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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 21 May 2016 11:34:12 +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/2016/May/21/t14638269101fy2nygp3smmvvg.htm/, Retrieved Mon, 20 May 2024 13:46:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295425, Retrieved Mon, 20 May 2024 13:46:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2016-04-25 20:57:38] [984d31b28aa27320c9bb8a4be001f13a]
- RMPD    [Exponential Smoothing] [] [2016-05-21 10:34:12] [9d122f8260d20611f07666190c7f1fd6] [Current]
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Dataseries X:
45564.6
47295.5
46465.5
50679.5
47452.8
49415.4
48165.3
51814
49030.7
50820.8
49729.5
53501.6
50524.9
52095
51290.3
55064
52505.2
54318.3
53039.6
57607.6
54236.4
56586.4
55614
60085.9
56963.5
59152.8
57804.6
62541.5
59449.3
61704.7
60399
65724.7
62679.4
65526.5
64274.8
68769.1
63542.8
66198
64544.9
71041.8
66087.2
69005.8
66897
73702
68485.3
71457
69774.6
76479.7
71204.7
73783.9
71651
78541.6
72714.4
75258
73168.1
79701.6
73944.5
76401.2
73948.1
80583.3





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=295425&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=295425&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295425&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'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.568190457627314
beta0.0138088433568704
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.568190457627314 \tabularnewline
beta & 0.0138088433568704 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295425&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.568190457627314[/C][/ROW]
[ROW][C]beta[/C][C]0.0138088433568704[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295425&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295425&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.568190457627314
beta0.0138088433568704
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
547452.846443.08751009.71249999999
649415.449080.6062652633334.793734736719
748165.348111.81943782653.4805621740452
85181452313.7377614603-499.737761460347
949030.749216.2552361984-185.555236198445
1050820.850880.867491801-60.0674918010263
1149729.549560.822044453168.677955547028
1253501.653584.7847948443-83.1847948442883
1350524.950858.3943176887-333.494317688739
145209552490.7186814059-395.71868140591
1551290.351073.6832379862216.616762013771
165506455011.453092206352.5469077937232
1752505.252250.4884613439254.711538656098
1854318.354191.1622286425127.137771357477
1953039.653340.7290023539-301.12900235394
2057607.656914.5193467545693.08065324551
2154236.454610.8677779537-374.467777953745
2256586.456140.0950004321446.304999567903
235561455289.7187801169324.281219883058
2460085.959656.7163751555429.183624844482
2556963.556748.6187972595214.881202740537
2659152.858978.2254313629174.574568637065
2757804.657929.7309564404-125.130956440371
2862541.562092.1160048233449.383995176679
2959449.359108.558050942340.741949058051
3061704.761398.8600781251305.839921874925
316039960303.150840880195.8491591199272
3265724.764848.5267644792876.173235520793
3362679.462073.2533670587606.146632941345
3465526.564514.06680876741012.43319123261
3564274.863749.4871118061525.312888193883
3668769.168899.527208065-130.427208065041
3763542.865451.5107373806-1908.71073738059
386619866634.9106846189-436.910684618895
3964544.964821.1788563717-276.278856371704
4071041.869211.01243417051830.78756582951
4166087.266103.2525740757-16.0525740756711
4269005.869006.2229205189-0.422920518889441
436689767521.9291211102-624.929121110239
447370272632.84629465011069.15370534989
4568485.368298.2062892162187.093710783767
467145771328.3014883312128.698511668801
4769774.669653.6686500466120.93134995336
4876479.775931.7129489737547.987051026284
4971204.770927.7951928877276.904807112267
5073783.973992.1353501101-208.235350110117
517165172128.4931256106-477.493125610636
5278541.678252.0169580373289.583041962687
5372714.472983.2850418193-268.885041819332
547525875522.8066013567-264.806601356657
5573168.173505.0913294912-336.991329491182
5679701.680035.1184097674-333.518409767406
5773944.574161.7461189541-217.246118954135
5876401.276723.3264650416-322.126465041583
5973948.174632.379738312-684.279738312005
6080583.380954.3628543935-371.062854393516

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 47452.8 & 46443.0875 & 1009.71249999999 \tabularnewline
6 & 49415.4 & 49080.6062652633 & 334.793734736719 \tabularnewline
7 & 48165.3 & 48111.819437826 & 53.4805621740452 \tabularnewline
8 & 51814 & 52313.7377614603 & -499.737761460347 \tabularnewline
9 & 49030.7 & 49216.2552361984 & -185.555236198445 \tabularnewline
10 & 50820.8 & 50880.867491801 & -60.0674918010263 \tabularnewline
11 & 49729.5 & 49560.822044453 & 168.677955547028 \tabularnewline
12 & 53501.6 & 53584.7847948443 & -83.1847948442883 \tabularnewline
13 & 50524.9 & 50858.3943176887 & -333.494317688739 \tabularnewline
14 & 52095 & 52490.7186814059 & -395.71868140591 \tabularnewline
15 & 51290.3 & 51073.6832379862 & 216.616762013771 \tabularnewline
16 & 55064 & 55011.4530922063 & 52.5469077937232 \tabularnewline
17 & 52505.2 & 52250.4884613439 & 254.711538656098 \tabularnewline
18 & 54318.3 & 54191.1622286425 & 127.137771357477 \tabularnewline
19 & 53039.6 & 53340.7290023539 & -301.12900235394 \tabularnewline
20 & 57607.6 & 56914.5193467545 & 693.08065324551 \tabularnewline
21 & 54236.4 & 54610.8677779537 & -374.467777953745 \tabularnewline
22 & 56586.4 & 56140.0950004321 & 446.304999567903 \tabularnewline
23 & 55614 & 55289.7187801169 & 324.281219883058 \tabularnewline
24 & 60085.9 & 59656.7163751555 & 429.183624844482 \tabularnewline
25 & 56963.5 & 56748.6187972595 & 214.881202740537 \tabularnewline
26 & 59152.8 & 58978.2254313629 & 174.574568637065 \tabularnewline
27 & 57804.6 & 57929.7309564404 & -125.130956440371 \tabularnewline
28 & 62541.5 & 62092.1160048233 & 449.383995176679 \tabularnewline
29 & 59449.3 & 59108.558050942 & 340.741949058051 \tabularnewline
30 & 61704.7 & 61398.8600781251 & 305.839921874925 \tabularnewline
31 & 60399 & 60303.1508408801 & 95.8491591199272 \tabularnewline
32 & 65724.7 & 64848.5267644792 & 876.173235520793 \tabularnewline
33 & 62679.4 & 62073.2533670587 & 606.146632941345 \tabularnewline
34 & 65526.5 & 64514.0668087674 & 1012.43319123261 \tabularnewline
35 & 64274.8 & 63749.4871118061 & 525.312888193883 \tabularnewline
36 & 68769.1 & 68899.527208065 & -130.427208065041 \tabularnewline
37 & 63542.8 & 65451.5107373806 & -1908.71073738059 \tabularnewline
38 & 66198 & 66634.9106846189 & -436.910684618895 \tabularnewline
39 & 64544.9 & 64821.1788563717 & -276.278856371704 \tabularnewline
40 & 71041.8 & 69211.0124341705 & 1830.78756582951 \tabularnewline
41 & 66087.2 & 66103.2525740757 & -16.0525740756711 \tabularnewline
42 & 69005.8 & 69006.2229205189 & -0.422920518889441 \tabularnewline
43 & 66897 & 67521.9291211102 & -624.929121110239 \tabularnewline
44 & 73702 & 72632.8462946501 & 1069.15370534989 \tabularnewline
45 & 68485.3 & 68298.2062892162 & 187.093710783767 \tabularnewline
46 & 71457 & 71328.3014883312 & 128.698511668801 \tabularnewline
47 & 69774.6 & 69653.6686500466 & 120.93134995336 \tabularnewline
48 & 76479.7 & 75931.7129489737 & 547.987051026284 \tabularnewline
49 & 71204.7 & 70927.7951928877 & 276.904807112267 \tabularnewline
50 & 73783.9 & 73992.1353501101 & -208.235350110117 \tabularnewline
51 & 71651 & 72128.4931256106 & -477.493125610636 \tabularnewline
52 & 78541.6 & 78252.0169580373 & 289.583041962687 \tabularnewline
53 & 72714.4 & 72983.2850418193 & -268.885041819332 \tabularnewline
54 & 75258 & 75522.8066013567 & -264.806601356657 \tabularnewline
55 & 73168.1 & 73505.0913294912 & -336.991329491182 \tabularnewline
56 & 79701.6 & 80035.1184097674 & -333.518409767406 \tabularnewline
57 & 73944.5 & 74161.7461189541 & -217.246118954135 \tabularnewline
58 & 76401.2 & 76723.3264650416 & -322.126465041583 \tabularnewline
59 & 73948.1 & 74632.379738312 & -684.279738312005 \tabularnewline
60 & 80583.3 & 80954.3628543935 & -371.062854393516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295425&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]5[/C][C]47452.8[/C][C]46443.0875[/C][C]1009.71249999999[/C][/ROW]
[ROW][C]6[/C][C]49415.4[/C][C]49080.6062652633[/C][C]334.793734736719[/C][/ROW]
[ROW][C]7[/C][C]48165.3[/C][C]48111.819437826[/C][C]53.4805621740452[/C][/ROW]
[ROW][C]8[/C][C]51814[/C][C]52313.7377614603[/C][C]-499.737761460347[/C][/ROW]
[ROW][C]9[/C][C]49030.7[/C][C]49216.2552361984[/C][C]-185.555236198445[/C][/ROW]
[ROW][C]10[/C][C]50820.8[/C][C]50880.867491801[/C][C]-60.0674918010263[/C][/ROW]
[ROW][C]11[/C][C]49729.5[/C][C]49560.822044453[/C][C]168.677955547028[/C][/ROW]
[ROW][C]12[/C][C]53501.6[/C][C]53584.7847948443[/C][C]-83.1847948442883[/C][/ROW]
[ROW][C]13[/C][C]50524.9[/C][C]50858.3943176887[/C][C]-333.494317688739[/C][/ROW]
[ROW][C]14[/C][C]52095[/C][C]52490.7186814059[/C][C]-395.71868140591[/C][/ROW]
[ROW][C]15[/C][C]51290.3[/C][C]51073.6832379862[/C][C]216.616762013771[/C][/ROW]
[ROW][C]16[/C][C]55064[/C][C]55011.4530922063[/C][C]52.5469077937232[/C][/ROW]
[ROW][C]17[/C][C]52505.2[/C][C]52250.4884613439[/C][C]254.711538656098[/C][/ROW]
[ROW][C]18[/C][C]54318.3[/C][C]54191.1622286425[/C][C]127.137771357477[/C][/ROW]
[ROW][C]19[/C][C]53039.6[/C][C]53340.7290023539[/C][C]-301.12900235394[/C][/ROW]
[ROW][C]20[/C][C]57607.6[/C][C]56914.5193467545[/C][C]693.08065324551[/C][/ROW]
[ROW][C]21[/C][C]54236.4[/C][C]54610.8677779537[/C][C]-374.467777953745[/C][/ROW]
[ROW][C]22[/C][C]56586.4[/C][C]56140.0950004321[/C][C]446.304999567903[/C][/ROW]
[ROW][C]23[/C][C]55614[/C][C]55289.7187801169[/C][C]324.281219883058[/C][/ROW]
[ROW][C]24[/C][C]60085.9[/C][C]59656.7163751555[/C][C]429.183624844482[/C][/ROW]
[ROW][C]25[/C][C]56963.5[/C][C]56748.6187972595[/C][C]214.881202740537[/C][/ROW]
[ROW][C]26[/C][C]59152.8[/C][C]58978.2254313629[/C][C]174.574568637065[/C][/ROW]
[ROW][C]27[/C][C]57804.6[/C][C]57929.7309564404[/C][C]-125.130956440371[/C][/ROW]
[ROW][C]28[/C][C]62541.5[/C][C]62092.1160048233[/C][C]449.383995176679[/C][/ROW]
[ROW][C]29[/C][C]59449.3[/C][C]59108.558050942[/C][C]340.741949058051[/C][/ROW]
[ROW][C]30[/C][C]61704.7[/C][C]61398.8600781251[/C][C]305.839921874925[/C][/ROW]
[ROW][C]31[/C][C]60399[/C][C]60303.1508408801[/C][C]95.8491591199272[/C][/ROW]
[ROW][C]32[/C][C]65724.7[/C][C]64848.5267644792[/C][C]876.173235520793[/C][/ROW]
[ROW][C]33[/C][C]62679.4[/C][C]62073.2533670587[/C][C]606.146632941345[/C][/ROW]
[ROW][C]34[/C][C]65526.5[/C][C]64514.0668087674[/C][C]1012.43319123261[/C][/ROW]
[ROW][C]35[/C][C]64274.8[/C][C]63749.4871118061[/C][C]525.312888193883[/C][/ROW]
[ROW][C]36[/C][C]68769.1[/C][C]68899.527208065[/C][C]-130.427208065041[/C][/ROW]
[ROW][C]37[/C][C]63542.8[/C][C]65451.5107373806[/C][C]-1908.71073738059[/C][/ROW]
[ROW][C]38[/C][C]66198[/C][C]66634.9106846189[/C][C]-436.910684618895[/C][/ROW]
[ROW][C]39[/C][C]64544.9[/C][C]64821.1788563717[/C][C]-276.278856371704[/C][/ROW]
[ROW][C]40[/C][C]71041.8[/C][C]69211.0124341705[/C][C]1830.78756582951[/C][/ROW]
[ROW][C]41[/C][C]66087.2[/C][C]66103.2525740757[/C][C]-16.0525740756711[/C][/ROW]
[ROW][C]42[/C][C]69005.8[/C][C]69006.2229205189[/C][C]-0.422920518889441[/C][/ROW]
[ROW][C]43[/C][C]66897[/C][C]67521.9291211102[/C][C]-624.929121110239[/C][/ROW]
[ROW][C]44[/C][C]73702[/C][C]72632.8462946501[/C][C]1069.15370534989[/C][/ROW]
[ROW][C]45[/C][C]68485.3[/C][C]68298.2062892162[/C][C]187.093710783767[/C][/ROW]
[ROW][C]46[/C][C]71457[/C][C]71328.3014883312[/C][C]128.698511668801[/C][/ROW]
[ROW][C]47[/C][C]69774.6[/C][C]69653.6686500466[/C][C]120.93134995336[/C][/ROW]
[ROW][C]48[/C][C]76479.7[/C][C]75931.7129489737[/C][C]547.987051026284[/C][/ROW]
[ROW][C]49[/C][C]71204.7[/C][C]70927.7951928877[/C][C]276.904807112267[/C][/ROW]
[ROW][C]50[/C][C]73783.9[/C][C]73992.1353501101[/C][C]-208.235350110117[/C][/ROW]
[ROW][C]51[/C][C]71651[/C][C]72128.4931256106[/C][C]-477.493125610636[/C][/ROW]
[ROW][C]52[/C][C]78541.6[/C][C]78252.0169580373[/C][C]289.583041962687[/C][/ROW]
[ROW][C]53[/C][C]72714.4[/C][C]72983.2850418193[/C][C]-268.885041819332[/C][/ROW]
[ROW][C]54[/C][C]75258[/C][C]75522.8066013567[/C][C]-264.806601356657[/C][/ROW]
[ROW][C]55[/C][C]73168.1[/C][C]73505.0913294912[/C][C]-336.991329491182[/C][/ROW]
[ROW][C]56[/C][C]79701.6[/C][C]80035.1184097674[/C][C]-333.518409767406[/C][/ROW]
[ROW][C]57[/C][C]73944.5[/C][C]74161.7461189541[/C][C]-217.246118954135[/C][/ROW]
[ROW][C]58[/C][C]76401.2[/C][C]76723.3264650416[/C][C]-322.126465041583[/C][/ROW]
[ROW][C]59[/C][C]73948.1[/C][C]74632.379738312[/C][C]-684.279738312005[/C][/ROW]
[ROW][C]60[/C][C]80583.3[/C][C]80954.3628543935[/C][C]-371.062854393516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295425&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295425&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
547452.846443.08751009.71249999999
649415.449080.6062652633334.793734736719
748165.348111.81943782653.4805621740452
85181452313.7377614603-499.737761460347
949030.749216.2552361984-185.555236198445
1050820.850880.867491801-60.0674918010263
1149729.549560.822044453168.677955547028
1253501.653584.7847948443-83.1847948442883
1350524.950858.3943176887-333.494317688739
145209552490.7186814059-395.71868140591
1551290.351073.6832379862216.616762013771
165506455011.453092206352.5469077937232
1752505.252250.4884613439254.711538656098
1854318.354191.1622286425127.137771357477
1953039.653340.7290023539-301.12900235394
2057607.656914.5193467545693.08065324551
2154236.454610.8677779537-374.467777953745
2256586.456140.0950004321446.304999567903
235561455289.7187801169324.281219883058
2460085.959656.7163751555429.183624844482
2556963.556748.6187972595214.881202740537
2659152.858978.2254313629174.574568637065
2757804.657929.7309564404-125.130956440371
2862541.562092.1160048233449.383995176679
2959449.359108.558050942340.741949058051
3061704.761398.8600781251305.839921874925
316039960303.150840880195.8491591199272
3265724.764848.5267644792876.173235520793
3362679.462073.2533670587606.146632941345
3465526.564514.06680876741012.43319123261
3564274.863749.4871118061525.312888193883
3668769.168899.527208065-130.427208065041
3763542.865451.5107373806-1908.71073738059
386619866634.9106846189-436.910684618895
3964544.964821.1788563717-276.278856371704
4071041.869211.01243417051830.78756582951
4166087.266103.2525740757-16.0525740756711
4269005.869006.2229205189-0.422920518889441
436689767521.9291211102-624.929121110239
447370272632.84629465011069.15370534989
4568485.368298.2062892162187.093710783767
467145771328.3014883312128.698511668801
4769774.669653.6686500466120.93134995336
4876479.775931.7129489737547.987051026284
4971204.770927.7951928877276.904807112267
5073783.973992.1353501101-208.235350110117
517165172128.4931256106-477.493125610636
5278541.678252.0169580373289.583041962687
5372714.472983.2850418193-268.885041819332
547525875522.8066013567-264.806601356657
5573168.173505.0913294912-336.991329491182
5679701.680035.1184097674-333.518409767406
5773944.574161.7461189541-217.246118954135
5876401.276723.3264650416-322.126465041583
5973948.174632.379738312-684.279738312005
6080583.380954.3628543935-371.062854393516







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6175097.353433255374024.962591616576169.7442748942
6277726.27492157276488.688469248778963.8613738954
6375653.695865285474266.726347758177040.6653828127
6482496.818859500180971.57908951684022.0586294843

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 75097.3534332553 & 74024.9625916165 & 76169.7442748942 \tabularnewline
62 & 77726.274921572 & 76488.6884692487 & 78963.8613738954 \tabularnewline
63 & 75653.6958652854 & 74266.7263477581 & 77040.6653828127 \tabularnewline
64 & 82496.8188595001 & 80971.579089516 & 84022.0586294843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295425&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]61[/C][C]75097.3534332553[/C][C]74024.9625916165[/C][C]76169.7442748942[/C][/ROW]
[ROW][C]62[/C][C]77726.274921572[/C][C]76488.6884692487[/C][C]78963.8613738954[/C][/ROW]
[ROW][C]63[/C][C]75653.6958652854[/C][C]74266.7263477581[/C][C]77040.6653828127[/C][/ROW]
[ROW][C]64[/C][C]82496.8188595001[/C][C]80971.579089516[/C][C]84022.0586294843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295425&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295425&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
6175097.353433255374024.962591616576169.7442748942
6277726.27492157276488.688469248778963.8613738954
6375653.695865285474266.726347758177040.6653828127
6482496.818859500180971.57908951684022.0586294843



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')