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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2016 12:48:13 +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/Dec/19/t1482148254z95pu6rj6deyqii.htm/, Retrieved Tue, 21 May 2024 06:48:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301310, Retrieved Tue, 21 May 2024 06:48:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-19 11:48:13] [2e2b863c9581eba851d0277c64dc678f] [Current]
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Dataseries X:
5900
6350
8520
6600
4920
4990
3890
5110
6730
7380
6600
6540
6120
5640
6850
6620
6020
5830
5050
5590
6150
5410
5420
5500
4030
5690
6680
4950
5290
6720
4580
4500
5350
4890
5160
5040
4980
5480
5620
4790
4880
4790
4400
5170
6100
5420
5450
4750
4620
4600
3960
4270
4610
4050
4430
4660
5570
5360
5070
5390
3380
4360
3820
3990
5560
6230
6240
6320
6890
6000
6160
6430
6090
5550
5740
6790
6390
6510
6340
8750
7620
6380
5820
5930
5560
5960
4910
4000
5250
4650
4280
4760
7000
6770
6330
7750
6090
6560
8550
7050
7490
7800
6160
5040
6700
7650
5980
5530
5940
5830
7130
5790
4960
4900
4330
5100
6160
7850
5570
5860
7250




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301310&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301310&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.437310297895343
beta0
gamma0.397248566024519

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.437310297895343 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.397248566024519 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301310&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]0.437310297895343[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.397248566024519[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301310&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
alpha0.437310297895343
beta0
gamma0.397248566024519







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1361206018.36271367522101.637286324783
1456405510.99884819928129.001151800717
1568506778.101482886271.8985171138011
1666206682.3158807209-62.3158807209038
1760206182.83694025667-162.83694025667
1858306010.64910530209-180.649105302095
1950503744.838493812011305.16150618799
2055905552.5381634487237.4618365512815
2161507284.60971291477-1134.60971291477
2254107503.7056372625-2093.7056372625
2354205757.96237055684-337.962370556843
2455005465.8570481753134.142951824685
2540304996.6959617099-966.695961709899
2656904028.25554657561661.7444534244
2766805952.87859179465727.121408205352
2849506113.62807471521-1163.62807471521
2952905110.06473166402179.935268335983
3067205083.793201479451636.20679852055
3145803944.6321813841635.367818615898
3245005176.05821134046-676.058211340462
3353506334.10966505309-984.10966505309
3448906404.63632590838-1514.63632590838
3551605304.58324655597-144.583246555968
3650405180.22044491267-140.220444912668
3749804411.09325180633568.906748193665
3854804701.71689604703778.283103952975
3956206031.07907692155-411.079076921549
4047905271.44692639514-481.446926395136
4148804866.5320178822613.4679821177388
4247905092.97962179976-302.979621799762
4344002882.077198052331517.92280194767
4451704206.31359628068963.686403719317
4561006012.5842301469487.415769853058
4654206433.11260590853-1013.11260590853
4754505858.62579652583-408.625796525827
4847505619.76967561591-869.769675615913
4946204690.11264547104-70.1126454710375
5046004748.08793878709-148.087938787093
5139605406.48315726635-1446.48315726635
5242704178.3289779744391.6710220255682
5346104134.67163016464475.32836983536
5440504492.36073993718-442.360739937176
5544302627.527607225931802.47239277407
5646603952.31329702576707.686702974243
5755705450.76188604317119.238113956834
5853605639.20794897216-279.207948972164
5950705520.78473618749-450.78473618749
6053905160.41365663128229.586343368717
6133804890.26181320879-1510.26181320879
6243604301.0154087677258.9845912322762
6338204759.73830966037-939.738309660373
6439904097.00890162428-107.008901624277
6555604052.224813043851507.77518695615
6662304656.284632801951573.71536719805
6762404174.884679112982065.11532088702
6863205369.81192368801950.188076311988
6968906842.774314219347.2256857807033
7060006910.6648777634-910.664877763405
7161606477.74688661992-317.746886619918
7264306327.63639578968102.363604210324
7360905612.94452115087477.055478849133
7455506243.54243757353-693.542437573528
7557406149.9353090441-409.935309044095
7667905905.03227941261884.967720587391
7763906654.99871962237-264.998719622373
7865106498.5457095222811.4542904777154
7963405443.79438924497896.205610755026
8087505878.328282955792871.67171704421
8176207989.73817099201-369.738170992008
8263807661.17109336388-1281.17109336388
8358207198.76050008062-1378.76050008062
8459306678.5641520922-748.564152092199
8555605675.50681129021-115.50681129021
8659605785.31010280625174.689897193746
8749106134.78395793589-1224.78395793589
8840005822.98588943148-1822.98588943148
8952505131.68700242957118.312997570433
9046505204.65505278598-554.655052785979
9142804100.10469455477179.895305445227
9247604662.9600655449797.0399344550278
9370004836.450078809072163.54992119093
9467705411.985487295851358.01451270415
9563306081.90400419299248.095995807013
9677506414.015080948991335.98491905101
9760906464.05835239925-374.058352399254
9865606525.6613886526934.3386113473061
9985506500.937040910642049.06295908936
10070507487.11125466396-437.111254663964
10174907835.80364815143-345.803648151426
10278007555.38172473066244.61827526934
10361606964.55415911015-804.554159110154
10450407078.3791728653-2038.3791728653
10567006779.95059758227-79.9505975822694
10676506194.320667051881455.67933294812
10759806658.85150753412-678.851507534123
10855306828.77217961969-1298.77217961969
10959405344.36703885652595.632961143476
11058305921.31409701545-91.3140970154527
11171306291.98717975381838.012820246188
11257906192.8279492151-402.827949215095
11349606576.92256242279-1616.92256242279
11449005872.60288909777-972.602889097765
11543304514.95289616258-184.952896162579
11651004623.94188330167476.058116698328
11761605862.86561870444297.134381295565
11878505785.394624148762064.60537585124
11955706039.08837299829-469.088372998289
12058606162.17119600738-302.171196007378
12172505537.041909208491712.95809079151

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6120 & 6018.36271367522 & 101.637286324783 \tabularnewline
14 & 5640 & 5510.99884819928 & 129.001151800717 \tabularnewline
15 & 6850 & 6778.1014828862 & 71.8985171138011 \tabularnewline
16 & 6620 & 6682.3158807209 & -62.3158807209038 \tabularnewline
17 & 6020 & 6182.83694025667 & -162.83694025667 \tabularnewline
18 & 5830 & 6010.64910530209 & -180.649105302095 \tabularnewline
19 & 5050 & 3744.83849381201 & 1305.16150618799 \tabularnewline
20 & 5590 & 5552.53816344872 & 37.4618365512815 \tabularnewline
21 & 6150 & 7284.60971291477 & -1134.60971291477 \tabularnewline
22 & 5410 & 7503.7056372625 & -2093.7056372625 \tabularnewline
23 & 5420 & 5757.96237055684 & -337.962370556843 \tabularnewline
24 & 5500 & 5465.85704817531 & 34.142951824685 \tabularnewline
25 & 4030 & 4996.6959617099 & -966.695961709899 \tabularnewline
26 & 5690 & 4028.2555465756 & 1661.7444534244 \tabularnewline
27 & 6680 & 5952.87859179465 & 727.121408205352 \tabularnewline
28 & 4950 & 6113.62807471521 & -1163.62807471521 \tabularnewline
29 & 5290 & 5110.06473166402 & 179.935268335983 \tabularnewline
30 & 6720 & 5083.79320147945 & 1636.20679852055 \tabularnewline
31 & 4580 & 3944.6321813841 & 635.367818615898 \tabularnewline
32 & 4500 & 5176.05821134046 & -676.058211340462 \tabularnewline
33 & 5350 & 6334.10966505309 & -984.10966505309 \tabularnewline
34 & 4890 & 6404.63632590838 & -1514.63632590838 \tabularnewline
35 & 5160 & 5304.58324655597 & -144.583246555968 \tabularnewline
36 & 5040 & 5180.22044491267 & -140.220444912668 \tabularnewline
37 & 4980 & 4411.09325180633 & 568.906748193665 \tabularnewline
38 & 5480 & 4701.71689604703 & 778.283103952975 \tabularnewline
39 & 5620 & 6031.07907692155 & -411.079076921549 \tabularnewline
40 & 4790 & 5271.44692639514 & -481.446926395136 \tabularnewline
41 & 4880 & 4866.53201788226 & 13.4679821177388 \tabularnewline
42 & 4790 & 5092.97962179976 & -302.979621799762 \tabularnewline
43 & 4400 & 2882.07719805233 & 1517.92280194767 \tabularnewline
44 & 5170 & 4206.31359628068 & 963.686403719317 \tabularnewline
45 & 6100 & 6012.58423014694 & 87.415769853058 \tabularnewline
46 & 5420 & 6433.11260590853 & -1013.11260590853 \tabularnewline
47 & 5450 & 5858.62579652583 & -408.625796525827 \tabularnewline
48 & 4750 & 5619.76967561591 & -869.769675615913 \tabularnewline
49 & 4620 & 4690.11264547104 & -70.1126454710375 \tabularnewline
50 & 4600 & 4748.08793878709 & -148.087938787093 \tabularnewline
51 & 3960 & 5406.48315726635 & -1446.48315726635 \tabularnewline
52 & 4270 & 4178.32897797443 & 91.6710220255682 \tabularnewline
53 & 4610 & 4134.67163016464 & 475.32836983536 \tabularnewline
54 & 4050 & 4492.36073993718 & -442.360739937176 \tabularnewline
55 & 4430 & 2627.52760722593 & 1802.47239277407 \tabularnewline
56 & 4660 & 3952.31329702576 & 707.686702974243 \tabularnewline
57 & 5570 & 5450.76188604317 & 119.238113956834 \tabularnewline
58 & 5360 & 5639.20794897216 & -279.207948972164 \tabularnewline
59 & 5070 & 5520.78473618749 & -450.78473618749 \tabularnewline
60 & 5390 & 5160.41365663128 & 229.586343368717 \tabularnewline
61 & 3380 & 4890.26181320879 & -1510.26181320879 \tabularnewline
62 & 4360 & 4301.01540876772 & 58.9845912322762 \tabularnewline
63 & 3820 & 4759.73830966037 & -939.738309660373 \tabularnewline
64 & 3990 & 4097.00890162428 & -107.008901624277 \tabularnewline
65 & 5560 & 4052.22481304385 & 1507.77518695615 \tabularnewline
66 & 6230 & 4656.28463280195 & 1573.71536719805 \tabularnewline
67 & 6240 & 4174.88467911298 & 2065.11532088702 \tabularnewline
68 & 6320 & 5369.81192368801 & 950.188076311988 \tabularnewline
69 & 6890 & 6842.7743142193 & 47.2256857807033 \tabularnewline
70 & 6000 & 6910.6648777634 & -910.664877763405 \tabularnewline
71 & 6160 & 6477.74688661992 & -317.746886619918 \tabularnewline
72 & 6430 & 6327.63639578968 & 102.363604210324 \tabularnewline
73 & 6090 & 5612.94452115087 & 477.055478849133 \tabularnewline
74 & 5550 & 6243.54243757353 & -693.542437573528 \tabularnewline
75 & 5740 & 6149.9353090441 & -409.935309044095 \tabularnewline
76 & 6790 & 5905.03227941261 & 884.967720587391 \tabularnewline
77 & 6390 & 6654.99871962237 & -264.998719622373 \tabularnewline
78 & 6510 & 6498.54570952228 & 11.4542904777154 \tabularnewline
79 & 6340 & 5443.79438924497 & 896.205610755026 \tabularnewline
80 & 8750 & 5878.32828295579 & 2871.67171704421 \tabularnewline
81 & 7620 & 7989.73817099201 & -369.738170992008 \tabularnewline
82 & 6380 & 7661.17109336388 & -1281.17109336388 \tabularnewline
83 & 5820 & 7198.76050008062 & -1378.76050008062 \tabularnewline
84 & 5930 & 6678.5641520922 & -748.564152092199 \tabularnewline
85 & 5560 & 5675.50681129021 & -115.50681129021 \tabularnewline
86 & 5960 & 5785.31010280625 & 174.689897193746 \tabularnewline
87 & 4910 & 6134.78395793589 & -1224.78395793589 \tabularnewline
88 & 4000 & 5822.98588943148 & -1822.98588943148 \tabularnewline
89 & 5250 & 5131.68700242957 & 118.312997570433 \tabularnewline
90 & 4650 & 5204.65505278598 & -554.655052785979 \tabularnewline
91 & 4280 & 4100.10469455477 & 179.895305445227 \tabularnewline
92 & 4760 & 4662.96006554497 & 97.0399344550278 \tabularnewline
93 & 7000 & 4836.45007880907 & 2163.54992119093 \tabularnewline
94 & 6770 & 5411.98548729585 & 1358.01451270415 \tabularnewline
95 & 6330 & 6081.90400419299 & 248.095995807013 \tabularnewline
96 & 7750 & 6414.01508094899 & 1335.98491905101 \tabularnewline
97 & 6090 & 6464.05835239925 & -374.058352399254 \tabularnewline
98 & 6560 & 6525.66138865269 & 34.3386113473061 \tabularnewline
99 & 8550 & 6500.93704091064 & 2049.06295908936 \tabularnewline
100 & 7050 & 7487.11125466396 & -437.111254663964 \tabularnewline
101 & 7490 & 7835.80364815143 & -345.803648151426 \tabularnewline
102 & 7800 & 7555.38172473066 & 244.61827526934 \tabularnewline
103 & 6160 & 6964.55415911015 & -804.554159110154 \tabularnewline
104 & 5040 & 7078.3791728653 & -2038.3791728653 \tabularnewline
105 & 6700 & 6779.95059758227 & -79.9505975822694 \tabularnewline
106 & 7650 & 6194.32066705188 & 1455.67933294812 \tabularnewline
107 & 5980 & 6658.85150753412 & -678.851507534123 \tabularnewline
108 & 5530 & 6828.77217961969 & -1298.77217961969 \tabularnewline
109 & 5940 & 5344.36703885652 & 595.632961143476 \tabularnewline
110 & 5830 & 5921.31409701545 & -91.3140970154527 \tabularnewline
111 & 7130 & 6291.98717975381 & 838.012820246188 \tabularnewline
112 & 5790 & 6192.8279492151 & -402.827949215095 \tabularnewline
113 & 4960 & 6576.92256242279 & -1616.92256242279 \tabularnewline
114 & 4900 & 5872.60288909777 & -972.602889097765 \tabularnewline
115 & 4330 & 4514.95289616258 & -184.952896162579 \tabularnewline
116 & 5100 & 4623.94188330167 & 476.058116698328 \tabularnewline
117 & 6160 & 5862.86561870444 & 297.134381295565 \tabularnewline
118 & 7850 & 5785.39462414876 & 2064.60537585124 \tabularnewline
119 & 5570 & 6039.08837299829 & -469.088372998289 \tabularnewline
120 & 5860 & 6162.17119600738 & -302.171196007378 \tabularnewline
121 & 7250 & 5537.04190920849 & 1712.95809079151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301310&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]13[/C][C]6120[/C][C]6018.36271367522[/C][C]101.637286324783[/C][/ROW]
[ROW][C]14[/C][C]5640[/C][C]5510.99884819928[/C][C]129.001151800717[/C][/ROW]
[ROW][C]15[/C][C]6850[/C][C]6778.1014828862[/C][C]71.8985171138011[/C][/ROW]
[ROW][C]16[/C][C]6620[/C][C]6682.3158807209[/C][C]-62.3158807209038[/C][/ROW]
[ROW][C]17[/C][C]6020[/C][C]6182.83694025667[/C][C]-162.83694025667[/C][/ROW]
[ROW][C]18[/C][C]5830[/C][C]6010.64910530209[/C][C]-180.649105302095[/C][/ROW]
[ROW][C]19[/C][C]5050[/C][C]3744.83849381201[/C][C]1305.16150618799[/C][/ROW]
[ROW][C]20[/C][C]5590[/C][C]5552.53816344872[/C][C]37.4618365512815[/C][/ROW]
[ROW][C]21[/C][C]6150[/C][C]7284.60971291477[/C][C]-1134.60971291477[/C][/ROW]
[ROW][C]22[/C][C]5410[/C][C]7503.7056372625[/C][C]-2093.7056372625[/C][/ROW]
[ROW][C]23[/C][C]5420[/C][C]5757.96237055684[/C][C]-337.962370556843[/C][/ROW]
[ROW][C]24[/C][C]5500[/C][C]5465.85704817531[/C][C]34.142951824685[/C][/ROW]
[ROW][C]25[/C][C]4030[/C][C]4996.6959617099[/C][C]-966.695961709899[/C][/ROW]
[ROW][C]26[/C][C]5690[/C][C]4028.2555465756[/C][C]1661.7444534244[/C][/ROW]
[ROW][C]27[/C][C]6680[/C][C]5952.87859179465[/C][C]727.121408205352[/C][/ROW]
[ROW][C]28[/C][C]4950[/C][C]6113.62807471521[/C][C]-1163.62807471521[/C][/ROW]
[ROW][C]29[/C][C]5290[/C][C]5110.06473166402[/C][C]179.935268335983[/C][/ROW]
[ROW][C]30[/C][C]6720[/C][C]5083.79320147945[/C][C]1636.20679852055[/C][/ROW]
[ROW][C]31[/C][C]4580[/C][C]3944.6321813841[/C][C]635.367818615898[/C][/ROW]
[ROW][C]32[/C][C]4500[/C][C]5176.05821134046[/C][C]-676.058211340462[/C][/ROW]
[ROW][C]33[/C][C]5350[/C][C]6334.10966505309[/C][C]-984.10966505309[/C][/ROW]
[ROW][C]34[/C][C]4890[/C][C]6404.63632590838[/C][C]-1514.63632590838[/C][/ROW]
[ROW][C]35[/C][C]5160[/C][C]5304.58324655597[/C][C]-144.583246555968[/C][/ROW]
[ROW][C]36[/C][C]5040[/C][C]5180.22044491267[/C][C]-140.220444912668[/C][/ROW]
[ROW][C]37[/C][C]4980[/C][C]4411.09325180633[/C][C]568.906748193665[/C][/ROW]
[ROW][C]38[/C][C]5480[/C][C]4701.71689604703[/C][C]778.283103952975[/C][/ROW]
[ROW][C]39[/C][C]5620[/C][C]6031.07907692155[/C][C]-411.079076921549[/C][/ROW]
[ROW][C]40[/C][C]4790[/C][C]5271.44692639514[/C][C]-481.446926395136[/C][/ROW]
[ROW][C]41[/C][C]4880[/C][C]4866.53201788226[/C][C]13.4679821177388[/C][/ROW]
[ROW][C]42[/C][C]4790[/C][C]5092.97962179976[/C][C]-302.979621799762[/C][/ROW]
[ROW][C]43[/C][C]4400[/C][C]2882.07719805233[/C][C]1517.92280194767[/C][/ROW]
[ROW][C]44[/C][C]5170[/C][C]4206.31359628068[/C][C]963.686403719317[/C][/ROW]
[ROW][C]45[/C][C]6100[/C][C]6012.58423014694[/C][C]87.415769853058[/C][/ROW]
[ROW][C]46[/C][C]5420[/C][C]6433.11260590853[/C][C]-1013.11260590853[/C][/ROW]
[ROW][C]47[/C][C]5450[/C][C]5858.62579652583[/C][C]-408.625796525827[/C][/ROW]
[ROW][C]48[/C][C]4750[/C][C]5619.76967561591[/C][C]-869.769675615913[/C][/ROW]
[ROW][C]49[/C][C]4620[/C][C]4690.11264547104[/C][C]-70.1126454710375[/C][/ROW]
[ROW][C]50[/C][C]4600[/C][C]4748.08793878709[/C][C]-148.087938787093[/C][/ROW]
[ROW][C]51[/C][C]3960[/C][C]5406.48315726635[/C][C]-1446.48315726635[/C][/ROW]
[ROW][C]52[/C][C]4270[/C][C]4178.32897797443[/C][C]91.6710220255682[/C][/ROW]
[ROW][C]53[/C][C]4610[/C][C]4134.67163016464[/C][C]475.32836983536[/C][/ROW]
[ROW][C]54[/C][C]4050[/C][C]4492.36073993718[/C][C]-442.360739937176[/C][/ROW]
[ROW][C]55[/C][C]4430[/C][C]2627.52760722593[/C][C]1802.47239277407[/C][/ROW]
[ROW][C]56[/C][C]4660[/C][C]3952.31329702576[/C][C]707.686702974243[/C][/ROW]
[ROW][C]57[/C][C]5570[/C][C]5450.76188604317[/C][C]119.238113956834[/C][/ROW]
[ROW][C]58[/C][C]5360[/C][C]5639.20794897216[/C][C]-279.207948972164[/C][/ROW]
[ROW][C]59[/C][C]5070[/C][C]5520.78473618749[/C][C]-450.78473618749[/C][/ROW]
[ROW][C]60[/C][C]5390[/C][C]5160.41365663128[/C][C]229.586343368717[/C][/ROW]
[ROW][C]61[/C][C]3380[/C][C]4890.26181320879[/C][C]-1510.26181320879[/C][/ROW]
[ROW][C]62[/C][C]4360[/C][C]4301.01540876772[/C][C]58.9845912322762[/C][/ROW]
[ROW][C]63[/C][C]3820[/C][C]4759.73830966037[/C][C]-939.738309660373[/C][/ROW]
[ROW][C]64[/C][C]3990[/C][C]4097.00890162428[/C][C]-107.008901624277[/C][/ROW]
[ROW][C]65[/C][C]5560[/C][C]4052.22481304385[/C][C]1507.77518695615[/C][/ROW]
[ROW][C]66[/C][C]6230[/C][C]4656.28463280195[/C][C]1573.71536719805[/C][/ROW]
[ROW][C]67[/C][C]6240[/C][C]4174.88467911298[/C][C]2065.11532088702[/C][/ROW]
[ROW][C]68[/C][C]6320[/C][C]5369.81192368801[/C][C]950.188076311988[/C][/ROW]
[ROW][C]69[/C][C]6890[/C][C]6842.7743142193[/C][C]47.2256857807033[/C][/ROW]
[ROW][C]70[/C][C]6000[/C][C]6910.6648777634[/C][C]-910.664877763405[/C][/ROW]
[ROW][C]71[/C][C]6160[/C][C]6477.74688661992[/C][C]-317.746886619918[/C][/ROW]
[ROW][C]72[/C][C]6430[/C][C]6327.63639578968[/C][C]102.363604210324[/C][/ROW]
[ROW][C]73[/C][C]6090[/C][C]5612.94452115087[/C][C]477.055478849133[/C][/ROW]
[ROW][C]74[/C][C]5550[/C][C]6243.54243757353[/C][C]-693.542437573528[/C][/ROW]
[ROW][C]75[/C][C]5740[/C][C]6149.9353090441[/C][C]-409.935309044095[/C][/ROW]
[ROW][C]76[/C][C]6790[/C][C]5905.03227941261[/C][C]884.967720587391[/C][/ROW]
[ROW][C]77[/C][C]6390[/C][C]6654.99871962237[/C][C]-264.998719622373[/C][/ROW]
[ROW][C]78[/C][C]6510[/C][C]6498.54570952228[/C][C]11.4542904777154[/C][/ROW]
[ROW][C]79[/C][C]6340[/C][C]5443.79438924497[/C][C]896.205610755026[/C][/ROW]
[ROW][C]80[/C][C]8750[/C][C]5878.32828295579[/C][C]2871.67171704421[/C][/ROW]
[ROW][C]81[/C][C]7620[/C][C]7989.73817099201[/C][C]-369.738170992008[/C][/ROW]
[ROW][C]82[/C][C]6380[/C][C]7661.17109336388[/C][C]-1281.17109336388[/C][/ROW]
[ROW][C]83[/C][C]5820[/C][C]7198.76050008062[/C][C]-1378.76050008062[/C][/ROW]
[ROW][C]84[/C][C]5930[/C][C]6678.5641520922[/C][C]-748.564152092199[/C][/ROW]
[ROW][C]85[/C][C]5560[/C][C]5675.50681129021[/C][C]-115.50681129021[/C][/ROW]
[ROW][C]86[/C][C]5960[/C][C]5785.31010280625[/C][C]174.689897193746[/C][/ROW]
[ROW][C]87[/C][C]4910[/C][C]6134.78395793589[/C][C]-1224.78395793589[/C][/ROW]
[ROW][C]88[/C][C]4000[/C][C]5822.98588943148[/C][C]-1822.98588943148[/C][/ROW]
[ROW][C]89[/C][C]5250[/C][C]5131.68700242957[/C][C]118.312997570433[/C][/ROW]
[ROW][C]90[/C][C]4650[/C][C]5204.65505278598[/C][C]-554.655052785979[/C][/ROW]
[ROW][C]91[/C][C]4280[/C][C]4100.10469455477[/C][C]179.895305445227[/C][/ROW]
[ROW][C]92[/C][C]4760[/C][C]4662.96006554497[/C][C]97.0399344550278[/C][/ROW]
[ROW][C]93[/C][C]7000[/C][C]4836.45007880907[/C][C]2163.54992119093[/C][/ROW]
[ROW][C]94[/C][C]6770[/C][C]5411.98548729585[/C][C]1358.01451270415[/C][/ROW]
[ROW][C]95[/C][C]6330[/C][C]6081.90400419299[/C][C]248.095995807013[/C][/ROW]
[ROW][C]96[/C][C]7750[/C][C]6414.01508094899[/C][C]1335.98491905101[/C][/ROW]
[ROW][C]97[/C][C]6090[/C][C]6464.05835239925[/C][C]-374.058352399254[/C][/ROW]
[ROW][C]98[/C][C]6560[/C][C]6525.66138865269[/C][C]34.3386113473061[/C][/ROW]
[ROW][C]99[/C][C]8550[/C][C]6500.93704091064[/C][C]2049.06295908936[/C][/ROW]
[ROW][C]100[/C][C]7050[/C][C]7487.11125466396[/C][C]-437.111254663964[/C][/ROW]
[ROW][C]101[/C][C]7490[/C][C]7835.80364815143[/C][C]-345.803648151426[/C][/ROW]
[ROW][C]102[/C][C]7800[/C][C]7555.38172473066[/C][C]244.61827526934[/C][/ROW]
[ROW][C]103[/C][C]6160[/C][C]6964.55415911015[/C][C]-804.554159110154[/C][/ROW]
[ROW][C]104[/C][C]5040[/C][C]7078.3791728653[/C][C]-2038.3791728653[/C][/ROW]
[ROW][C]105[/C][C]6700[/C][C]6779.95059758227[/C][C]-79.9505975822694[/C][/ROW]
[ROW][C]106[/C][C]7650[/C][C]6194.32066705188[/C][C]1455.67933294812[/C][/ROW]
[ROW][C]107[/C][C]5980[/C][C]6658.85150753412[/C][C]-678.851507534123[/C][/ROW]
[ROW][C]108[/C][C]5530[/C][C]6828.77217961969[/C][C]-1298.77217961969[/C][/ROW]
[ROW][C]109[/C][C]5940[/C][C]5344.36703885652[/C][C]595.632961143476[/C][/ROW]
[ROW][C]110[/C][C]5830[/C][C]5921.31409701545[/C][C]-91.3140970154527[/C][/ROW]
[ROW][C]111[/C][C]7130[/C][C]6291.98717975381[/C][C]838.012820246188[/C][/ROW]
[ROW][C]112[/C][C]5790[/C][C]6192.8279492151[/C][C]-402.827949215095[/C][/ROW]
[ROW][C]113[/C][C]4960[/C][C]6576.92256242279[/C][C]-1616.92256242279[/C][/ROW]
[ROW][C]114[/C][C]4900[/C][C]5872.60288909777[/C][C]-972.602889097765[/C][/ROW]
[ROW][C]115[/C][C]4330[/C][C]4514.95289616258[/C][C]-184.952896162579[/C][/ROW]
[ROW][C]116[/C][C]5100[/C][C]4623.94188330167[/C][C]476.058116698328[/C][/ROW]
[ROW][C]117[/C][C]6160[/C][C]5862.86561870444[/C][C]297.134381295565[/C][/ROW]
[ROW][C]118[/C][C]7850[/C][C]5785.39462414876[/C][C]2064.60537585124[/C][/ROW]
[ROW][C]119[/C][C]5570[/C][C]6039.08837299829[/C][C]-469.088372998289[/C][/ROW]
[ROW][C]120[/C][C]5860[/C][C]6162.17119600738[/C][C]-302.171196007378[/C][/ROW]
[ROW][C]121[/C][C]7250[/C][C]5537.04190920849[/C][C]1712.95809079151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301310&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301310&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
1361206018.36271367522101.637286324783
1456405510.99884819928129.001151800717
1568506778.101482886271.8985171138011
1666206682.3158807209-62.3158807209038
1760206182.83694025667-162.83694025667
1858306010.64910530209-180.649105302095
1950503744.838493812011305.16150618799
2055905552.5381634487237.4618365512815
2161507284.60971291477-1134.60971291477
2254107503.7056372625-2093.7056372625
2354205757.96237055684-337.962370556843
2455005465.8570481753134.142951824685
2540304996.6959617099-966.695961709899
2656904028.25554657561661.7444534244
2766805952.87859179465727.121408205352
2849506113.62807471521-1163.62807471521
2952905110.06473166402179.935268335983
3067205083.793201479451636.20679852055
3145803944.6321813841635.367818615898
3245005176.05821134046-676.058211340462
3353506334.10966505309-984.10966505309
3448906404.63632590838-1514.63632590838
3551605304.58324655597-144.583246555968
3650405180.22044491267-140.220444912668
3749804411.09325180633568.906748193665
3854804701.71689604703778.283103952975
3956206031.07907692155-411.079076921549
4047905271.44692639514-481.446926395136
4148804866.5320178822613.4679821177388
4247905092.97962179976-302.979621799762
4344002882.077198052331517.92280194767
4451704206.31359628068963.686403719317
4561006012.5842301469487.415769853058
4654206433.11260590853-1013.11260590853
4754505858.62579652583-408.625796525827
4847505619.76967561591-869.769675615913
4946204690.11264547104-70.1126454710375
5046004748.08793878709-148.087938787093
5139605406.48315726635-1446.48315726635
5242704178.3289779744391.6710220255682
5346104134.67163016464475.32836983536
5440504492.36073993718-442.360739937176
5544302627.527607225931802.47239277407
5646603952.31329702576707.686702974243
5755705450.76188604317119.238113956834
5853605639.20794897216-279.207948972164
5950705520.78473618749-450.78473618749
6053905160.41365663128229.586343368717
6133804890.26181320879-1510.26181320879
6243604301.0154087677258.9845912322762
6338204759.73830966037-939.738309660373
6439904097.00890162428-107.008901624277
6555604052.224813043851507.77518695615
6662304656.284632801951573.71536719805
6762404174.884679112982065.11532088702
6863205369.81192368801950.188076311988
6968906842.774314219347.2256857807033
7060006910.6648777634-910.664877763405
7161606477.74688661992-317.746886619918
7264306327.63639578968102.363604210324
7360905612.94452115087477.055478849133
7455506243.54243757353-693.542437573528
7557406149.9353090441-409.935309044095
7667905905.03227941261884.967720587391
7763906654.99871962237-264.998719622373
7865106498.5457095222811.4542904777154
7963405443.79438924497896.205610755026
8087505878.328282955792871.67171704421
8176207989.73817099201-369.738170992008
8263807661.17109336388-1281.17109336388
8358207198.76050008062-1378.76050008062
8459306678.5641520922-748.564152092199
8555605675.50681129021-115.50681129021
8659605785.31010280625174.689897193746
8749106134.78395793589-1224.78395793589
8840005822.98588943148-1822.98588943148
8952505131.68700242957118.312997570433
9046505204.65505278598-554.655052785979
9142804100.10469455477179.895305445227
9247604662.9600655449797.0399344550278
9370004836.450078809072163.54992119093
9467705411.985487295851358.01451270415
9563306081.90400419299248.095995807013
9677506414.015080948991335.98491905101
9760906464.05835239925-374.058352399254
9865606525.6613886526934.3386113473061
9985506500.937040910642049.06295908936
10070507487.11125466396-437.111254663964
10174907835.80364815143-345.803648151426
10278007555.38172473066244.61827526934
10361606964.55415911015-804.554159110154
10450407078.3791728653-2038.3791728653
10567006779.95059758227-79.9505975822694
10676506194.320667051881455.67933294812
10759806658.85150753412-678.851507534123
10855306828.77217961969-1298.77217961969
10959405344.36703885652595.632961143476
11058305921.31409701545-91.3140970154527
11171306291.98717975381838.012820246188
11257906192.8279492151-402.827949215095
11349606576.92256242279-1616.92256242279
11449005872.60288909777-972.602889097765
11543304514.95289616258-184.952896162579
11651004623.94188330167476.058116698328
11761605862.86561870444297.134381295565
11878505785.394624148762064.60537585124
11955706039.08837299829-469.088372998289
12058606162.17119600738-302.171196007378
12172505537.041909208491712.95809079151







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1226449.055072336654541.065904077878357.04424059543
1237067.391037290144984.93619341249149.84588116789
1246324.397915620124081.004573518278567.79125772198
1256613.269590413794219.734715383989006.80446544359
1266760.070084538334225.271333437779294.8688356389
1276003.810924197073335.215747108948672.4061012852
1286341.43597381353545.439598677249137.43234894975
1297332.180185402974414.3400183663810250.0203524396
1307519.847952116964485.0519538710810554.6439503628
1316304.317830402943156.909013365319451.72664744057
1326669.84843841773413.719176216469925.97770061895
1336627.29889625293265.963851548159988.63394095765

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 6449.05507233665 & 4541.06590407787 & 8357.04424059543 \tabularnewline
123 & 7067.39103729014 & 4984.9361934124 & 9149.84588116789 \tabularnewline
124 & 6324.39791562012 & 4081.00457351827 & 8567.79125772198 \tabularnewline
125 & 6613.26959041379 & 4219.73471538398 & 9006.80446544359 \tabularnewline
126 & 6760.07008453833 & 4225.27133343777 & 9294.8688356389 \tabularnewline
127 & 6003.81092419707 & 3335.21574710894 & 8672.4061012852 \tabularnewline
128 & 6341.4359738135 & 3545.43959867724 & 9137.43234894975 \tabularnewline
129 & 7332.18018540297 & 4414.34001836638 & 10250.0203524396 \tabularnewline
130 & 7519.84795211696 & 4485.05195387108 & 10554.6439503628 \tabularnewline
131 & 6304.31783040294 & 3156.90901336531 & 9451.72664744057 \tabularnewline
132 & 6669.8484384177 & 3413.71917621646 & 9925.97770061895 \tabularnewline
133 & 6627.2988962529 & 3265.96385154815 & 9988.63394095765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301310&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]122[/C][C]6449.05507233665[/C][C]4541.06590407787[/C][C]8357.04424059543[/C][/ROW]
[ROW][C]123[/C][C]7067.39103729014[/C][C]4984.9361934124[/C][C]9149.84588116789[/C][/ROW]
[ROW][C]124[/C][C]6324.39791562012[/C][C]4081.00457351827[/C][C]8567.79125772198[/C][/ROW]
[ROW][C]125[/C][C]6613.26959041379[/C][C]4219.73471538398[/C][C]9006.80446544359[/C][/ROW]
[ROW][C]126[/C][C]6760.07008453833[/C][C]4225.27133343777[/C][C]9294.8688356389[/C][/ROW]
[ROW][C]127[/C][C]6003.81092419707[/C][C]3335.21574710894[/C][C]8672.4061012852[/C][/ROW]
[ROW][C]128[/C][C]6341.4359738135[/C][C]3545.43959867724[/C][C]9137.43234894975[/C][/ROW]
[ROW][C]129[/C][C]7332.18018540297[/C][C]4414.34001836638[/C][C]10250.0203524396[/C][/ROW]
[ROW][C]130[/C][C]7519.84795211696[/C][C]4485.05195387108[/C][C]10554.6439503628[/C][/ROW]
[ROW][C]131[/C][C]6304.31783040294[/C][C]3156.90901336531[/C][C]9451.72664744057[/C][/ROW]
[ROW][C]132[/C][C]6669.8484384177[/C][C]3413.71917621646[/C][C]9925.97770061895[/C][/ROW]
[ROW][C]133[/C][C]6627.2988962529[/C][C]3265.96385154815[/C][C]9988.63394095765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301310&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301310&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
1226449.055072336654541.065904077878357.04424059543
1237067.391037290144984.93619341249149.84588116789
1246324.397915620124081.004573518278567.79125772198
1256613.269590413794219.734715383989006.80446544359
1266760.070084538334225.271333437779294.8688356389
1276003.810924197073335.215747108948672.4061012852
1286341.43597381353545.439598677249137.43234894975
1297332.180185402974414.3400183663810250.0203524396
1307519.847952116964485.0519538710810554.6439503628
1316304.317830402943156.909013365319451.72664744057
1326669.84843841773413.719176216469925.97770061895
1336627.29889625293265.963851548159988.63394095765



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')