Free Statistics

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 computationWed, 07 Dec 2016 14:05:32 +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/07/t1481115961yjzjtss0muedkq0.htm/, Retrieved Tue, 07 May 2024 13:07:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298081, Retrieved Tue, 07 May 2024 13:07:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-07 13:05:32] [c3c00422a8efeb721f46880d0369ae73] [Current]
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Dataseries X:
2700
3900
3850
3800
3800
3700
3950
3950
4150
4050
4200
3850
2950
4050
4200
4050
4100
4000
4100
4100
4300
4250
4300
3700
2900
4150
4300
4000
4100
4050
4100
4150
4200
4350
4450
3900
3100
4500
4450
4300
4350
4200
4250
4350
4550
4600
4700
4000
3200
4550
4700
4500
4550
4450
4550
4600
4850
4950
5050
4250
3550
5000
5000
4750
4750
4800
4900
4950
5100
5150
5150
4550
3700
5350
5200
5100
5050
4950
4950
4900
5200
5300
5500
4750
3950
5400
5300
5200
5100
5250
5200
5250
5500
5550
5600
4800
3700
4800
5400
5200
5250
5150
5100
5300
5650
5700
5800
5150
4100
5700
5900
5500
5800
5450
5950
6100
6400
6100
6150
5500
4500
6400
6150
5800
6150
6050




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=298081&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=298081&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298081&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
alpha0.383065219482735
beta0
gamma0.292386202823828

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.383065219482735 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.292386202823828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298081&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]0.383065219482735[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.292386202823828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298081&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298081&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
alpha0.383065219482735
beta0
gamma0.292386202823828







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329502847.24171596798102.75828403202
1440503968.2890300467581.7109699532534
1542004153.1065305034646.8934694965419
1640504025.1127915326824.8872084673162
1741004089.5665114153710.4334885846306
1840004013.18790122027-13.1879012202653
1941004160.90915146583-60.909151465833
2041004137.57745714048-37.5774571404772
2143004327.35665838073-27.3566583807269
2242504203.9759897405846.0240102594171
2343004371.07512808762-71.0751280876202
2437003973.66764019305-273.667640193053
2529002982.43192601907-82.4319260190673
2641504045.30608608756104.693913912442
2743004234.8909972744365.1090027255705
2840004106.67435067715-106.674350677145
2941004118.35009815025-18.3500981502548
3040504026.2861105977123.7138894022851
3141004180.40581002149-80.4058100214943
3241504153.71426686846-3.7142668684628
3342004359.93001573768-159.930015737682
3443504199.33000456358150.669995436419
3544504386.0156000885963.9843999114064
3639003994.66394693949-94.6639469394909
3731003074.8682252590325.1317747409676
3845004268.66658278138231.333417218615
3944504507.18465890307-57.1846589030738
4043004290.838868814639.16113118537214
4143504365.91516671231-15.9151667123069
4242004276.54731298066-76.5473129806624
4342504378.93513107075-128.935131070748
4443504347.490748918182.50925108181673
4545504535.1094768801914.8905231198132
4646004493.20262832627106.797371673733
4747004652.8975973143447.1024026856649
4840004200.33867783194-200.338677831939
4932003221.19404495584-21.1940449558351
5045504481.8790247481168.1209752518917
5147004607.7482008634592.2517991365539
5245004453.0958915578946.9041084421124
5345504540.109255179259.89074482075375
5444504444.803644259685.19635574032236
5545504574.04250119412-24.0425011941197
5646004607.91709994049-7.91709994049324
5748504803.7967620831246.2032379168841
5849504787.25606223993162.74393776007
5950504963.3878815930686.6121184069425
6042504444.56864574704-194.568645747036
6135503438.88743397304111.112566026964
6250004873.731354371126.268645629005
6350005033.70258636383-33.7025863638301
6447504805.86299011657-55.862990116565
6547504849.86502709063-99.8650270906346
6648004704.8068626268295.1931373731832
6749004870.114939056729.8850609432975
6849504929.5352339870620.464766012944
6951005159.80365567485-59.8036556748457
7051505121.2607666489228.739233351077
7151505236.4375380942-86.4375380941974
7245504576.37512797561-26.375127975607
7337003642.5583692135657.4416307864385
7453505123.46084685005226.539153149951
7552005296.41901941446-96.4190194144649
7651005028.9654159280471.0345840719574
7750505115.83295635495-65.8329563549496
7849505013.33975228297-63.3397522829728
7949505110.93786767799-160.937867677986
8049005096.49838549262-196.498385492616
8152005232.20026454781-32.2002645478069
8253005219.8594210125180.1405789874925
8355005335.27244198437164.727558015627
8447504756.56170641666-6.56170641666449
8539503806.48486603883143.515133961172
8654005424.81465087121-24.8146508712125
8753005443.40327490056-143.403274900563
8852005182.0004644516817.999535548317
8951005224.21172329046-124.211723290457
9052505097.93309515242152.066904847581
9152005263.17922398626-63.1792239862589
9252505280.22255079994-30.2225507999447
9355005521.8397442649-21.8397442649011
9455505533.7407857346116.2592142653903
9556005643.81291776112-43.8129177611181
9648004929.06145590094-129.061455900943
9737003933.85047430243-233.85047430243
9848005360.46856011467-560.46856011467
9954005152.79366399346247.206336006545
10052005074.3159828593125.684017140704
10152505132.02856482735117.971435172645
10251505147.839956371042.16004362895546
10351005216.44221654288-116.442216542879
10453005218.7012350130681.2987649869438
10556505503.9454773837146.054522616299
10657005587.10848062361112.891519376387
10758005724.5077989054875.4922010945211
10851505022.39865444023127.601345559775
10941004062.3038967455837.6961032544177
11057005633.4740391333366.5259608666711
11159005827.1131664848472.8868335151583
11255005637.06382271576-137.063822715759
11358005591.72081713186208.279182868139
11454505615.07216082741-165.07216082741
11559505600.27857175839349.721428241607
11661005824.01473940762275.985260592384
11764006226.45056941868173.549430581324
11861006314.31729675337-214.317296753367
11961506326.60750305046-176.607503050461
12055005474.1316527500625.8683472499433
12145004379.388247683120.611752316995
12264006116.78230694514283.217693054865
12361506409.24588428776-259.245884287757
12458006033.25790221848-233.257902218477
12561506016.36263501784133.637364982158
12660505934.5513994706115.448600529403

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2950 & 2847.24171596798 & 102.75828403202 \tabularnewline
14 & 4050 & 3968.28903004675 & 81.7109699532534 \tabularnewline
15 & 4200 & 4153.10653050346 & 46.8934694965419 \tabularnewline
16 & 4050 & 4025.11279153268 & 24.8872084673162 \tabularnewline
17 & 4100 & 4089.56651141537 & 10.4334885846306 \tabularnewline
18 & 4000 & 4013.18790122027 & -13.1879012202653 \tabularnewline
19 & 4100 & 4160.90915146583 & -60.909151465833 \tabularnewline
20 & 4100 & 4137.57745714048 & -37.5774571404772 \tabularnewline
21 & 4300 & 4327.35665838073 & -27.3566583807269 \tabularnewline
22 & 4250 & 4203.97598974058 & 46.0240102594171 \tabularnewline
23 & 4300 & 4371.07512808762 & -71.0751280876202 \tabularnewline
24 & 3700 & 3973.66764019305 & -273.667640193053 \tabularnewline
25 & 2900 & 2982.43192601907 & -82.4319260190673 \tabularnewline
26 & 4150 & 4045.30608608756 & 104.693913912442 \tabularnewline
27 & 4300 & 4234.89099727443 & 65.1090027255705 \tabularnewline
28 & 4000 & 4106.67435067715 & -106.674350677145 \tabularnewline
29 & 4100 & 4118.35009815025 & -18.3500981502548 \tabularnewline
30 & 4050 & 4026.28611059771 & 23.7138894022851 \tabularnewline
31 & 4100 & 4180.40581002149 & -80.4058100214943 \tabularnewline
32 & 4150 & 4153.71426686846 & -3.7142668684628 \tabularnewline
33 & 4200 & 4359.93001573768 & -159.930015737682 \tabularnewline
34 & 4350 & 4199.33000456358 & 150.669995436419 \tabularnewline
35 & 4450 & 4386.01560008859 & 63.9843999114064 \tabularnewline
36 & 3900 & 3994.66394693949 & -94.6639469394909 \tabularnewline
37 & 3100 & 3074.86822525903 & 25.1317747409676 \tabularnewline
38 & 4500 & 4268.66658278138 & 231.333417218615 \tabularnewline
39 & 4450 & 4507.18465890307 & -57.1846589030738 \tabularnewline
40 & 4300 & 4290.83886881463 & 9.16113118537214 \tabularnewline
41 & 4350 & 4365.91516671231 & -15.9151667123069 \tabularnewline
42 & 4200 & 4276.54731298066 & -76.5473129806624 \tabularnewline
43 & 4250 & 4378.93513107075 & -128.935131070748 \tabularnewline
44 & 4350 & 4347.49074891818 & 2.50925108181673 \tabularnewline
45 & 4550 & 4535.10947688019 & 14.8905231198132 \tabularnewline
46 & 4600 & 4493.20262832627 & 106.797371673733 \tabularnewline
47 & 4700 & 4652.89759731434 & 47.1024026856649 \tabularnewline
48 & 4000 & 4200.33867783194 & -200.338677831939 \tabularnewline
49 & 3200 & 3221.19404495584 & -21.1940449558351 \tabularnewline
50 & 4550 & 4481.87902474811 & 68.1209752518917 \tabularnewline
51 & 4700 & 4607.74820086345 & 92.2517991365539 \tabularnewline
52 & 4500 & 4453.09589155789 & 46.9041084421124 \tabularnewline
53 & 4550 & 4540.10925517925 & 9.89074482075375 \tabularnewline
54 & 4450 & 4444.80364425968 & 5.19635574032236 \tabularnewline
55 & 4550 & 4574.04250119412 & -24.0425011941197 \tabularnewline
56 & 4600 & 4607.91709994049 & -7.91709994049324 \tabularnewline
57 & 4850 & 4803.79676208312 & 46.2032379168841 \tabularnewline
58 & 4950 & 4787.25606223993 & 162.74393776007 \tabularnewline
59 & 5050 & 4963.38788159306 & 86.6121184069425 \tabularnewline
60 & 4250 & 4444.56864574704 & -194.568645747036 \tabularnewline
61 & 3550 & 3438.88743397304 & 111.112566026964 \tabularnewline
62 & 5000 & 4873.731354371 & 126.268645629005 \tabularnewline
63 & 5000 & 5033.70258636383 & -33.7025863638301 \tabularnewline
64 & 4750 & 4805.86299011657 & -55.862990116565 \tabularnewline
65 & 4750 & 4849.86502709063 & -99.8650270906346 \tabularnewline
66 & 4800 & 4704.80686262682 & 95.1931373731832 \tabularnewline
67 & 4900 & 4870.1149390567 & 29.8850609432975 \tabularnewline
68 & 4950 & 4929.53523398706 & 20.464766012944 \tabularnewline
69 & 5100 & 5159.80365567485 & -59.8036556748457 \tabularnewline
70 & 5150 & 5121.26076664892 & 28.739233351077 \tabularnewline
71 & 5150 & 5236.4375380942 & -86.4375380941974 \tabularnewline
72 & 4550 & 4576.37512797561 & -26.375127975607 \tabularnewline
73 & 3700 & 3642.55836921356 & 57.4416307864385 \tabularnewline
74 & 5350 & 5123.46084685005 & 226.539153149951 \tabularnewline
75 & 5200 & 5296.41901941446 & -96.4190194144649 \tabularnewline
76 & 5100 & 5028.96541592804 & 71.0345840719574 \tabularnewline
77 & 5050 & 5115.83295635495 & -65.8329563549496 \tabularnewline
78 & 4950 & 5013.33975228297 & -63.3397522829728 \tabularnewline
79 & 4950 & 5110.93786767799 & -160.937867677986 \tabularnewline
80 & 4900 & 5096.49838549262 & -196.498385492616 \tabularnewline
81 & 5200 & 5232.20026454781 & -32.2002645478069 \tabularnewline
82 & 5300 & 5219.85942101251 & 80.1405789874925 \tabularnewline
83 & 5500 & 5335.27244198437 & 164.727558015627 \tabularnewline
84 & 4750 & 4756.56170641666 & -6.56170641666449 \tabularnewline
85 & 3950 & 3806.48486603883 & 143.515133961172 \tabularnewline
86 & 5400 & 5424.81465087121 & -24.8146508712125 \tabularnewline
87 & 5300 & 5443.40327490056 & -143.403274900563 \tabularnewline
88 & 5200 & 5182.00046445168 & 17.999535548317 \tabularnewline
89 & 5100 & 5224.21172329046 & -124.211723290457 \tabularnewline
90 & 5250 & 5097.93309515242 & 152.066904847581 \tabularnewline
91 & 5200 & 5263.17922398626 & -63.1792239862589 \tabularnewline
92 & 5250 & 5280.22255079994 & -30.2225507999447 \tabularnewline
93 & 5500 & 5521.8397442649 & -21.8397442649011 \tabularnewline
94 & 5550 & 5533.74078573461 & 16.2592142653903 \tabularnewline
95 & 5600 & 5643.81291776112 & -43.8129177611181 \tabularnewline
96 & 4800 & 4929.06145590094 & -129.061455900943 \tabularnewline
97 & 3700 & 3933.85047430243 & -233.85047430243 \tabularnewline
98 & 4800 & 5360.46856011467 & -560.46856011467 \tabularnewline
99 & 5400 & 5152.79366399346 & 247.206336006545 \tabularnewline
100 & 5200 & 5074.3159828593 & 125.684017140704 \tabularnewline
101 & 5250 & 5132.02856482735 & 117.971435172645 \tabularnewline
102 & 5150 & 5147.83995637104 & 2.16004362895546 \tabularnewline
103 & 5100 & 5216.44221654288 & -116.442216542879 \tabularnewline
104 & 5300 & 5218.70123501306 & 81.2987649869438 \tabularnewline
105 & 5650 & 5503.9454773837 & 146.054522616299 \tabularnewline
106 & 5700 & 5587.10848062361 & 112.891519376387 \tabularnewline
107 & 5800 & 5724.50779890548 & 75.4922010945211 \tabularnewline
108 & 5150 & 5022.39865444023 & 127.601345559775 \tabularnewline
109 & 4100 & 4062.30389674558 & 37.6961032544177 \tabularnewline
110 & 5700 & 5633.47403913333 & 66.5259608666711 \tabularnewline
111 & 5900 & 5827.11316648484 & 72.8868335151583 \tabularnewline
112 & 5500 & 5637.06382271576 & -137.063822715759 \tabularnewline
113 & 5800 & 5591.72081713186 & 208.279182868139 \tabularnewline
114 & 5450 & 5615.07216082741 & -165.07216082741 \tabularnewline
115 & 5950 & 5600.27857175839 & 349.721428241607 \tabularnewline
116 & 6100 & 5824.01473940762 & 275.985260592384 \tabularnewline
117 & 6400 & 6226.45056941868 & 173.549430581324 \tabularnewline
118 & 6100 & 6314.31729675337 & -214.317296753367 \tabularnewline
119 & 6150 & 6326.60750305046 & -176.607503050461 \tabularnewline
120 & 5500 & 5474.13165275006 & 25.8683472499433 \tabularnewline
121 & 4500 & 4379.388247683 & 120.611752316995 \tabularnewline
122 & 6400 & 6116.78230694514 & 283.217693054865 \tabularnewline
123 & 6150 & 6409.24588428776 & -259.245884287757 \tabularnewline
124 & 5800 & 6033.25790221848 & -233.257902218477 \tabularnewline
125 & 6150 & 6016.36263501784 & 133.637364982158 \tabularnewline
126 & 6050 & 5934.5513994706 & 115.448600529403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298081&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]2950[/C][C]2847.24171596798[/C][C]102.75828403202[/C][/ROW]
[ROW][C]14[/C][C]4050[/C][C]3968.28903004675[/C][C]81.7109699532534[/C][/ROW]
[ROW][C]15[/C][C]4200[/C][C]4153.10653050346[/C][C]46.8934694965419[/C][/ROW]
[ROW][C]16[/C][C]4050[/C][C]4025.11279153268[/C][C]24.8872084673162[/C][/ROW]
[ROW][C]17[/C][C]4100[/C][C]4089.56651141537[/C][C]10.4334885846306[/C][/ROW]
[ROW][C]18[/C][C]4000[/C][C]4013.18790122027[/C][C]-13.1879012202653[/C][/ROW]
[ROW][C]19[/C][C]4100[/C][C]4160.90915146583[/C][C]-60.909151465833[/C][/ROW]
[ROW][C]20[/C][C]4100[/C][C]4137.57745714048[/C][C]-37.5774571404772[/C][/ROW]
[ROW][C]21[/C][C]4300[/C][C]4327.35665838073[/C][C]-27.3566583807269[/C][/ROW]
[ROW][C]22[/C][C]4250[/C][C]4203.97598974058[/C][C]46.0240102594171[/C][/ROW]
[ROW][C]23[/C][C]4300[/C][C]4371.07512808762[/C][C]-71.0751280876202[/C][/ROW]
[ROW][C]24[/C][C]3700[/C][C]3973.66764019305[/C][C]-273.667640193053[/C][/ROW]
[ROW][C]25[/C][C]2900[/C][C]2982.43192601907[/C][C]-82.4319260190673[/C][/ROW]
[ROW][C]26[/C][C]4150[/C][C]4045.30608608756[/C][C]104.693913912442[/C][/ROW]
[ROW][C]27[/C][C]4300[/C][C]4234.89099727443[/C][C]65.1090027255705[/C][/ROW]
[ROW][C]28[/C][C]4000[/C][C]4106.67435067715[/C][C]-106.674350677145[/C][/ROW]
[ROW][C]29[/C][C]4100[/C][C]4118.35009815025[/C][C]-18.3500981502548[/C][/ROW]
[ROW][C]30[/C][C]4050[/C][C]4026.28611059771[/C][C]23.7138894022851[/C][/ROW]
[ROW][C]31[/C][C]4100[/C][C]4180.40581002149[/C][C]-80.4058100214943[/C][/ROW]
[ROW][C]32[/C][C]4150[/C][C]4153.71426686846[/C][C]-3.7142668684628[/C][/ROW]
[ROW][C]33[/C][C]4200[/C][C]4359.93001573768[/C][C]-159.930015737682[/C][/ROW]
[ROW][C]34[/C][C]4350[/C][C]4199.33000456358[/C][C]150.669995436419[/C][/ROW]
[ROW][C]35[/C][C]4450[/C][C]4386.01560008859[/C][C]63.9843999114064[/C][/ROW]
[ROW][C]36[/C][C]3900[/C][C]3994.66394693949[/C][C]-94.6639469394909[/C][/ROW]
[ROW][C]37[/C][C]3100[/C][C]3074.86822525903[/C][C]25.1317747409676[/C][/ROW]
[ROW][C]38[/C][C]4500[/C][C]4268.66658278138[/C][C]231.333417218615[/C][/ROW]
[ROW][C]39[/C][C]4450[/C][C]4507.18465890307[/C][C]-57.1846589030738[/C][/ROW]
[ROW][C]40[/C][C]4300[/C][C]4290.83886881463[/C][C]9.16113118537214[/C][/ROW]
[ROW][C]41[/C][C]4350[/C][C]4365.91516671231[/C][C]-15.9151667123069[/C][/ROW]
[ROW][C]42[/C][C]4200[/C][C]4276.54731298066[/C][C]-76.5473129806624[/C][/ROW]
[ROW][C]43[/C][C]4250[/C][C]4378.93513107075[/C][C]-128.935131070748[/C][/ROW]
[ROW][C]44[/C][C]4350[/C][C]4347.49074891818[/C][C]2.50925108181673[/C][/ROW]
[ROW][C]45[/C][C]4550[/C][C]4535.10947688019[/C][C]14.8905231198132[/C][/ROW]
[ROW][C]46[/C][C]4600[/C][C]4493.20262832627[/C][C]106.797371673733[/C][/ROW]
[ROW][C]47[/C][C]4700[/C][C]4652.89759731434[/C][C]47.1024026856649[/C][/ROW]
[ROW][C]48[/C][C]4000[/C][C]4200.33867783194[/C][C]-200.338677831939[/C][/ROW]
[ROW][C]49[/C][C]3200[/C][C]3221.19404495584[/C][C]-21.1940449558351[/C][/ROW]
[ROW][C]50[/C][C]4550[/C][C]4481.87902474811[/C][C]68.1209752518917[/C][/ROW]
[ROW][C]51[/C][C]4700[/C][C]4607.74820086345[/C][C]92.2517991365539[/C][/ROW]
[ROW][C]52[/C][C]4500[/C][C]4453.09589155789[/C][C]46.9041084421124[/C][/ROW]
[ROW][C]53[/C][C]4550[/C][C]4540.10925517925[/C][C]9.89074482075375[/C][/ROW]
[ROW][C]54[/C][C]4450[/C][C]4444.80364425968[/C][C]5.19635574032236[/C][/ROW]
[ROW][C]55[/C][C]4550[/C][C]4574.04250119412[/C][C]-24.0425011941197[/C][/ROW]
[ROW][C]56[/C][C]4600[/C][C]4607.91709994049[/C][C]-7.91709994049324[/C][/ROW]
[ROW][C]57[/C][C]4850[/C][C]4803.79676208312[/C][C]46.2032379168841[/C][/ROW]
[ROW][C]58[/C][C]4950[/C][C]4787.25606223993[/C][C]162.74393776007[/C][/ROW]
[ROW][C]59[/C][C]5050[/C][C]4963.38788159306[/C][C]86.6121184069425[/C][/ROW]
[ROW][C]60[/C][C]4250[/C][C]4444.56864574704[/C][C]-194.568645747036[/C][/ROW]
[ROW][C]61[/C][C]3550[/C][C]3438.88743397304[/C][C]111.112566026964[/C][/ROW]
[ROW][C]62[/C][C]5000[/C][C]4873.731354371[/C][C]126.268645629005[/C][/ROW]
[ROW][C]63[/C][C]5000[/C][C]5033.70258636383[/C][C]-33.7025863638301[/C][/ROW]
[ROW][C]64[/C][C]4750[/C][C]4805.86299011657[/C][C]-55.862990116565[/C][/ROW]
[ROW][C]65[/C][C]4750[/C][C]4849.86502709063[/C][C]-99.8650270906346[/C][/ROW]
[ROW][C]66[/C][C]4800[/C][C]4704.80686262682[/C][C]95.1931373731832[/C][/ROW]
[ROW][C]67[/C][C]4900[/C][C]4870.1149390567[/C][C]29.8850609432975[/C][/ROW]
[ROW][C]68[/C][C]4950[/C][C]4929.53523398706[/C][C]20.464766012944[/C][/ROW]
[ROW][C]69[/C][C]5100[/C][C]5159.80365567485[/C][C]-59.8036556748457[/C][/ROW]
[ROW][C]70[/C][C]5150[/C][C]5121.26076664892[/C][C]28.739233351077[/C][/ROW]
[ROW][C]71[/C][C]5150[/C][C]5236.4375380942[/C][C]-86.4375380941974[/C][/ROW]
[ROW][C]72[/C][C]4550[/C][C]4576.37512797561[/C][C]-26.375127975607[/C][/ROW]
[ROW][C]73[/C][C]3700[/C][C]3642.55836921356[/C][C]57.4416307864385[/C][/ROW]
[ROW][C]74[/C][C]5350[/C][C]5123.46084685005[/C][C]226.539153149951[/C][/ROW]
[ROW][C]75[/C][C]5200[/C][C]5296.41901941446[/C][C]-96.4190194144649[/C][/ROW]
[ROW][C]76[/C][C]5100[/C][C]5028.96541592804[/C][C]71.0345840719574[/C][/ROW]
[ROW][C]77[/C][C]5050[/C][C]5115.83295635495[/C][C]-65.8329563549496[/C][/ROW]
[ROW][C]78[/C][C]4950[/C][C]5013.33975228297[/C][C]-63.3397522829728[/C][/ROW]
[ROW][C]79[/C][C]4950[/C][C]5110.93786767799[/C][C]-160.937867677986[/C][/ROW]
[ROW][C]80[/C][C]4900[/C][C]5096.49838549262[/C][C]-196.498385492616[/C][/ROW]
[ROW][C]81[/C][C]5200[/C][C]5232.20026454781[/C][C]-32.2002645478069[/C][/ROW]
[ROW][C]82[/C][C]5300[/C][C]5219.85942101251[/C][C]80.1405789874925[/C][/ROW]
[ROW][C]83[/C][C]5500[/C][C]5335.27244198437[/C][C]164.727558015627[/C][/ROW]
[ROW][C]84[/C][C]4750[/C][C]4756.56170641666[/C][C]-6.56170641666449[/C][/ROW]
[ROW][C]85[/C][C]3950[/C][C]3806.48486603883[/C][C]143.515133961172[/C][/ROW]
[ROW][C]86[/C][C]5400[/C][C]5424.81465087121[/C][C]-24.8146508712125[/C][/ROW]
[ROW][C]87[/C][C]5300[/C][C]5443.40327490056[/C][C]-143.403274900563[/C][/ROW]
[ROW][C]88[/C][C]5200[/C][C]5182.00046445168[/C][C]17.999535548317[/C][/ROW]
[ROW][C]89[/C][C]5100[/C][C]5224.21172329046[/C][C]-124.211723290457[/C][/ROW]
[ROW][C]90[/C][C]5250[/C][C]5097.93309515242[/C][C]152.066904847581[/C][/ROW]
[ROW][C]91[/C][C]5200[/C][C]5263.17922398626[/C][C]-63.1792239862589[/C][/ROW]
[ROW][C]92[/C][C]5250[/C][C]5280.22255079994[/C][C]-30.2225507999447[/C][/ROW]
[ROW][C]93[/C][C]5500[/C][C]5521.8397442649[/C][C]-21.8397442649011[/C][/ROW]
[ROW][C]94[/C][C]5550[/C][C]5533.74078573461[/C][C]16.2592142653903[/C][/ROW]
[ROW][C]95[/C][C]5600[/C][C]5643.81291776112[/C][C]-43.8129177611181[/C][/ROW]
[ROW][C]96[/C][C]4800[/C][C]4929.06145590094[/C][C]-129.061455900943[/C][/ROW]
[ROW][C]97[/C][C]3700[/C][C]3933.85047430243[/C][C]-233.85047430243[/C][/ROW]
[ROW][C]98[/C][C]4800[/C][C]5360.46856011467[/C][C]-560.46856011467[/C][/ROW]
[ROW][C]99[/C][C]5400[/C][C]5152.79366399346[/C][C]247.206336006545[/C][/ROW]
[ROW][C]100[/C][C]5200[/C][C]5074.3159828593[/C][C]125.684017140704[/C][/ROW]
[ROW][C]101[/C][C]5250[/C][C]5132.02856482735[/C][C]117.971435172645[/C][/ROW]
[ROW][C]102[/C][C]5150[/C][C]5147.83995637104[/C][C]2.16004362895546[/C][/ROW]
[ROW][C]103[/C][C]5100[/C][C]5216.44221654288[/C][C]-116.442216542879[/C][/ROW]
[ROW][C]104[/C][C]5300[/C][C]5218.70123501306[/C][C]81.2987649869438[/C][/ROW]
[ROW][C]105[/C][C]5650[/C][C]5503.9454773837[/C][C]146.054522616299[/C][/ROW]
[ROW][C]106[/C][C]5700[/C][C]5587.10848062361[/C][C]112.891519376387[/C][/ROW]
[ROW][C]107[/C][C]5800[/C][C]5724.50779890548[/C][C]75.4922010945211[/C][/ROW]
[ROW][C]108[/C][C]5150[/C][C]5022.39865444023[/C][C]127.601345559775[/C][/ROW]
[ROW][C]109[/C][C]4100[/C][C]4062.30389674558[/C][C]37.6961032544177[/C][/ROW]
[ROW][C]110[/C][C]5700[/C][C]5633.47403913333[/C][C]66.5259608666711[/C][/ROW]
[ROW][C]111[/C][C]5900[/C][C]5827.11316648484[/C][C]72.8868335151583[/C][/ROW]
[ROW][C]112[/C][C]5500[/C][C]5637.06382271576[/C][C]-137.063822715759[/C][/ROW]
[ROW][C]113[/C][C]5800[/C][C]5591.72081713186[/C][C]208.279182868139[/C][/ROW]
[ROW][C]114[/C][C]5450[/C][C]5615.07216082741[/C][C]-165.07216082741[/C][/ROW]
[ROW][C]115[/C][C]5950[/C][C]5600.27857175839[/C][C]349.721428241607[/C][/ROW]
[ROW][C]116[/C][C]6100[/C][C]5824.01473940762[/C][C]275.985260592384[/C][/ROW]
[ROW][C]117[/C][C]6400[/C][C]6226.45056941868[/C][C]173.549430581324[/C][/ROW]
[ROW][C]118[/C][C]6100[/C][C]6314.31729675337[/C][C]-214.317296753367[/C][/ROW]
[ROW][C]119[/C][C]6150[/C][C]6326.60750305046[/C][C]-176.607503050461[/C][/ROW]
[ROW][C]120[/C][C]5500[/C][C]5474.13165275006[/C][C]25.8683472499433[/C][/ROW]
[ROW][C]121[/C][C]4500[/C][C]4379.388247683[/C][C]120.611752316995[/C][/ROW]
[ROW][C]122[/C][C]6400[/C][C]6116.78230694514[/C][C]283.217693054865[/C][/ROW]
[ROW][C]123[/C][C]6150[/C][C]6409.24588428776[/C][C]-259.245884287757[/C][/ROW]
[ROW][C]124[/C][C]5800[/C][C]6033.25790221848[/C][C]-233.257902218477[/C][/ROW]
[ROW][C]125[/C][C]6150[/C][C]6016.36263501784[/C][C]133.637364982158[/C][/ROW]
[ROW][C]126[/C][C]6050[/C][C]5934.5513994706[/C][C]115.448600529403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298081&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298081&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
1329502847.24171596798102.75828403202
1440503968.2890300467581.7109699532534
1542004153.1065305034646.8934694965419
1640504025.1127915326824.8872084673162
1741004089.5665114153710.4334885846306
1840004013.18790122027-13.1879012202653
1941004160.90915146583-60.909151465833
2041004137.57745714048-37.5774571404772
2143004327.35665838073-27.3566583807269
2242504203.9759897405846.0240102594171
2343004371.07512808762-71.0751280876202
2437003973.66764019305-273.667640193053
2529002982.43192601907-82.4319260190673
2641504045.30608608756104.693913912442
2743004234.8909972744365.1090027255705
2840004106.67435067715-106.674350677145
2941004118.35009815025-18.3500981502548
3040504026.2861105977123.7138894022851
3141004180.40581002149-80.4058100214943
3241504153.71426686846-3.7142668684628
3342004359.93001573768-159.930015737682
3443504199.33000456358150.669995436419
3544504386.0156000885963.9843999114064
3639003994.66394693949-94.6639469394909
3731003074.8682252590325.1317747409676
3845004268.66658278138231.333417218615
3944504507.18465890307-57.1846589030738
4043004290.838868814639.16113118537214
4143504365.91516671231-15.9151667123069
4242004276.54731298066-76.5473129806624
4342504378.93513107075-128.935131070748
4443504347.490748918182.50925108181673
4545504535.1094768801914.8905231198132
4646004493.20262832627106.797371673733
4747004652.8975973143447.1024026856649
4840004200.33867783194-200.338677831939
4932003221.19404495584-21.1940449558351
5045504481.8790247481168.1209752518917
5147004607.7482008634592.2517991365539
5245004453.0958915578946.9041084421124
5345504540.109255179259.89074482075375
5444504444.803644259685.19635574032236
5545504574.04250119412-24.0425011941197
5646004607.91709994049-7.91709994049324
5748504803.7967620831246.2032379168841
5849504787.25606223993162.74393776007
5950504963.3878815930686.6121184069425
6042504444.56864574704-194.568645747036
6135503438.88743397304111.112566026964
6250004873.731354371126.268645629005
6350005033.70258636383-33.7025863638301
6447504805.86299011657-55.862990116565
6547504849.86502709063-99.8650270906346
6648004704.8068626268295.1931373731832
6749004870.114939056729.8850609432975
6849504929.5352339870620.464766012944
6951005159.80365567485-59.8036556748457
7051505121.2607666489228.739233351077
7151505236.4375380942-86.4375380941974
7245504576.37512797561-26.375127975607
7337003642.5583692135657.4416307864385
7453505123.46084685005226.539153149951
7552005296.41901941446-96.4190194144649
7651005028.9654159280471.0345840719574
7750505115.83295635495-65.8329563549496
7849505013.33975228297-63.3397522829728
7949505110.93786767799-160.937867677986
8049005096.49838549262-196.498385492616
8152005232.20026454781-32.2002645478069
8253005219.8594210125180.1405789874925
8355005335.27244198437164.727558015627
8447504756.56170641666-6.56170641666449
8539503806.48486603883143.515133961172
8654005424.81465087121-24.8146508712125
8753005443.40327490056-143.403274900563
8852005182.0004644516817.999535548317
8951005224.21172329046-124.211723290457
9052505097.93309515242152.066904847581
9152005263.17922398626-63.1792239862589
9252505280.22255079994-30.2225507999447
9355005521.8397442649-21.8397442649011
9455505533.7407857346116.2592142653903
9556005643.81291776112-43.8129177611181
9648004929.06145590094-129.061455900943
9737003933.85047430243-233.85047430243
9848005360.46856011467-560.46856011467
9954005152.79366399346247.206336006545
10052005074.3159828593125.684017140704
10152505132.02856482735117.971435172645
10251505147.839956371042.16004362895546
10351005216.44221654288-116.442216542879
10453005218.7012350130681.2987649869438
10556505503.9454773837146.054522616299
10657005587.10848062361112.891519376387
10758005724.5077989054875.4922010945211
10851505022.39865444023127.601345559775
10941004062.3038967455837.6961032544177
11057005633.4740391333366.5259608666711
11159005827.1131664848472.8868335151583
11255005637.06382271576-137.063822715759
11358005591.72081713186208.279182868139
11454505615.07216082741-165.07216082741
11559505600.27857175839349.721428241607
11661005824.01473940762275.985260592384
11764006226.45056941868173.549430581324
11861006314.31729675337-214.317296753367
11961506326.60750305046-176.607503050461
12055005474.1316527500625.8683472499433
12145004379.388247683120.611752316995
12264006116.78230694514283.217693054865
12361506409.24588428776-259.245884287757
12458006033.25790221848-233.257902218477
12561506016.36263501784133.637364982158
12660505934.5513994706115.448600529403







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1276128.697823088835982.880221209556274.5154249681
1286207.574614463376030.693262787126384.45596613963
1296495.367281346766288.308851329016702.42571136452
1306444.450145664366216.34377038036672.55652094843
1316548.62099570336297.735329505786799.50666190081
1325760.825321933845514.053019771776007.59762409592
1334618.453294674124388.514031638164848.39255771008
1346403.547490148046086.576705081256720.51827521483
1356490.290753501226155.313851207536825.26765579491
1366207.144571489165871.114052041946543.17509093638
1376351.817016825975995.541312408356708.09272124359
1386208.807555330635877.439817100146540.17529356112

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 6128.69782308883 & 5982.88022120955 & 6274.5154249681 \tabularnewline
128 & 6207.57461446337 & 6030.69326278712 & 6384.45596613963 \tabularnewline
129 & 6495.36728134676 & 6288.30885132901 & 6702.42571136452 \tabularnewline
130 & 6444.45014566436 & 6216.3437703803 & 6672.55652094843 \tabularnewline
131 & 6548.6209957033 & 6297.73532950578 & 6799.50666190081 \tabularnewline
132 & 5760.82532193384 & 5514.05301977177 & 6007.59762409592 \tabularnewline
133 & 4618.45329467412 & 4388.51403163816 & 4848.39255771008 \tabularnewline
134 & 6403.54749014804 & 6086.57670508125 & 6720.51827521483 \tabularnewline
135 & 6490.29075350122 & 6155.31385120753 & 6825.26765579491 \tabularnewline
136 & 6207.14457148916 & 5871.11405204194 & 6543.17509093638 \tabularnewline
137 & 6351.81701682597 & 5995.54131240835 & 6708.09272124359 \tabularnewline
138 & 6208.80755533063 & 5877.43981710014 & 6540.17529356112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298081&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]127[/C][C]6128.69782308883[/C][C]5982.88022120955[/C][C]6274.5154249681[/C][/ROW]
[ROW][C]128[/C][C]6207.57461446337[/C][C]6030.69326278712[/C][C]6384.45596613963[/C][/ROW]
[ROW][C]129[/C][C]6495.36728134676[/C][C]6288.30885132901[/C][C]6702.42571136452[/C][/ROW]
[ROW][C]130[/C][C]6444.45014566436[/C][C]6216.3437703803[/C][C]6672.55652094843[/C][/ROW]
[ROW][C]131[/C][C]6548.6209957033[/C][C]6297.73532950578[/C][C]6799.50666190081[/C][/ROW]
[ROW][C]132[/C][C]5760.82532193384[/C][C]5514.05301977177[/C][C]6007.59762409592[/C][/ROW]
[ROW][C]133[/C][C]4618.45329467412[/C][C]4388.51403163816[/C][C]4848.39255771008[/C][/ROW]
[ROW][C]134[/C][C]6403.54749014804[/C][C]6086.57670508125[/C][C]6720.51827521483[/C][/ROW]
[ROW][C]135[/C][C]6490.29075350122[/C][C]6155.31385120753[/C][C]6825.26765579491[/C][/ROW]
[ROW][C]136[/C][C]6207.14457148916[/C][C]5871.11405204194[/C][C]6543.17509093638[/C][/ROW]
[ROW][C]137[/C][C]6351.81701682597[/C][C]5995.54131240835[/C][C]6708.09272124359[/C][/ROW]
[ROW][C]138[/C][C]6208.80755533063[/C][C]5877.43981710014[/C][C]6540.17529356112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298081&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298081&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
1276128.697823088835982.880221209556274.5154249681
1286207.574614463376030.693262787126384.45596613963
1296495.367281346766288.308851329016702.42571136452
1306444.450145664366216.34377038036672.55652094843
1316548.62099570336297.735329505786799.50666190081
1325760.825321933845514.053019771776007.59762409592
1334618.453294674124388.514031638164848.39255771008
1346403.547490148046086.576705081256720.51827521483
1356490.290753501226155.313851207536825.26765579491
1366207.144571489165871.114052041946543.17509093638
1376351.817016825975995.541312408356708.09272124359
1386208.807555330635877.439817100146540.17529356112



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