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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 computationWed, 21 Dec 2016 13:31:53 +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/21/t1482323536xpvm7uwfjx9zyjp.htm/, Retrieved Mon, 06 May 2024 16:04:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302227, Retrieved Mon, 06 May 2024 16:04:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [n1787...] [2016-12-21 12:31:53] [b7f10b15eba379294ac5bdad7f2e1205] [Current]
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Dataseries X:
3560
2900
3380
3560
3100
2800
2780
4380
3480
3220
3840
4580
3660
5040
4320
4240
3160
4420
3280
5040
5580
4920
5200
4140
4360
4360
4480
4140
2620
4240
3920
4180
8140
8060
6780
5180
4820
3600
6480
5500
4080
3800
4560
7140
4740
5820
6800
4720
6220
3420
7600
2540
4220
5420
2040
4480
5340
4720
4220
3680
4940
2460
3900
5160
2500
3560
3340
6380
2900
7940
4640
3000
5500
4000
3340
2220
2060
3520
2560
2100
3720
4600
2800
2720
2920
2940
2900
2140
2020
3040
3900
2020
3280
3040
3060
2360
3120
3900
1960
2760
1760
2520
2160
2980
2800
3700
3660
2920




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302227&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302227&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302227&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.168285722245244
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.168285722245244 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302227&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]0.168285722245244[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302227&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302227&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
alpha0.168285722245244
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
229003560-660
333803448.93142331814-68.931423318139
435603437.33124895965122.668751040347
531003457.9746483254-357.9746483254
628003397.73262608647-597.732626086473
727803297.14275939596-517.142759395965
843803210.115016627121169.88498337288
934803406.9899559978973.0100440021129
1032203419.27650398394-199.27650398394
1138403385.74111358449454.258886415505
1245803462.186398371251117.81360162875
1336603650.29846765699.70153234309964
1450403651.931097034141388.06890296586
1543203885.52327489592434.476725104083
1642403958.63950437881281.360495621194
1731604005.9884585957-845.988458595698
1844203863.62067982978556.37932017022
1932803957.25137556694-677.251375566943
2050403843.279638688081196.72036131192
2155804044.670589017041535.32941098296
2249204303.04460782867616.955392171326
2352004406.86939159332793.130608406676
2441404540.34194886385-400.341948863851
2543604472.97011485423-112.970114854229
2643604453.95885748386-93.9588574838572
2744804438.1469232908541.8530767091515
2841404445.19019853303-305.190198533033
2926204393.83104555073-1773.83104555073
3042404095.32060690919144.679393090808
3139204119.66808306948-199.668083069482
3241804086.0667955008193.9332044991888
3381404101.874412662774038.12558733723
3480604781.433293644813278.56670635519
3567805333.169259753011446.83074024699
3651805576.65021584209-396.650215842094
3748205509.89964779037-689.899647790375
3836005393.79938728523-1793.79938728523
3964805091.928561832861388.07143816714
4055005325.52116633281174.478833667186
4140805354.883462873-1274.883462873
4238005140.3387785449-1340.3387785449
4345604914.77889914416-354.778899144165
4471404855.074675864322284.92532413568
4547405239.59498431294-499.594984312938
4658205155.52028154773664.479718452266
4768005267.342730884791532.65726911521
4847205525.26706637227-805.267066372267
4962205389.7521165075830.247883492499
5034205529.47098122362-2109.47098122362
5176005174.477133593022425.52286640698
5225405582.65800098867-3042.65800098867
5342205070.62210174702-850.622101747024
5454204927.47454699676492.525453003242
5520405010.35954857957-2970.35954857957
5644804510.4904466188-30.4904466188045
5753404505.35933978798834.640660212021
5847204645.8174461070174.1825538929934
5942204658.30131076689-438.301310766886
6036804584.54145812344-904.541458123444
6149404432.32004554237507.679954457626
6224604517.75533334771-2057.75533334771
6339004171.46449087129-271.464490871286
6451604125.780892961071034.21910703893
6525004299.82520234895-1799.82520234895
6635603996.94031825647-436.940318256466
6733403923.40950122061-583.40950122061
6863803825.230011942962554.76998805704
6929004255.16132455361-1355.16132455361
7079404027.107022292293912.89297770771
7146404685.59104311417-45.5910431141729
7230004677.91872149579-1677.91872149579
7355004395.548957580051104.45104241995
7440004581.41229893821-581.412298938208
7533404483.56891028912-1143.56891028912
7622204291.12259028391-2071.12259028391
7720603942.58222931954-1882.58222931954
7835203625.77051917244-105.770519172442
7925603607.97085096125-1047.97085096125
8021003431.61231941528-1331.61231941528
8137203207.52097849181512.479021508188
8246003293.763880761851306.23611923815
8328003513.58476951067-713.584769510669
8427203393.49864119036-673.49864119036
8529203280.15843592645-360.15843592645
8629403219.54891341385-279.54891341385
8729003172.50482261713-272.504822617127
8821403126.64615172769-986.646151727692
8920202960.60769148371-940.607691483707
9030402802.31684677294237.68315322706
9139002842.315527879281057.68447212072
9220203020.3087231777-1000.3087231777
9332802851.97104722952428.028952770479
9430402924.00220868838115.997791311624
9530602943.52298077811116.477019221894
9623602963.12440008284-603.124400082836
9731202861.62717481117258.372825188834
9839002905.10763230661994.892367693386
9919603072.53381296018-1112.53381296018
10027602885.31025672392-125.310256723918
10117602864.2223296664-1104.2223296664
10225202678.39747739916-158.397477399161
10321602651.74144351322-491.741443513219
10429802568.98837953368411.011620466322
10528002638.15576693504161.844233064959
10637002665.391840587611034.60815941239
10736602839.50162193514820.498378064858
10829202977.57978408884-57.5797840888381

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2900 & 3560 & -660 \tabularnewline
3 & 3380 & 3448.93142331814 & -68.931423318139 \tabularnewline
4 & 3560 & 3437.33124895965 & 122.668751040347 \tabularnewline
5 & 3100 & 3457.9746483254 & -357.9746483254 \tabularnewline
6 & 2800 & 3397.73262608647 & -597.732626086473 \tabularnewline
7 & 2780 & 3297.14275939596 & -517.142759395965 \tabularnewline
8 & 4380 & 3210.11501662712 & 1169.88498337288 \tabularnewline
9 & 3480 & 3406.98995599789 & 73.0100440021129 \tabularnewline
10 & 3220 & 3419.27650398394 & -199.27650398394 \tabularnewline
11 & 3840 & 3385.74111358449 & 454.258886415505 \tabularnewline
12 & 4580 & 3462.18639837125 & 1117.81360162875 \tabularnewline
13 & 3660 & 3650.2984676569 & 9.70153234309964 \tabularnewline
14 & 5040 & 3651.93109703414 & 1388.06890296586 \tabularnewline
15 & 4320 & 3885.52327489592 & 434.476725104083 \tabularnewline
16 & 4240 & 3958.63950437881 & 281.360495621194 \tabularnewline
17 & 3160 & 4005.9884585957 & -845.988458595698 \tabularnewline
18 & 4420 & 3863.62067982978 & 556.37932017022 \tabularnewline
19 & 3280 & 3957.25137556694 & -677.251375566943 \tabularnewline
20 & 5040 & 3843.27963868808 & 1196.72036131192 \tabularnewline
21 & 5580 & 4044.67058901704 & 1535.32941098296 \tabularnewline
22 & 4920 & 4303.04460782867 & 616.955392171326 \tabularnewline
23 & 5200 & 4406.86939159332 & 793.130608406676 \tabularnewline
24 & 4140 & 4540.34194886385 & -400.341948863851 \tabularnewline
25 & 4360 & 4472.97011485423 & -112.970114854229 \tabularnewline
26 & 4360 & 4453.95885748386 & -93.9588574838572 \tabularnewline
27 & 4480 & 4438.14692329085 & 41.8530767091515 \tabularnewline
28 & 4140 & 4445.19019853303 & -305.190198533033 \tabularnewline
29 & 2620 & 4393.83104555073 & -1773.83104555073 \tabularnewline
30 & 4240 & 4095.32060690919 & 144.679393090808 \tabularnewline
31 & 3920 & 4119.66808306948 & -199.668083069482 \tabularnewline
32 & 4180 & 4086.06679550081 & 93.9332044991888 \tabularnewline
33 & 8140 & 4101.87441266277 & 4038.12558733723 \tabularnewline
34 & 8060 & 4781.43329364481 & 3278.56670635519 \tabularnewline
35 & 6780 & 5333.16925975301 & 1446.83074024699 \tabularnewline
36 & 5180 & 5576.65021584209 & -396.650215842094 \tabularnewline
37 & 4820 & 5509.89964779037 & -689.899647790375 \tabularnewline
38 & 3600 & 5393.79938728523 & -1793.79938728523 \tabularnewline
39 & 6480 & 5091.92856183286 & 1388.07143816714 \tabularnewline
40 & 5500 & 5325.52116633281 & 174.478833667186 \tabularnewline
41 & 4080 & 5354.883462873 & -1274.883462873 \tabularnewline
42 & 3800 & 5140.3387785449 & -1340.3387785449 \tabularnewline
43 & 4560 & 4914.77889914416 & -354.778899144165 \tabularnewline
44 & 7140 & 4855.07467586432 & 2284.92532413568 \tabularnewline
45 & 4740 & 5239.59498431294 & -499.594984312938 \tabularnewline
46 & 5820 & 5155.52028154773 & 664.479718452266 \tabularnewline
47 & 6800 & 5267.34273088479 & 1532.65726911521 \tabularnewline
48 & 4720 & 5525.26706637227 & -805.267066372267 \tabularnewline
49 & 6220 & 5389.7521165075 & 830.247883492499 \tabularnewline
50 & 3420 & 5529.47098122362 & -2109.47098122362 \tabularnewline
51 & 7600 & 5174.47713359302 & 2425.52286640698 \tabularnewline
52 & 2540 & 5582.65800098867 & -3042.65800098867 \tabularnewline
53 & 4220 & 5070.62210174702 & -850.622101747024 \tabularnewline
54 & 5420 & 4927.47454699676 & 492.525453003242 \tabularnewline
55 & 2040 & 5010.35954857957 & -2970.35954857957 \tabularnewline
56 & 4480 & 4510.4904466188 & -30.4904466188045 \tabularnewline
57 & 5340 & 4505.35933978798 & 834.640660212021 \tabularnewline
58 & 4720 & 4645.81744610701 & 74.1825538929934 \tabularnewline
59 & 4220 & 4658.30131076689 & -438.301310766886 \tabularnewline
60 & 3680 & 4584.54145812344 & -904.541458123444 \tabularnewline
61 & 4940 & 4432.32004554237 & 507.679954457626 \tabularnewline
62 & 2460 & 4517.75533334771 & -2057.75533334771 \tabularnewline
63 & 3900 & 4171.46449087129 & -271.464490871286 \tabularnewline
64 & 5160 & 4125.78089296107 & 1034.21910703893 \tabularnewline
65 & 2500 & 4299.82520234895 & -1799.82520234895 \tabularnewline
66 & 3560 & 3996.94031825647 & -436.940318256466 \tabularnewline
67 & 3340 & 3923.40950122061 & -583.40950122061 \tabularnewline
68 & 6380 & 3825.23001194296 & 2554.76998805704 \tabularnewline
69 & 2900 & 4255.16132455361 & -1355.16132455361 \tabularnewline
70 & 7940 & 4027.10702229229 & 3912.89297770771 \tabularnewline
71 & 4640 & 4685.59104311417 & -45.5910431141729 \tabularnewline
72 & 3000 & 4677.91872149579 & -1677.91872149579 \tabularnewline
73 & 5500 & 4395.54895758005 & 1104.45104241995 \tabularnewline
74 & 4000 & 4581.41229893821 & -581.412298938208 \tabularnewline
75 & 3340 & 4483.56891028912 & -1143.56891028912 \tabularnewline
76 & 2220 & 4291.12259028391 & -2071.12259028391 \tabularnewline
77 & 2060 & 3942.58222931954 & -1882.58222931954 \tabularnewline
78 & 3520 & 3625.77051917244 & -105.770519172442 \tabularnewline
79 & 2560 & 3607.97085096125 & -1047.97085096125 \tabularnewline
80 & 2100 & 3431.61231941528 & -1331.61231941528 \tabularnewline
81 & 3720 & 3207.52097849181 & 512.479021508188 \tabularnewline
82 & 4600 & 3293.76388076185 & 1306.23611923815 \tabularnewline
83 & 2800 & 3513.58476951067 & -713.584769510669 \tabularnewline
84 & 2720 & 3393.49864119036 & -673.49864119036 \tabularnewline
85 & 2920 & 3280.15843592645 & -360.15843592645 \tabularnewline
86 & 2940 & 3219.54891341385 & -279.54891341385 \tabularnewline
87 & 2900 & 3172.50482261713 & -272.504822617127 \tabularnewline
88 & 2140 & 3126.64615172769 & -986.646151727692 \tabularnewline
89 & 2020 & 2960.60769148371 & -940.607691483707 \tabularnewline
90 & 3040 & 2802.31684677294 & 237.68315322706 \tabularnewline
91 & 3900 & 2842.31552787928 & 1057.68447212072 \tabularnewline
92 & 2020 & 3020.3087231777 & -1000.3087231777 \tabularnewline
93 & 3280 & 2851.97104722952 & 428.028952770479 \tabularnewline
94 & 3040 & 2924.00220868838 & 115.997791311624 \tabularnewline
95 & 3060 & 2943.52298077811 & 116.477019221894 \tabularnewline
96 & 2360 & 2963.12440008284 & -603.124400082836 \tabularnewline
97 & 3120 & 2861.62717481117 & 258.372825188834 \tabularnewline
98 & 3900 & 2905.10763230661 & 994.892367693386 \tabularnewline
99 & 1960 & 3072.53381296018 & -1112.53381296018 \tabularnewline
100 & 2760 & 2885.31025672392 & -125.310256723918 \tabularnewline
101 & 1760 & 2864.2223296664 & -1104.2223296664 \tabularnewline
102 & 2520 & 2678.39747739916 & -158.397477399161 \tabularnewline
103 & 2160 & 2651.74144351322 & -491.741443513219 \tabularnewline
104 & 2980 & 2568.98837953368 & 411.011620466322 \tabularnewline
105 & 2800 & 2638.15576693504 & 161.844233064959 \tabularnewline
106 & 3700 & 2665.39184058761 & 1034.60815941239 \tabularnewline
107 & 3660 & 2839.50162193514 & 820.498378064858 \tabularnewline
108 & 2920 & 2977.57978408884 & -57.5797840888381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302227&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]2[/C][C]2900[/C][C]3560[/C][C]-660[/C][/ROW]
[ROW][C]3[/C][C]3380[/C][C]3448.93142331814[/C][C]-68.931423318139[/C][/ROW]
[ROW][C]4[/C][C]3560[/C][C]3437.33124895965[/C][C]122.668751040347[/C][/ROW]
[ROW][C]5[/C][C]3100[/C][C]3457.9746483254[/C][C]-357.9746483254[/C][/ROW]
[ROW][C]6[/C][C]2800[/C][C]3397.73262608647[/C][C]-597.732626086473[/C][/ROW]
[ROW][C]7[/C][C]2780[/C][C]3297.14275939596[/C][C]-517.142759395965[/C][/ROW]
[ROW][C]8[/C][C]4380[/C][C]3210.11501662712[/C][C]1169.88498337288[/C][/ROW]
[ROW][C]9[/C][C]3480[/C][C]3406.98995599789[/C][C]73.0100440021129[/C][/ROW]
[ROW][C]10[/C][C]3220[/C][C]3419.27650398394[/C][C]-199.27650398394[/C][/ROW]
[ROW][C]11[/C][C]3840[/C][C]3385.74111358449[/C][C]454.258886415505[/C][/ROW]
[ROW][C]12[/C][C]4580[/C][C]3462.18639837125[/C][C]1117.81360162875[/C][/ROW]
[ROW][C]13[/C][C]3660[/C][C]3650.2984676569[/C][C]9.70153234309964[/C][/ROW]
[ROW][C]14[/C][C]5040[/C][C]3651.93109703414[/C][C]1388.06890296586[/C][/ROW]
[ROW][C]15[/C][C]4320[/C][C]3885.52327489592[/C][C]434.476725104083[/C][/ROW]
[ROW][C]16[/C][C]4240[/C][C]3958.63950437881[/C][C]281.360495621194[/C][/ROW]
[ROW][C]17[/C][C]3160[/C][C]4005.9884585957[/C][C]-845.988458595698[/C][/ROW]
[ROW][C]18[/C][C]4420[/C][C]3863.62067982978[/C][C]556.37932017022[/C][/ROW]
[ROW][C]19[/C][C]3280[/C][C]3957.25137556694[/C][C]-677.251375566943[/C][/ROW]
[ROW][C]20[/C][C]5040[/C][C]3843.27963868808[/C][C]1196.72036131192[/C][/ROW]
[ROW][C]21[/C][C]5580[/C][C]4044.67058901704[/C][C]1535.32941098296[/C][/ROW]
[ROW][C]22[/C][C]4920[/C][C]4303.04460782867[/C][C]616.955392171326[/C][/ROW]
[ROW][C]23[/C][C]5200[/C][C]4406.86939159332[/C][C]793.130608406676[/C][/ROW]
[ROW][C]24[/C][C]4140[/C][C]4540.34194886385[/C][C]-400.341948863851[/C][/ROW]
[ROW][C]25[/C][C]4360[/C][C]4472.97011485423[/C][C]-112.970114854229[/C][/ROW]
[ROW][C]26[/C][C]4360[/C][C]4453.95885748386[/C][C]-93.9588574838572[/C][/ROW]
[ROW][C]27[/C][C]4480[/C][C]4438.14692329085[/C][C]41.8530767091515[/C][/ROW]
[ROW][C]28[/C][C]4140[/C][C]4445.19019853303[/C][C]-305.190198533033[/C][/ROW]
[ROW][C]29[/C][C]2620[/C][C]4393.83104555073[/C][C]-1773.83104555073[/C][/ROW]
[ROW][C]30[/C][C]4240[/C][C]4095.32060690919[/C][C]144.679393090808[/C][/ROW]
[ROW][C]31[/C][C]3920[/C][C]4119.66808306948[/C][C]-199.668083069482[/C][/ROW]
[ROW][C]32[/C][C]4180[/C][C]4086.06679550081[/C][C]93.9332044991888[/C][/ROW]
[ROW][C]33[/C][C]8140[/C][C]4101.87441266277[/C][C]4038.12558733723[/C][/ROW]
[ROW][C]34[/C][C]8060[/C][C]4781.43329364481[/C][C]3278.56670635519[/C][/ROW]
[ROW][C]35[/C][C]6780[/C][C]5333.16925975301[/C][C]1446.83074024699[/C][/ROW]
[ROW][C]36[/C][C]5180[/C][C]5576.65021584209[/C][C]-396.650215842094[/C][/ROW]
[ROW][C]37[/C][C]4820[/C][C]5509.89964779037[/C][C]-689.899647790375[/C][/ROW]
[ROW][C]38[/C][C]3600[/C][C]5393.79938728523[/C][C]-1793.79938728523[/C][/ROW]
[ROW][C]39[/C][C]6480[/C][C]5091.92856183286[/C][C]1388.07143816714[/C][/ROW]
[ROW][C]40[/C][C]5500[/C][C]5325.52116633281[/C][C]174.478833667186[/C][/ROW]
[ROW][C]41[/C][C]4080[/C][C]5354.883462873[/C][C]-1274.883462873[/C][/ROW]
[ROW][C]42[/C][C]3800[/C][C]5140.3387785449[/C][C]-1340.3387785449[/C][/ROW]
[ROW][C]43[/C][C]4560[/C][C]4914.77889914416[/C][C]-354.778899144165[/C][/ROW]
[ROW][C]44[/C][C]7140[/C][C]4855.07467586432[/C][C]2284.92532413568[/C][/ROW]
[ROW][C]45[/C][C]4740[/C][C]5239.59498431294[/C][C]-499.594984312938[/C][/ROW]
[ROW][C]46[/C][C]5820[/C][C]5155.52028154773[/C][C]664.479718452266[/C][/ROW]
[ROW][C]47[/C][C]6800[/C][C]5267.34273088479[/C][C]1532.65726911521[/C][/ROW]
[ROW][C]48[/C][C]4720[/C][C]5525.26706637227[/C][C]-805.267066372267[/C][/ROW]
[ROW][C]49[/C][C]6220[/C][C]5389.7521165075[/C][C]830.247883492499[/C][/ROW]
[ROW][C]50[/C][C]3420[/C][C]5529.47098122362[/C][C]-2109.47098122362[/C][/ROW]
[ROW][C]51[/C][C]7600[/C][C]5174.47713359302[/C][C]2425.52286640698[/C][/ROW]
[ROW][C]52[/C][C]2540[/C][C]5582.65800098867[/C][C]-3042.65800098867[/C][/ROW]
[ROW][C]53[/C][C]4220[/C][C]5070.62210174702[/C][C]-850.622101747024[/C][/ROW]
[ROW][C]54[/C][C]5420[/C][C]4927.47454699676[/C][C]492.525453003242[/C][/ROW]
[ROW][C]55[/C][C]2040[/C][C]5010.35954857957[/C][C]-2970.35954857957[/C][/ROW]
[ROW][C]56[/C][C]4480[/C][C]4510.4904466188[/C][C]-30.4904466188045[/C][/ROW]
[ROW][C]57[/C][C]5340[/C][C]4505.35933978798[/C][C]834.640660212021[/C][/ROW]
[ROW][C]58[/C][C]4720[/C][C]4645.81744610701[/C][C]74.1825538929934[/C][/ROW]
[ROW][C]59[/C][C]4220[/C][C]4658.30131076689[/C][C]-438.301310766886[/C][/ROW]
[ROW][C]60[/C][C]3680[/C][C]4584.54145812344[/C][C]-904.541458123444[/C][/ROW]
[ROW][C]61[/C][C]4940[/C][C]4432.32004554237[/C][C]507.679954457626[/C][/ROW]
[ROW][C]62[/C][C]2460[/C][C]4517.75533334771[/C][C]-2057.75533334771[/C][/ROW]
[ROW][C]63[/C][C]3900[/C][C]4171.46449087129[/C][C]-271.464490871286[/C][/ROW]
[ROW][C]64[/C][C]5160[/C][C]4125.78089296107[/C][C]1034.21910703893[/C][/ROW]
[ROW][C]65[/C][C]2500[/C][C]4299.82520234895[/C][C]-1799.82520234895[/C][/ROW]
[ROW][C]66[/C][C]3560[/C][C]3996.94031825647[/C][C]-436.940318256466[/C][/ROW]
[ROW][C]67[/C][C]3340[/C][C]3923.40950122061[/C][C]-583.40950122061[/C][/ROW]
[ROW][C]68[/C][C]6380[/C][C]3825.23001194296[/C][C]2554.76998805704[/C][/ROW]
[ROW][C]69[/C][C]2900[/C][C]4255.16132455361[/C][C]-1355.16132455361[/C][/ROW]
[ROW][C]70[/C][C]7940[/C][C]4027.10702229229[/C][C]3912.89297770771[/C][/ROW]
[ROW][C]71[/C][C]4640[/C][C]4685.59104311417[/C][C]-45.5910431141729[/C][/ROW]
[ROW][C]72[/C][C]3000[/C][C]4677.91872149579[/C][C]-1677.91872149579[/C][/ROW]
[ROW][C]73[/C][C]5500[/C][C]4395.54895758005[/C][C]1104.45104241995[/C][/ROW]
[ROW][C]74[/C][C]4000[/C][C]4581.41229893821[/C][C]-581.412298938208[/C][/ROW]
[ROW][C]75[/C][C]3340[/C][C]4483.56891028912[/C][C]-1143.56891028912[/C][/ROW]
[ROW][C]76[/C][C]2220[/C][C]4291.12259028391[/C][C]-2071.12259028391[/C][/ROW]
[ROW][C]77[/C][C]2060[/C][C]3942.58222931954[/C][C]-1882.58222931954[/C][/ROW]
[ROW][C]78[/C][C]3520[/C][C]3625.77051917244[/C][C]-105.770519172442[/C][/ROW]
[ROW][C]79[/C][C]2560[/C][C]3607.97085096125[/C][C]-1047.97085096125[/C][/ROW]
[ROW][C]80[/C][C]2100[/C][C]3431.61231941528[/C][C]-1331.61231941528[/C][/ROW]
[ROW][C]81[/C][C]3720[/C][C]3207.52097849181[/C][C]512.479021508188[/C][/ROW]
[ROW][C]82[/C][C]4600[/C][C]3293.76388076185[/C][C]1306.23611923815[/C][/ROW]
[ROW][C]83[/C][C]2800[/C][C]3513.58476951067[/C][C]-713.584769510669[/C][/ROW]
[ROW][C]84[/C][C]2720[/C][C]3393.49864119036[/C][C]-673.49864119036[/C][/ROW]
[ROW][C]85[/C][C]2920[/C][C]3280.15843592645[/C][C]-360.15843592645[/C][/ROW]
[ROW][C]86[/C][C]2940[/C][C]3219.54891341385[/C][C]-279.54891341385[/C][/ROW]
[ROW][C]87[/C][C]2900[/C][C]3172.50482261713[/C][C]-272.504822617127[/C][/ROW]
[ROW][C]88[/C][C]2140[/C][C]3126.64615172769[/C][C]-986.646151727692[/C][/ROW]
[ROW][C]89[/C][C]2020[/C][C]2960.60769148371[/C][C]-940.607691483707[/C][/ROW]
[ROW][C]90[/C][C]3040[/C][C]2802.31684677294[/C][C]237.68315322706[/C][/ROW]
[ROW][C]91[/C][C]3900[/C][C]2842.31552787928[/C][C]1057.68447212072[/C][/ROW]
[ROW][C]92[/C][C]2020[/C][C]3020.3087231777[/C][C]-1000.3087231777[/C][/ROW]
[ROW][C]93[/C][C]3280[/C][C]2851.97104722952[/C][C]428.028952770479[/C][/ROW]
[ROW][C]94[/C][C]3040[/C][C]2924.00220868838[/C][C]115.997791311624[/C][/ROW]
[ROW][C]95[/C][C]3060[/C][C]2943.52298077811[/C][C]116.477019221894[/C][/ROW]
[ROW][C]96[/C][C]2360[/C][C]2963.12440008284[/C][C]-603.124400082836[/C][/ROW]
[ROW][C]97[/C][C]3120[/C][C]2861.62717481117[/C][C]258.372825188834[/C][/ROW]
[ROW][C]98[/C][C]3900[/C][C]2905.10763230661[/C][C]994.892367693386[/C][/ROW]
[ROW][C]99[/C][C]1960[/C][C]3072.53381296018[/C][C]-1112.53381296018[/C][/ROW]
[ROW][C]100[/C][C]2760[/C][C]2885.31025672392[/C][C]-125.310256723918[/C][/ROW]
[ROW][C]101[/C][C]1760[/C][C]2864.2223296664[/C][C]-1104.2223296664[/C][/ROW]
[ROW][C]102[/C][C]2520[/C][C]2678.39747739916[/C][C]-158.397477399161[/C][/ROW]
[ROW][C]103[/C][C]2160[/C][C]2651.74144351322[/C][C]-491.741443513219[/C][/ROW]
[ROW][C]104[/C][C]2980[/C][C]2568.98837953368[/C][C]411.011620466322[/C][/ROW]
[ROW][C]105[/C][C]2800[/C][C]2638.15576693504[/C][C]161.844233064959[/C][/ROW]
[ROW][C]106[/C][C]3700[/C][C]2665.39184058761[/C][C]1034.60815941239[/C][/ROW]
[ROW][C]107[/C][C]3660[/C][C]2839.50162193514[/C][C]820.498378064858[/C][/ROW]
[ROW][C]108[/C][C]2920[/C][C]2977.57978408884[/C][C]-57.5797840888381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302227&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302227&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
229003560-660
333803448.93142331814-68.931423318139
435603437.33124895965122.668751040347
531003457.9746483254-357.9746483254
628003397.73262608647-597.732626086473
727803297.14275939596-517.142759395965
843803210.115016627121169.88498337288
934803406.9899559978973.0100440021129
1032203419.27650398394-199.27650398394
1138403385.74111358449454.258886415505
1245803462.186398371251117.81360162875
1336603650.29846765699.70153234309964
1450403651.931097034141388.06890296586
1543203885.52327489592434.476725104083
1642403958.63950437881281.360495621194
1731604005.9884585957-845.988458595698
1844203863.62067982978556.37932017022
1932803957.25137556694-677.251375566943
2050403843.279638688081196.72036131192
2155804044.670589017041535.32941098296
2249204303.04460782867616.955392171326
2352004406.86939159332793.130608406676
2441404540.34194886385-400.341948863851
2543604472.97011485423-112.970114854229
2643604453.95885748386-93.9588574838572
2744804438.1469232908541.8530767091515
2841404445.19019853303-305.190198533033
2926204393.83104555073-1773.83104555073
3042404095.32060690919144.679393090808
3139204119.66808306948-199.668083069482
3241804086.0667955008193.9332044991888
3381404101.874412662774038.12558733723
3480604781.433293644813278.56670635519
3567805333.169259753011446.83074024699
3651805576.65021584209-396.650215842094
3748205509.89964779037-689.899647790375
3836005393.79938728523-1793.79938728523
3964805091.928561832861388.07143816714
4055005325.52116633281174.478833667186
4140805354.883462873-1274.883462873
4238005140.3387785449-1340.3387785449
4345604914.77889914416-354.778899144165
4471404855.074675864322284.92532413568
4547405239.59498431294-499.594984312938
4658205155.52028154773664.479718452266
4768005267.342730884791532.65726911521
4847205525.26706637227-805.267066372267
4962205389.7521165075830.247883492499
5034205529.47098122362-2109.47098122362
5176005174.477133593022425.52286640698
5225405582.65800098867-3042.65800098867
5342205070.62210174702-850.622101747024
5454204927.47454699676492.525453003242
5520405010.35954857957-2970.35954857957
5644804510.4904466188-30.4904466188045
5753404505.35933978798834.640660212021
5847204645.8174461070174.1825538929934
5942204658.30131076689-438.301310766886
6036804584.54145812344-904.541458123444
6149404432.32004554237507.679954457626
6224604517.75533334771-2057.75533334771
6339004171.46449087129-271.464490871286
6451604125.780892961071034.21910703893
6525004299.82520234895-1799.82520234895
6635603996.94031825647-436.940318256466
6733403923.40950122061-583.40950122061
6863803825.230011942962554.76998805704
6929004255.16132455361-1355.16132455361
7079404027.107022292293912.89297770771
7146404685.59104311417-45.5910431141729
7230004677.91872149579-1677.91872149579
7355004395.548957580051104.45104241995
7440004581.41229893821-581.412298938208
7533404483.56891028912-1143.56891028912
7622204291.12259028391-2071.12259028391
7720603942.58222931954-1882.58222931954
7835203625.77051917244-105.770519172442
7925603607.97085096125-1047.97085096125
8021003431.61231941528-1331.61231941528
8137203207.52097849181512.479021508188
8246003293.763880761851306.23611923815
8328003513.58476951067-713.584769510669
8427203393.49864119036-673.49864119036
8529203280.15843592645-360.15843592645
8629403219.54891341385-279.54891341385
8729003172.50482261713-272.504822617127
8821403126.64615172769-986.646151727692
8920202960.60769148371-940.607691483707
9030402802.31684677294237.68315322706
9139002842.315527879281057.68447212072
9220203020.3087231777-1000.3087231777
9332802851.97104722952428.028952770479
9430402924.00220868838115.997791311624
9530602943.52298077811116.477019221894
9623602963.12440008284-603.124400082836
9731202861.62717481117258.372825188834
9839002905.10763230661994.892367693386
9919603072.53381296018-1112.53381296018
10027602885.31025672392-125.310256723918
10117602864.2223296664-1104.2223296664
10225202678.39747739916-158.397477399161
10321602651.74144351322-491.741443513219
10429802568.98837953368411.011620466322
10528002638.15576693504161.844233064959
10637002665.391840587611034.60815941239
10736602839.50162193514820.498378064858
10829202977.57978408884-57.5797840888381







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092967.88992853672573.7143707476365362.06548632581
1102967.88992853672540.0494283905235395.73042868292
1112967.88992853672506.844949917765428.93490715569
1122967.88992853672474.0825423456645461.69731472778
1132967.88992853672441.745005525275494.03485154817
1142967.88992853672409.8162265703385525.96363050311
1152967.88992853672378.2810860032665557.49877107018
1162967.88992853672347.1253740673725588.65448300607
1172967.88992853672316.3357158911655619.44414118228
1182967.88992853672285.899504386435649.88035268701
1192967.88992853672255.8048399251345679.97501714831
1202967.88992853672226.04047597655709.73938109695

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2967.88992853672 & 573.714370747636 & 5362.06548632581 \tabularnewline
110 & 2967.88992853672 & 540.049428390523 & 5395.73042868292 \tabularnewline
111 & 2967.88992853672 & 506.84494991776 & 5428.93490715569 \tabularnewline
112 & 2967.88992853672 & 474.082542345664 & 5461.69731472778 \tabularnewline
113 & 2967.88992853672 & 441.74500552527 & 5494.03485154817 \tabularnewline
114 & 2967.88992853672 & 409.816226570338 & 5525.96363050311 \tabularnewline
115 & 2967.88992853672 & 378.281086003266 & 5557.49877107018 \tabularnewline
116 & 2967.88992853672 & 347.125374067372 & 5588.65448300607 \tabularnewline
117 & 2967.88992853672 & 316.335715891165 & 5619.44414118228 \tabularnewline
118 & 2967.88992853672 & 285.89950438643 & 5649.88035268701 \tabularnewline
119 & 2967.88992853672 & 255.804839925134 & 5679.97501714831 \tabularnewline
120 & 2967.88992853672 & 226.0404759765 & 5709.73938109695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302227&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]109[/C][C]2967.88992853672[/C][C]573.714370747636[/C][C]5362.06548632581[/C][/ROW]
[ROW][C]110[/C][C]2967.88992853672[/C][C]540.049428390523[/C][C]5395.73042868292[/C][/ROW]
[ROW][C]111[/C][C]2967.88992853672[/C][C]506.84494991776[/C][C]5428.93490715569[/C][/ROW]
[ROW][C]112[/C][C]2967.88992853672[/C][C]474.082542345664[/C][C]5461.69731472778[/C][/ROW]
[ROW][C]113[/C][C]2967.88992853672[/C][C]441.74500552527[/C][C]5494.03485154817[/C][/ROW]
[ROW][C]114[/C][C]2967.88992853672[/C][C]409.816226570338[/C][C]5525.96363050311[/C][/ROW]
[ROW][C]115[/C][C]2967.88992853672[/C][C]378.281086003266[/C][C]5557.49877107018[/C][/ROW]
[ROW][C]116[/C][C]2967.88992853672[/C][C]347.125374067372[/C][C]5588.65448300607[/C][/ROW]
[ROW][C]117[/C][C]2967.88992853672[/C][C]316.335715891165[/C][C]5619.44414118228[/C][/ROW]
[ROW][C]118[/C][C]2967.88992853672[/C][C]285.89950438643[/C][C]5649.88035268701[/C][/ROW]
[ROW][C]119[/C][C]2967.88992853672[/C][C]255.804839925134[/C][C]5679.97501714831[/C][/ROW]
[ROW][C]120[/C][C]2967.88992853672[/C][C]226.0404759765[/C][C]5709.73938109695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302227&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302227&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
1092967.88992853672573.7143707476365362.06548632581
1102967.88992853672540.0494283905235395.73042868292
1112967.88992853672506.844949917765428.93490715569
1122967.88992853672474.0825423456645461.69731472778
1132967.88992853672441.745005525275494.03485154817
1142967.88992853672409.8162265703385525.96363050311
1152967.88992853672378.2810860032665557.49877107018
1162967.88992853672347.1253740673725588.65448300607
1172967.88992853672316.3357158911655619.44414118228
1182967.88992853672285.899504386435649.88035268701
1192967.88992853672255.8048399251345679.97501714831
1202967.88992853672226.04047597655709.73938109695



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')