & 21467 & 21801.3527822319 & -334.352782231887 \tabularnewline
33 & 22052 & 21875.3186006376 & 176.681399362358 \tabularnewline
34 & 22680 & 22465.62094397 & 214.379056029986 \tabularnewline
35 & 24320 & 23100.0546226846 & 1219.9453773154 \tabularnewline
36 & 24977 & 24776.6661124091 & 200.333887590903 \tabularnewline
37 & 25204 & 25439.6782849239 & -235.678284923855 \tabularnewline
38 & 25739 & 25659.6054001315 & 79.3945998685485 \tabularnewline
39 & 26434 & 26196.9880925301 & 237.011907469921 \tabularnewline
40 & 27525 & 26899.1010003506 & 625.898999649398 \tabularnewline
41 & 30695 & 28008.8847059331 & 2686.11529406689 \tabularnewline
42 & 32436 & 31259.4970713031 & 1176.50292869693 \tabularnewline
43 & 30160 & 33035.8048200644 & -2875.80482006443 \tabularnewline
44 & 30236 & 30673.4997275765 & -437.49972757648 \tabularnewline
45 & 31293 & 30736.3700276092 & 556.629972390812 \tabularnewline
46 & 31077 & 31810.0749169374 & -733.074916937414 \tabularnewline
47 & 32226 & 31572.0747804659 & 653.925219534107 \tabularnewline
48 & 33865 & 32740.6995742483 & 1124.30042575174 \tabularnewline
49 & 32810 & 34413.4406861456 & -1603.44068614561 \tabularnewline
50 & 32242 & 33310.3202101831 & -1068.32021018311 \tabularnewline
51 & 32700 & 32710.2591071822 & -10.2591071822062 \tabularnewline
52 & 32819 & 33167.9512235637 & -348.951223563672 \tabularnewline
53 & 33947 & 33276.4789316288 & 670.521068371207 \tabularnewline
54 & 34148 & 34424.601779472 & -276.601779471988 \tabularnewline
55 & 35261 & 34617.3007494462 & 643.6992505538 \tabularnewline
56 & 39506 & 35749.6186541127 & 3756.3813458873 \tabularnewline
57 & 41591 & 40107.3505186728 & 1483.64948132719 \tabularnewline
58 & 39148 & 42236.8759693613 & -3088.87596936135 \tabularnewline
59 & 41216 & 39701.1764494358 & 1514.82355056419 \tabularnewline
60 & 40225 & 41814.6374576802 & -1589.63745768025 \tabularnewline
61 & 41126 & 40775.9312271147 & 350.068772885257 \tabularnewline
62 & 42362 & 41687.4370575557 & 674.56294244426 \tabularnewline
63 & 40740 & 42943.6812051176 & -2203.68120511764 \tabularnewline
64 & 40256 & 41255.5470541159 & -999.547054115908 \tabularnewline
65 & 39804 & 40741.5498858972 & -937.549885897242 \tabularnewline
66 & 41002 & 40261.4132999058 & 740.586700094231 \tabularnewline
67 & 41702 & 41481.6388707098 & 220.361129290177 \tabularnewline
68 & 42254 & 42188.2520759981 & 65.7479240018874 \tabularnewline
69 & 43605 & 42742.2252212625 & 862.774778737548 \tabularnewline
70 & 43271 & 44119.1177493491 & -848.11774934909 \tabularnewline
71 & 43221 & 43759.6650898753 & -538.665089875285 \tabularnewline
72 & 41373 & 43693.4993403511 & -2320.49934035106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233087&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]16661.3172046127[/C][C]-490.3172046127[/C][/ROW]
[ROW][C]5[/C][C]15937[/C][C]16889.6024119407[/C][C]-952.60241194065[/C][/ROW]
[ROW][C]6[/C][C]15713[/C][C]16627.0140881806[/C][C]-914.014088180578[/C][/ROW]
[ROW][C]7[/C][C]15594[/C][C]16375.5838294004[/C][C]-781.583829400379[/C][/ROW]
[ROW][C]8[/C][C]15683[/C][C]16233.1279035278[/C][C]-550.127903527782[/C][/ROW]
[ROW][C]9[/C][C]16438[/C][C]16305.6181462373[/C][C]132.381853762736[/C][/ROW]
[ROW][C]10[/C][C]17032[/C][C]17064.5910264734[/C][C]-32.5910264734339[/C][/ROW]
[ROW][C]11[/C][C]17696[/C][C]17657.6129449519[/C][C]38.3870550481079[/C][/ROW]
[ROW][C]12[/C][C]17745[/C][C]18322.7649697045[/C][C]-577.764969704462[/C][/ROW]
[ROW][C]13[/C][C]19394[/C][C]18354.4258030132[/C][C]1039.5741969868[/C][/ROW]
[ROW][C]14[/C][C]20148[/C][C]20034.6242162689[/C][C]113.375783731131[/C][/ROW]
[ROW][C]15[/C][C]20108[/C][C]20792.0267098709[/C][C]-684.02670987085[/C][/ROW]
[ROW][C]16[/C][C]18584[/C][C]20731.4985474421[/C][C]-2147.49854744211[/C][/ROW]
[ROW][C]17[/C][C]18441[/C][C]19143.0504807786[/C][C]-702.050480778613[/C][/ROW]
[ROW][C]18[/C][C]18391[/C][C]18978.9814112604[/C][C]-587.981411260378[/C][/ROW]
[ROW][C]19[/C][C]19178[/C][C]18911.3356413785[/C][C]266.664358621489[/C][/ROW]
[ROW][C]20[/C][C]18079[/C][C]19706.3384418375[/C][C]-1627.33844183753[/C][/ROW]
[ROW][C]21[/C][C]18483[/C][C]18558.5007760293[/C][C]-75.500776029312[/C][/ROW]
[ROW][C]22[/C][C]19644[/C][C]18960.2349402491[/C][C]683.765059750869[/C][/ROW]
[ROW][C]23[/C][C]19195[/C][C]20141.7552503585[/C][C]-946.755250358528[/C][/ROW]
[ROW][C]24[/C][C]19650[/C][C]19664.34240437[/C][C]-14.3424043699706[/C][/ROW]
[ROW][C]25[/C][C]20830[/C][C]20118.9119778935[/C][C]711.088022106476[/C][/ROW]
[ROW][C]26[/C][C]23595[/C][C]21320.2522709088[/C][C]2274.74772909118[/C][/ROW]
[ROW][C]27[/C][C]22937[/C][C]24153.51918241[/C][C]-1216.51918240998[/C][/ROW]
[ROW][C]28[/C][C]21814[/C][C]23459.0105154035[/C][C]-1645.01051540354[/C][/ROW]
[ROW][C]29[/C][C]21928[/C][C]22286.6424972109[/C][C]-358.642497210858[/C][/ROW]
[ROW][C]30[/C][C]21777[/C][C]22389.8793627742[/C][C]-612.879362774216[/C][/ROW]
[ROW][C]31[/C][C]21383[/C][C]22220.4863864084[/C][C]-837.486386408385[/C][/ROW]
[ROW][C]32[/C][C]21467[/C][C]21801.3527822319[/C][C]-334.352782231887[/C][/ROW]
[ROW][C]33[/C][C]22052[/C][C]21875.3186006376[/C][C]176.681399362358[/C][/ROW]
[ROW][C]34[/C][C]22680[/C][C]22465.62094397[/C][C]214.379056029986[/C][/ROW]
[ROW][C]35[/C][C]24320[/C][C]23100.0546226846[/C][C]1219.9453773154[/C][/ROW]
[ROW][C]36[/C][C]24977[/C][C]24776.6661124091[/C][C]200.333887590903[/C][/ROW]
[ROW][C]37[/C][C]25204[/C][C]25439.6782849239[/C][C]-235.678284923855[/C][/ROW]
[ROW][C]38[/C][C]25739[/C][C]25659.6054001315[/C][C]79.3945998685485[/C][/ROW]
[ROW][C]39[/C][C]26434[/C][C]26196.9880925301[/C][C]237.011907469921[/C][/ROW]
[ROW][C]40[/C][C]27525[/C][C]26899.1010003506[/C][C]625.898999649398[/C][/ROW]
[ROW][C]41[/C][C]30695[/C][C]28008.8847059331[/C][C]2686.11529406689[/C][/ROW]
[ROW][C]42[/C][C]32436[/C][C]31259.4970713031[/C][C]1176.50292869693[/C][/ROW]
[ROW][C]43[/C][C]30160[/C][C]33035.8048200644[/C][C]-2875.80482006443[/C][/ROW]
[ROW][C]44[/C][C]30236[/C][C]30673.4997275765[/C][C]-437.49972757648[/C][/ROW]
[ROW][C]45[/C][C]31293[/C][C]30736.3700276092[/C][C]556.629972390812[/C][/ROW]
[ROW][C]46[/C][C]31077[/C][C]31810.0749169374[/C][C]-733.074916937414[/C][/ROW]
[ROW][C]47[/C][C]32226[/C][C]31572.0747804659[/C][C]653.925219534107[/C][/ROW]
[ROW][C]48[/C][C]33865[/C][C]32740.6995742483[/C][C]1124.30042575174[/C][/ROW]
[ROW][C]49[/C][C]32810[/C][C]34413.4406861456[/C][C]-1603.44068614561[/C][/ROW]
[ROW][C]50[/C][C]32242[/C][C]33310.3202101831[/C][C]-1068.32021018311[/C][/ROW]
[ROW][C]51[/C][C]32700[/C][C]32710.2591071822[/C][C]-10.2591071822062[/C][/ROW]
[ROW][C]52[/C][C]32819[/C][C]33167.9512235637[/C][C]-348.951223563672[/C][/ROW]
[ROW][C]53[/C][C]33947[/C][C]33276.4789316288[/C][C]670.521068371207[/C][/ROW]
[ROW][C]54[/C][C]34148[/C][C]34424.601779472[/C][C]-276.601779471988[/C][/ROW]
[ROW][C]55[/C][C]35261[/C][C]34617.3007494462[/C][C]643.6992505538[/C][/ROW]
[ROW][C]56[/C][C]39506[/C][C]35749.6186541127[/C][C]3756.3813458873[/C][/ROW]
[ROW][C]57[/C][C]41591[/C][C]40107.3505186728[/C][C]1483.64948132719[/C][/ROW]
[ROW][C]58[/C][C]39148[/C][C]42236.8759693613[/C][C]-3088.87596936135[/C][/ROW]
[ROW][C]59[/C][C]41216[/C][C]39701.1764494358[/C][C]1514.82355056419[/C][/ROW]
[ROW][C]60[/C][C]40225[/C][C]41814.6374576802[/C][C]-1589.63745768025[/C][/ROW]
[ROW][C]61[/C][C]41126[/C][C]40775.9312271147[/C][C]350.068772885257[/C][/ROW]
[ROW][C]62[/C][C]42362[/C][C]41687.4370575557[/C][C]674.56294244426[/C][/ROW]
[ROW][C]63[/C][C]40740[/C][C]42943.6812051176[/C][C]-2203.68120511764[/C][/ROW]
[ROW][C]64[/C][C]40256[/C][C]41255.5470541159[/C][C]-999.547054115908[/C][/ROW]
[ROW][C]65[/C][C]39804[/C][C]40741.5498858972[/C][C]-937.549885897242[/C][/ROW]
[ROW][C]66[/C][C]41002[/C][C]40261.4132999058[/C][C]740.586700094231[/C][/ROW]
[ROW][C]67[/C][C]41702[/C][C]41481.6388707098[/C][C]220.361129290177[/C][/ROW]
[ROW][C]68[/C][C]42254[/C][C]42188.2520759981[/C][C]65.7479240018874[/C][/ROW]
[ROW][C]69[/C][C]43605[/C][C]42742.2252212625[/C][C]862.774778737548[/C][/ROW]
[ROW][C]70[/C][C]43271[/C][C]44119.1177493491[/C][C]-848.11774934909[/C][/ROW]
[ROW][C]71[/C][C]43221[/C][C]43759.6650898753[/C][C]-538.665089875285[/C][/ROW]
[ROW][C]72[/C][C]41373[/C][C]43693.4993403511[/C][C]-2320.49934035106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233087&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233087&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
41617116661.3172046127-490.3172046127
51593716889.6024119407-952.60241194065
61571316627.0140881806-914.014088180578
71559416375.5838294004-781.583829400379
81568316233.1279035278-550.127903527782
91643816305.6181462373132.381853762736
101703217064.5910264734-32.5910264734339
111769617657.612944951938.3870550481079
121774518322.7649697045-577.764969704462
131939418354.42580301321039.5741969868
142014820034.6242162689113.375783731131
152010820792.0267098709-684.02670987085
161858420731.4985474421-2147.49854744211
171844119143.0504807786-702.050480778613
181839118978.9814112604-587.981411260378
191917818911.3356413785266.664358621489
201807919706.3384418375-1627.33844183753
211848318558.5007760293-75.500776029312
221964418960.2349402491683.765059750869
231919520141.7552503585-946.755250358528
241965019664.34240437-14.3424043699706
252083020118.9119778935711.088022106476
262359521320.25227090882274.74772909118
272293724153.51918241-1216.51918240998
282181423459.0105154035-1645.01051540354
292192822286.6424972109-358.642497210858
302177722389.8793627742-612.879362774216
312138322220.4863864084-837.486386408385
322146721801.3527822319-334.352782231887
332205221875.3186006376176.681399362358
342268022465.62094397214.379056029986
352432023100.05462268461219.9453773154
362497724776.6661124091200.333887590903
372520425439.6782849239-235.678284923855
382573925659.605400131579.3945998685485
392643426196.9880925301237.011907469921
402752526899.1010003506625.898999649398
413069528008.88470593312686.11529406689
423243631259.49707130311176.50292869693
433016033035.8048200644-2875.80482006443
443023630673.4997275765-437.49972757648
453129330736.3700276092556.629972390812
463107731810.0749169374-733.074916937414
473222631572.0747804659653.925219534107
483386532740.69957424831124.30042575174
493281034413.4406861456-1603.44068614561
503224233310.3202101831-1068.32021018311
513270032710.2591071822-10.2591071822062
523281933167.9512235637-348.951223563672
533394733276.4789316288670.521068371207
543414834424.601779472-276.601779471988
553526134617.3007494462643.6992505538
563950635749.61865411273756.3813458873
574159140107.35051867281483.64948132719
583914842236.8759693613-3088.87596936135
594121639701.17644943581514.82355056419
604022541814.6374576802-1589.63745768025
614112640775.9312271147350.068772885257
624236241687.4370575557674.56294244426
634074042943.6812051176-2203.68120511764
644025641255.5470541159-999.547054115908
653980440741.5498858972-937.549885897242
664100240261.4132999058740.586700094231
674170241481.6388707098220.361129290177
684225442188.252075998165.7479240018874
694360542742.2252212625862.774778737548
704327144119.1177493491-848.11774934909
714322143759.6650898753-538.665089875285
724137343693.4993403511-2320.49934035106







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7341775.859388157539451.539882564144100.1788937509
7442178.718776315138841.946087199145515.491465431
7542581.578164472638433.746941748946729.4093871963
7642984.437552630138124.031376994847844.8437282654
7743387.296940787637873.594336670948900.9995449044
7843790.156328945237662.649502867449917.6631550229
7944193.015717102737479.629828367750906.4016058377
8044595.875105260237317.119828640951874.6303818795
8144998.734493417737170.052856697152827.4161301384
8245401.593881575337034.801492871953768.3862702786
8345804.453269732836908.674163635254700.2323758304
8446207.312657890336789.616513740255625.0088020404

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 41775.8593881575 & 39451.5398825641 & 44100.1788937509 \tabularnewline
74 & 42178.7187763151 & 38841.9460871991 & 45515.491465431 \tabularnewline
75 & 42581.5781644726 & 38433.7469417489 & 46729.4093871963 \tabularnewline
76 & 42984.4375526301 & 38124.0313769948 & 47844.8437282654 \tabularnewline
77 & 43387.2969407876 & 37873.5943366709 & 48900.9995449044 \tabularnewline
78 & 43790.1563289452 & 37662.6495028674 & 49917.6631550229 \tabularnewline
79 & 44193.0157171027 & 37479.6298283677 & 50906.4016058377 \tabularnewline
80 & 44595.8751052602 & 37317.1198286409 & 51874.6303818795 \tabularnewline
81 & 44998.7344934177 & 37170.0528566971 & 52827.4161301384 \tabularnewline
82 & 45401.5938815753 & 37034.8014928719 & 53768.3862702786 \tabularnewline
83 & 45804.4532697328 & 36908.6741636352 & 54700.2323758304 \tabularnewline
84 & 46207.3126578903 & 36789.6165137402 & 55625.0088020404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233087&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]41775.8593881575[/C][C]39451.5398825641[/C][C]44100.1788937509[/C][/ROW]
[ROW][C]74[/C][C]42178.7187763151[/C][C]38841.9460871991[/C][C]45515.491465431[/C][/ROW]
[ROW][C]75[/C][C]42581.5781644726[/C][C]38433.7469417489[/C][C]46729.4093871963[/C][/ROW]
[ROW][C]76[/C][C]42984.4375526301[/C][C]38124.0313769948[/C][C]47844.8437282654[/C][/ROW]
[ROW][C]77[/C][C]43387.2969407876[/C][C]37873.5943366709[/C][C]48900.9995449044[/C][/ROW]
[ROW][C]78[/C][C]43790.1563289452[/C][C]37662.6495028674[/C][C]49917.6631550229[/C][/ROW]
[ROW][C]79[/C][C]44193.0157171027[/C][C]37479.6298283677[/C][C]50906.4016058377[/C][/ROW]
[ROW][C]80[/C][C]44595.8751052602[/C][C]37317.1198286409[/C][C]51874.6303818795[/C][/ROW]
[ROW][C]81[/C][C]44998.7344934177[/C][C]37170.0528566971[/C][C]52827.4161301384[/C][/ROW]
[ROW][C]82[/C][C]45401.5938815753[/C][C]37034.8014928719[/C][C]53768.3862702786[/C][/ROW]
[ROW][C]83[/C][C]45804.4532697328[/C][C]36908.6741636352[/C][C]54700.2323758304[/C][/ROW]
[ROW][C]84[/C][C]46207.3126578903[/C][C]36789.6165137402[/C][C]55625.0088020404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233087&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233087&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
7341775.859388157539451.539882564144100.1788937509
7442178.718776315138841.946087199145515.491465431
7542581.578164472638433.746941748946729.4093871963
7642984.437552630138124.031376994847844.8437282654
7743387.296940787637873.594336670948900.9995449044
7843790.156328945237662.649502867449917.6631550229
7944193.015717102737479.629828367750906.4016058377
8044595.875105260237317.119828640951874.6303818795
8144998.734493417737170.052856697152827.4161301384
8245401.593881575337034.801492871953768.3862702786
8345804.453269732836908.674163635254700.2323758304
8446207.312657890336789.616513740255625.0088020404



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')