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, 21 Dec 2016 14:39:45 +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/t1482327654980asm5kvnn5wut.htm/, Retrieved Fri, 01 Nov 2024 03:33:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302282, Retrieved Fri, 01 Nov 2024 03:33:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-21 13:39:45] [e6ca2edb1c884165f9811941c39250b2] [Current]
Feedback Forum

Post a new message
Dataseries X:
7020
6240
6040
6580
5900
6100
6460
8740
6940
7260
7380
7640
6640
5860
6160
5580
6140
5680
5740
6280
7060
6820
6560
6100
5860
5780
5220
5080
4840
5040
4420
5160
5240
5560
6120
5300
5540
4520
5160
4740
4480
4520
4640
4720
4700
5060
5500
4980
5100
4620
4960
4640
4660
4920
4540
4660
4840
5260
4640
5020
6420
4300
4680
4540
4240
4540
4740
5160
5200
5420
5140
4600
4800
4840
4720
4600
4340
4460
4360
4720
4920
5000
4680
4480
4840
4480
4500
4380
4460
4540
4920
4600
4880
5120
4560
4520
4600
4580
4360
4540
4420
4680
4760
4940
4780
5340
5140
4700




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=302282&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=302282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302282&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
alpha0.0264291419005073
beta1
gamma0.645394641006907

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0264291419005073 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.645394641006907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302282&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]0.0264291419005073[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.645394641006907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302282&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
alpha0.0264291419005073
beta1
gamma0.645394641006907







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1366406780.53418803419-140.534188034188
1458606073.89250532604-213.892505326045
1561606404.6590298659-244.659029865896
1655805763.97962667867-183.979626678667
1761406299.20817105508-159.208171055083
1856805856.71700173606-176.717001736056
1957405990.759276998-250.759276998
2062808207.88399261243-1927.88399261243
2170606228.89808819123831.10191180877
2268206490.62845743379329.371542566211
2365606542.8035307883217.1964692116835
2461006703.01590608967-603.01590608967
2558605522.59651921308337.403480786916
2657804723.158007165891056.84199283411
2752205042.42708157222177.572918427775
2850804436.44315982524643.556840174762
2948405016.38780805551-176.387808055512
3050404569.26729197272470.732708027283
3144204697.83526564213-277.835265642128
3251605883.66627338534-723.666273385345
3352405725.12941544248-485.12941544248
3455605657.07862846447-97.0786284644691
3561205510.822670468609.177329531998
3653005321.61445695975-21.6144569597473
3755404787.46414428197752.535855718029
3845204502.0213983875217.9786016124808
3951604264.87431919192895.125680808082
4047404013.13190877567726.868091224334
4144804124.76042147335355.239578526648
4245204157.03476844416362.965231555838
4346403868.28744863359771.712551366411
4447204885.34962362982-165.349623629816
4547004989.83087993976-289.830879939756
4650605274.31071826366-214.310718263657
4755005669.16734021302-169.167340213022
4849805142.9109639603-162.910963960304
4951005167.59246545037-67.5924654503733
5046204453.38789191805166.612108081953
5149604829.70491858571130.29508141429
5246404490.20385847357149.796141526428
5346604375.99894502053284.001054979466
5449204432.28825184743487.711748152571
5545404428.00946896503111.990531034975
5646604845.74900540042-185.749005400424
5748404877.84022721394-37.8402272139429
5852605229.4573364991730.5426635008316
5946405678.64699255154-1038.64699255154
6050205129.85902524211-109.859025242111
6164205213.753834844921206.24616515508
6243004711.96069334588-411.960693345875
6346805066.4614819581-386.4614819581
6445404728.19309370367-188.193093703667
6542404683.08547636882-443.085476368821
6645404822.64538046993-282.645380469935
6747404516.05496387337223.94503612663
6851604706.75927507891453.240724921087
6952004822.64982043941377.35017956059
7054205213.15546485229206.844535147714
7151404984.80015142813155.199848571873
7246005072.31649661005-472.316496610046
7348005985.1702937753-1185.1702937753
7448404351.77136389247488.228636107534
7547204718.253934190731.74606580926593
7646004497.2534187209102.746581279103
7743404289.794386579750.2056134202958
7844604546.35704606177-86.357046061773
7943604571.6067866438-211.606786643802
8047204891.70634861641-171.706348616414
8149204923.70984660228-3.70984660227623
8250005167.25287281196-167.252872811957
8346804856.91667065683-176.916670656829
8444804492.94238233083-12.9423823308289
8548404933.74411397014-93.7441139701377
8644804373.21503842618106.784961573817
8745004406.4251903214693.5748096785373
8843804236.22499840376143.775001596244
8944603982.83216815071477.167831849294
9045404162.15120121949377.848798780507
9149204130.51852483161789.48147516839
9246004538.1529513673761.8470486326341
9348804724.06619159216155.933808407844
9451204915.46614383233204.533856167668
9545604665.1077078193-105.107707819299
9645204464.1841860716255.8158139283842
9746004915.97134376589-315.971343765895
9845804529.6345961631850.3654038368168
9943604605.62775645795-245.627756457946
10045404501.6151194115838.3848805884199
10144204495.7444660224-75.7444660223982
10246804624.255997855255.7440021447992
10347604860.45298708893-100.452987088934
10449404781.54547842513158.454521574869
10547805025.86165846951-245.861658469511
10653405223.29207608013116.707923919866
10751404759.84427871857380.155721281425
10847004669.4764010066230.523598993379

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6640 & 6780.53418803419 & -140.534188034188 \tabularnewline
14 & 5860 & 6073.89250532604 & -213.892505326045 \tabularnewline
15 & 6160 & 6404.6590298659 & -244.659029865896 \tabularnewline
16 & 5580 & 5763.97962667867 & -183.979626678667 \tabularnewline
17 & 6140 & 6299.20817105508 & -159.208171055083 \tabularnewline
18 & 5680 & 5856.71700173606 & -176.717001736056 \tabularnewline
19 & 5740 & 5990.759276998 & -250.759276998 \tabularnewline
20 & 6280 & 8207.88399261243 & -1927.88399261243 \tabularnewline
21 & 7060 & 6228.89808819123 & 831.10191180877 \tabularnewline
22 & 6820 & 6490.62845743379 & 329.371542566211 \tabularnewline
23 & 6560 & 6542.80353078832 & 17.1964692116835 \tabularnewline
24 & 6100 & 6703.01590608967 & -603.01590608967 \tabularnewline
25 & 5860 & 5522.59651921308 & 337.403480786916 \tabularnewline
26 & 5780 & 4723.15800716589 & 1056.84199283411 \tabularnewline
27 & 5220 & 5042.42708157222 & 177.572918427775 \tabularnewline
28 & 5080 & 4436.44315982524 & 643.556840174762 \tabularnewline
29 & 4840 & 5016.38780805551 & -176.387808055512 \tabularnewline
30 & 5040 & 4569.26729197272 & 470.732708027283 \tabularnewline
31 & 4420 & 4697.83526564213 & -277.835265642128 \tabularnewline
32 & 5160 & 5883.66627338534 & -723.666273385345 \tabularnewline
33 & 5240 & 5725.12941544248 & -485.12941544248 \tabularnewline
34 & 5560 & 5657.07862846447 & -97.0786284644691 \tabularnewline
35 & 6120 & 5510.822670468 & 609.177329531998 \tabularnewline
36 & 5300 & 5321.61445695975 & -21.6144569597473 \tabularnewline
37 & 5540 & 4787.46414428197 & 752.535855718029 \tabularnewline
38 & 4520 & 4502.02139838752 & 17.9786016124808 \tabularnewline
39 & 5160 & 4264.87431919192 & 895.125680808082 \tabularnewline
40 & 4740 & 4013.13190877567 & 726.868091224334 \tabularnewline
41 & 4480 & 4124.76042147335 & 355.239578526648 \tabularnewline
42 & 4520 & 4157.03476844416 & 362.965231555838 \tabularnewline
43 & 4640 & 3868.28744863359 & 771.712551366411 \tabularnewline
44 & 4720 & 4885.34962362982 & -165.349623629816 \tabularnewline
45 & 4700 & 4989.83087993976 & -289.830879939756 \tabularnewline
46 & 5060 & 5274.31071826366 & -214.310718263657 \tabularnewline
47 & 5500 & 5669.16734021302 & -169.167340213022 \tabularnewline
48 & 4980 & 5142.9109639603 & -162.910963960304 \tabularnewline
49 & 5100 & 5167.59246545037 & -67.5924654503733 \tabularnewline
50 & 4620 & 4453.38789191805 & 166.612108081953 \tabularnewline
51 & 4960 & 4829.70491858571 & 130.29508141429 \tabularnewline
52 & 4640 & 4490.20385847357 & 149.796141526428 \tabularnewline
53 & 4660 & 4375.99894502053 & 284.001054979466 \tabularnewline
54 & 4920 & 4432.28825184743 & 487.711748152571 \tabularnewline
55 & 4540 & 4428.00946896503 & 111.990531034975 \tabularnewline
56 & 4660 & 4845.74900540042 & -185.749005400424 \tabularnewline
57 & 4840 & 4877.84022721394 & -37.8402272139429 \tabularnewline
58 & 5260 & 5229.45733649917 & 30.5426635008316 \tabularnewline
59 & 4640 & 5678.64699255154 & -1038.64699255154 \tabularnewline
60 & 5020 & 5129.85902524211 & -109.859025242111 \tabularnewline
61 & 6420 & 5213.75383484492 & 1206.24616515508 \tabularnewline
62 & 4300 & 4711.96069334588 & -411.960693345875 \tabularnewline
63 & 4680 & 5066.4614819581 & -386.4614819581 \tabularnewline
64 & 4540 & 4728.19309370367 & -188.193093703667 \tabularnewline
65 & 4240 & 4683.08547636882 & -443.085476368821 \tabularnewline
66 & 4540 & 4822.64538046993 & -282.645380469935 \tabularnewline
67 & 4740 & 4516.05496387337 & 223.94503612663 \tabularnewline
68 & 5160 & 4706.75927507891 & 453.240724921087 \tabularnewline
69 & 5200 & 4822.64982043941 & 377.35017956059 \tabularnewline
70 & 5420 & 5213.15546485229 & 206.844535147714 \tabularnewline
71 & 5140 & 4984.80015142813 & 155.199848571873 \tabularnewline
72 & 4600 & 5072.31649661005 & -472.316496610046 \tabularnewline
73 & 4800 & 5985.1702937753 & -1185.1702937753 \tabularnewline
74 & 4840 & 4351.77136389247 & 488.228636107534 \tabularnewline
75 & 4720 & 4718.25393419073 & 1.74606580926593 \tabularnewline
76 & 4600 & 4497.2534187209 & 102.746581279103 \tabularnewline
77 & 4340 & 4289.7943865797 & 50.2056134202958 \tabularnewline
78 & 4460 & 4546.35704606177 & -86.357046061773 \tabularnewline
79 & 4360 & 4571.6067866438 & -211.606786643802 \tabularnewline
80 & 4720 & 4891.70634861641 & -171.706348616414 \tabularnewline
81 & 4920 & 4923.70984660228 & -3.70984660227623 \tabularnewline
82 & 5000 & 5167.25287281196 & -167.252872811957 \tabularnewline
83 & 4680 & 4856.91667065683 & -176.916670656829 \tabularnewline
84 & 4480 & 4492.94238233083 & -12.9423823308289 \tabularnewline
85 & 4840 & 4933.74411397014 & -93.7441139701377 \tabularnewline
86 & 4480 & 4373.21503842618 & 106.784961573817 \tabularnewline
87 & 4500 & 4406.42519032146 & 93.5748096785373 \tabularnewline
88 & 4380 & 4236.22499840376 & 143.775001596244 \tabularnewline
89 & 4460 & 3982.83216815071 & 477.167831849294 \tabularnewline
90 & 4540 & 4162.15120121949 & 377.848798780507 \tabularnewline
91 & 4920 & 4130.51852483161 & 789.48147516839 \tabularnewline
92 & 4600 & 4538.15295136737 & 61.8470486326341 \tabularnewline
93 & 4880 & 4724.06619159216 & 155.933808407844 \tabularnewline
94 & 5120 & 4915.46614383233 & 204.533856167668 \tabularnewline
95 & 4560 & 4665.1077078193 & -105.107707819299 \tabularnewline
96 & 4520 & 4464.18418607162 & 55.8158139283842 \tabularnewline
97 & 4600 & 4915.97134376589 & -315.971343765895 \tabularnewline
98 & 4580 & 4529.63459616318 & 50.3654038368168 \tabularnewline
99 & 4360 & 4605.62775645795 & -245.627756457946 \tabularnewline
100 & 4540 & 4501.61511941158 & 38.3848805884199 \tabularnewline
101 & 4420 & 4495.7444660224 & -75.7444660223982 \tabularnewline
102 & 4680 & 4624.2559978552 & 55.7440021447992 \tabularnewline
103 & 4760 & 4860.45298708893 & -100.452987088934 \tabularnewline
104 & 4940 & 4781.54547842513 & 158.454521574869 \tabularnewline
105 & 4780 & 5025.86165846951 & -245.861658469511 \tabularnewline
106 & 5340 & 5223.29207608013 & 116.707923919866 \tabularnewline
107 & 5140 & 4759.84427871857 & 380.155721281425 \tabularnewline
108 & 4700 & 4669.47640100662 & 30.523598993379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302282&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]6640[/C][C]6780.53418803419[/C][C]-140.534188034188[/C][/ROW]
[ROW][C]14[/C][C]5860[/C][C]6073.89250532604[/C][C]-213.892505326045[/C][/ROW]
[ROW][C]15[/C][C]6160[/C][C]6404.6590298659[/C][C]-244.659029865896[/C][/ROW]
[ROW][C]16[/C][C]5580[/C][C]5763.97962667867[/C][C]-183.979626678667[/C][/ROW]
[ROW][C]17[/C][C]6140[/C][C]6299.20817105508[/C][C]-159.208171055083[/C][/ROW]
[ROW][C]18[/C][C]5680[/C][C]5856.71700173606[/C][C]-176.717001736056[/C][/ROW]
[ROW][C]19[/C][C]5740[/C][C]5990.759276998[/C][C]-250.759276998[/C][/ROW]
[ROW][C]20[/C][C]6280[/C][C]8207.88399261243[/C][C]-1927.88399261243[/C][/ROW]
[ROW][C]21[/C][C]7060[/C][C]6228.89808819123[/C][C]831.10191180877[/C][/ROW]
[ROW][C]22[/C][C]6820[/C][C]6490.62845743379[/C][C]329.371542566211[/C][/ROW]
[ROW][C]23[/C][C]6560[/C][C]6542.80353078832[/C][C]17.1964692116835[/C][/ROW]
[ROW][C]24[/C][C]6100[/C][C]6703.01590608967[/C][C]-603.01590608967[/C][/ROW]
[ROW][C]25[/C][C]5860[/C][C]5522.59651921308[/C][C]337.403480786916[/C][/ROW]
[ROW][C]26[/C][C]5780[/C][C]4723.15800716589[/C][C]1056.84199283411[/C][/ROW]
[ROW][C]27[/C][C]5220[/C][C]5042.42708157222[/C][C]177.572918427775[/C][/ROW]
[ROW][C]28[/C][C]5080[/C][C]4436.44315982524[/C][C]643.556840174762[/C][/ROW]
[ROW][C]29[/C][C]4840[/C][C]5016.38780805551[/C][C]-176.387808055512[/C][/ROW]
[ROW][C]30[/C][C]5040[/C][C]4569.26729197272[/C][C]470.732708027283[/C][/ROW]
[ROW][C]31[/C][C]4420[/C][C]4697.83526564213[/C][C]-277.835265642128[/C][/ROW]
[ROW][C]32[/C][C]5160[/C][C]5883.66627338534[/C][C]-723.666273385345[/C][/ROW]
[ROW][C]33[/C][C]5240[/C][C]5725.12941544248[/C][C]-485.12941544248[/C][/ROW]
[ROW][C]34[/C][C]5560[/C][C]5657.07862846447[/C][C]-97.0786284644691[/C][/ROW]
[ROW][C]35[/C][C]6120[/C][C]5510.822670468[/C][C]609.177329531998[/C][/ROW]
[ROW][C]36[/C][C]5300[/C][C]5321.61445695975[/C][C]-21.6144569597473[/C][/ROW]
[ROW][C]37[/C][C]5540[/C][C]4787.46414428197[/C][C]752.535855718029[/C][/ROW]
[ROW][C]38[/C][C]4520[/C][C]4502.02139838752[/C][C]17.9786016124808[/C][/ROW]
[ROW][C]39[/C][C]5160[/C][C]4264.87431919192[/C][C]895.125680808082[/C][/ROW]
[ROW][C]40[/C][C]4740[/C][C]4013.13190877567[/C][C]726.868091224334[/C][/ROW]
[ROW][C]41[/C][C]4480[/C][C]4124.76042147335[/C][C]355.239578526648[/C][/ROW]
[ROW][C]42[/C][C]4520[/C][C]4157.03476844416[/C][C]362.965231555838[/C][/ROW]
[ROW][C]43[/C][C]4640[/C][C]3868.28744863359[/C][C]771.712551366411[/C][/ROW]
[ROW][C]44[/C][C]4720[/C][C]4885.34962362982[/C][C]-165.349623629816[/C][/ROW]
[ROW][C]45[/C][C]4700[/C][C]4989.83087993976[/C][C]-289.830879939756[/C][/ROW]
[ROW][C]46[/C][C]5060[/C][C]5274.31071826366[/C][C]-214.310718263657[/C][/ROW]
[ROW][C]47[/C][C]5500[/C][C]5669.16734021302[/C][C]-169.167340213022[/C][/ROW]
[ROW][C]48[/C][C]4980[/C][C]5142.9109639603[/C][C]-162.910963960304[/C][/ROW]
[ROW][C]49[/C][C]5100[/C][C]5167.59246545037[/C][C]-67.5924654503733[/C][/ROW]
[ROW][C]50[/C][C]4620[/C][C]4453.38789191805[/C][C]166.612108081953[/C][/ROW]
[ROW][C]51[/C][C]4960[/C][C]4829.70491858571[/C][C]130.29508141429[/C][/ROW]
[ROW][C]52[/C][C]4640[/C][C]4490.20385847357[/C][C]149.796141526428[/C][/ROW]
[ROW][C]53[/C][C]4660[/C][C]4375.99894502053[/C][C]284.001054979466[/C][/ROW]
[ROW][C]54[/C][C]4920[/C][C]4432.28825184743[/C][C]487.711748152571[/C][/ROW]
[ROW][C]55[/C][C]4540[/C][C]4428.00946896503[/C][C]111.990531034975[/C][/ROW]
[ROW][C]56[/C][C]4660[/C][C]4845.74900540042[/C][C]-185.749005400424[/C][/ROW]
[ROW][C]57[/C][C]4840[/C][C]4877.84022721394[/C][C]-37.8402272139429[/C][/ROW]
[ROW][C]58[/C][C]5260[/C][C]5229.45733649917[/C][C]30.5426635008316[/C][/ROW]
[ROW][C]59[/C][C]4640[/C][C]5678.64699255154[/C][C]-1038.64699255154[/C][/ROW]
[ROW][C]60[/C][C]5020[/C][C]5129.85902524211[/C][C]-109.859025242111[/C][/ROW]
[ROW][C]61[/C][C]6420[/C][C]5213.75383484492[/C][C]1206.24616515508[/C][/ROW]
[ROW][C]62[/C][C]4300[/C][C]4711.96069334588[/C][C]-411.960693345875[/C][/ROW]
[ROW][C]63[/C][C]4680[/C][C]5066.4614819581[/C][C]-386.4614819581[/C][/ROW]
[ROW][C]64[/C][C]4540[/C][C]4728.19309370367[/C][C]-188.193093703667[/C][/ROW]
[ROW][C]65[/C][C]4240[/C][C]4683.08547636882[/C][C]-443.085476368821[/C][/ROW]
[ROW][C]66[/C][C]4540[/C][C]4822.64538046993[/C][C]-282.645380469935[/C][/ROW]
[ROW][C]67[/C][C]4740[/C][C]4516.05496387337[/C][C]223.94503612663[/C][/ROW]
[ROW][C]68[/C][C]5160[/C][C]4706.75927507891[/C][C]453.240724921087[/C][/ROW]
[ROW][C]69[/C][C]5200[/C][C]4822.64982043941[/C][C]377.35017956059[/C][/ROW]
[ROW][C]70[/C][C]5420[/C][C]5213.15546485229[/C][C]206.844535147714[/C][/ROW]
[ROW][C]71[/C][C]5140[/C][C]4984.80015142813[/C][C]155.199848571873[/C][/ROW]
[ROW][C]72[/C][C]4600[/C][C]5072.31649661005[/C][C]-472.316496610046[/C][/ROW]
[ROW][C]73[/C][C]4800[/C][C]5985.1702937753[/C][C]-1185.1702937753[/C][/ROW]
[ROW][C]74[/C][C]4840[/C][C]4351.77136389247[/C][C]488.228636107534[/C][/ROW]
[ROW][C]75[/C][C]4720[/C][C]4718.25393419073[/C][C]1.74606580926593[/C][/ROW]
[ROW][C]76[/C][C]4600[/C][C]4497.2534187209[/C][C]102.746581279103[/C][/ROW]
[ROW][C]77[/C][C]4340[/C][C]4289.7943865797[/C][C]50.2056134202958[/C][/ROW]
[ROW][C]78[/C][C]4460[/C][C]4546.35704606177[/C][C]-86.357046061773[/C][/ROW]
[ROW][C]79[/C][C]4360[/C][C]4571.6067866438[/C][C]-211.606786643802[/C][/ROW]
[ROW][C]80[/C][C]4720[/C][C]4891.70634861641[/C][C]-171.706348616414[/C][/ROW]
[ROW][C]81[/C][C]4920[/C][C]4923.70984660228[/C][C]-3.70984660227623[/C][/ROW]
[ROW][C]82[/C][C]5000[/C][C]5167.25287281196[/C][C]-167.252872811957[/C][/ROW]
[ROW][C]83[/C][C]4680[/C][C]4856.91667065683[/C][C]-176.916670656829[/C][/ROW]
[ROW][C]84[/C][C]4480[/C][C]4492.94238233083[/C][C]-12.9423823308289[/C][/ROW]
[ROW][C]85[/C][C]4840[/C][C]4933.74411397014[/C][C]-93.7441139701377[/C][/ROW]
[ROW][C]86[/C][C]4480[/C][C]4373.21503842618[/C][C]106.784961573817[/C][/ROW]
[ROW][C]87[/C][C]4500[/C][C]4406.42519032146[/C][C]93.5748096785373[/C][/ROW]
[ROW][C]88[/C][C]4380[/C][C]4236.22499840376[/C][C]143.775001596244[/C][/ROW]
[ROW][C]89[/C][C]4460[/C][C]3982.83216815071[/C][C]477.167831849294[/C][/ROW]
[ROW][C]90[/C][C]4540[/C][C]4162.15120121949[/C][C]377.848798780507[/C][/ROW]
[ROW][C]91[/C][C]4920[/C][C]4130.51852483161[/C][C]789.48147516839[/C][/ROW]
[ROW][C]92[/C][C]4600[/C][C]4538.15295136737[/C][C]61.8470486326341[/C][/ROW]
[ROW][C]93[/C][C]4880[/C][C]4724.06619159216[/C][C]155.933808407844[/C][/ROW]
[ROW][C]94[/C][C]5120[/C][C]4915.46614383233[/C][C]204.533856167668[/C][/ROW]
[ROW][C]95[/C][C]4560[/C][C]4665.1077078193[/C][C]-105.107707819299[/C][/ROW]
[ROW][C]96[/C][C]4520[/C][C]4464.18418607162[/C][C]55.8158139283842[/C][/ROW]
[ROW][C]97[/C][C]4600[/C][C]4915.97134376589[/C][C]-315.971343765895[/C][/ROW]
[ROW][C]98[/C][C]4580[/C][C]4529.63459616318[/C][C]50.3654038368168[/C][/ROW]
[ROW][C]99[/C][C]4360[/C][C]4605.62775645795[/C][C]-245.627756457946[/C][/ROW]
[ROW][C]100[/C][C]4540[/C][C]4501.61511941158[/C][C]38.3848805884199[/C][/ROW]
[ROW][C]101[/C][C]4420[/C][C]4495.7444660224[/C][C]-75.7444660223982[/C][/ROW]
[ROW][C]102[/C][C]4680[/C][C]4624.2559978552[/C][C]55.7440021447992[/C][/ROW]
[ROW][C]103[/C][C]4760[/C][C]4860.45298708893[/C][C]-100.452987088934[/C][/ROW]
[ROW][C]104[/C][C]4940[/C][C]4781.54547842513[/C][C]158.454521574869[/C][/ROW]
[ROW][C]105[/C][C]4780[/C][C]5025.86165846951[/C][C]-245.861658469511[/C][/ROW]
[ROW][C]106[/C][C]5340[/C][C]5223.29207608013[/C][C]116.707923919866[/C][/ROW]
[ROW][C]107[/C][C]5140[/C][C]4759.84427871857[/C][C]380.155721281425[/C][/ROW]
[ROW][C]108[/C][C]4700[/C][C]4669.47640100662[/C][C]30.523598993379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302282&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302282&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
1366406780.53418803419-140.534188034188
1458606073.89250532604-213.892505326045
1561606404.6590298659-244.659029865896
1655805763.97962667867-183.979626678667
1761406299.20817105508-159.208171055083
1856805856.71700173606-176.717001736056
1957405990.759276998-250.759276998
2062808207.88399261243-1927.88399261243
2170606228.89808819123831.10191180877
2268206490.62845743379329.371542566211
2365606542.8035307883217.1964692116835
2461006703.01590608967-603.01590608967
2558605522.59651921308337.403480786916
2657804723.158007165891056.84199283411
2752205042.42708157222177.572918427775
2850804436.44315982524643.556840174762
2948405016.38780805551-176.387808055512
3050404569.26729197272470.732708027283
3144204697.83526564213-277.835265642128
3251605883.66627338534-723.666273385345
3352405725.12941544248-485.12941544248
3455605657.07862846447-97.0786284644691
3561205510.822670468609.177329531998
3653005321.61445695975-21.6144569597473
3755404787.46414428197752.535855718029
3845204502.0213983875217.9786016124808
3951604264.87431919192895.125680808082
4047404013.13190877567726.868091224334
4144804124.76042147335355.239578526648
4245204157.03476844416362.965231555838
4346403868.28744863359771.712551366411
4447204885.34962362982-165.349623629816
4547004989.83087993976-289.830879939756
4650605274.31071826366-214.310718263657
4755005669.16734021302-169.167340213022
4849805142.9109639603-162.910963960304
4951005167.59246545037-67.5924654503733
5046204453.38789191805166.612108081953
5149604829.70491858571130.29508141429
5246404490.20385847357149.796141526428
5346604375.99894502053284.001054979466
5449204432.28825184743487.711748152571
5545404428.00946896503111.990531034975
5646604845.74900540042-185.749005400424
5748404877.84022721394-37.8402272139429
5852605229.4573364991730.5426635008316
5946405678.64699255154-1038.64699255154
6050205129.85902524211-109.859025242111
6164205213.753834844921206.24616515508
6243004711.96069334588-411.960693345875
6346805066.4614819581-386.4614819581
6445404728.19309370367-188.193093703667
6542404683.08547636882-443.085476368821
6645404822.64538046993-282.645380469935
6747404516.05496387337223.94503612663
6851604706.75927507891453.240724921087
6952004822.64982043941377.35017956059
7054205213.15546485229206.844535147714
7151404984.80015142813155.199848571873
7246005072.31649661005-472.316496610046
7348005985.1702937753-1185.1702937753
7448404351.77136389247488.228636107534
7547204718.253934190731.74606580926593
7646004497.2534187209102.746581279103
7743404289.794386579750.2056134202958
7844604546.35704606177-86.357046061773
7943604571.6067866438-211.606786643802
8047204891.70634861641-171.706348616414
8149204923.70984660228-3.70984660227623
8250005167.25287281196-167.252872811957
8346804856.91667065683-176.916670656829
8444804492.94238233083-12.9423823308289
8548404933.74411397014-93.7441139701377
8644804373.21503842618106.784961573817
8745004406.4251903214693.5748096785373
8843804236.22499840376143.775001596244
8944603982.83216815071477.167831849294
9045404162.15120121949377.848798780507
9149204130.51852483161789.48147516839
9246004538.1529513673761.8470486326341
9348804724.06619159216155.933808407844
9451204915.46614383233204.533856167668
9545604665.1077078193-105.107707819299
9645204464.1841860716255.8158139283842
9746004915.97134376589-315.971343765895
9845804529.6345961631850.3654038368168
9943604605.62775645795-245.627756457946
10045404501.6151194115838.3848805884199
10144204495.7444660224-75.7444660223982
10246804624.255997855255.7440021447992
10347604860.45298708893-100.452987088934
10449404781.54547842513158.454521574869
10547805025.86165846951-245.861658469511
10653405223.29207608013116.707923919866
10751404759.84427871857380.155721281425
10847004669.4764010066230.523598993379







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1094882.935152660134010.026924482045755.84338083822
1104739.431019719793865.304190146025613.55784929357
1114631.077052539853754.214561758075507.93954332162
1124721.471207155843839.766276252765603.17613805891
1134651.319151088773762.100698639155540.53760353839
1144874.898344863383974.970619757555774.82606996921
1155020.451066032224106.148371313235934.75376075122
1165118.508014885314185.763437133426051.25259263719
1175112.029874355384156.454932574586067.60481613617
1185557.712630898554574.683153542076540.74210825503
1195267.568353124744252.311061113236282.82564513624
1204948.273054709963895.947446387346000.59866303257

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 4882.93515266013 & 4010.02692448204 & 5755.84338083822 \tabularnewline
110 & 4739.43101971979 & 3865.30419014602 & 5613.55784929357 \tabularnewline
111 & 4631.07705253985 & 3754.21456175807 & 5507.93954332162 \tabularnewline
112 & 4721.47120715584 & 3839.76627625276 & 5603.17613805891 \tabularnewline
113 & 4651.31915108877 & 3762.10069863915 & 5540.53760353839 \tabularnewline
114 & 4874.89834486338 & 3974.97061975755 & 5774.82606996921 \tabularnewline
115 & 5020.45106603222 & 4106.14837131323 & 5934.75376075122 \tabularnewline
116 & 5118.50801488531 & 4185.76343713342 & 6051.25259263719 \tabularnewline
117 & 5112.02987435538 & 4156.45493257458 & 6067.60481613617 \tabularnewline
118 & 5557.71263089855 & 4574.68315354207 & 6540.74210825503 \tabularnewline
119 & 5267.56835312474 & 4252.31106111323 & 6282.82564513624 \tabularnewline
120 & 4948.27305470996 & 3895.94744638734 & 6000.59866303257 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302282&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]4882.93515266013[/C][C]4010.02692448204[/C][C]5755.84338083822[/C][/ROW]
[ROW][C]110[/C][C]4739.43101971979[/C][C]3865.30419014602[/C][C]5613.55784929357[/C][/ROW]
[ROW][C]111[/C][C]4631.07705253985[/C][C]3754.21456175807[/C][C]5507.93954332162[/C][/ROW]
[ROW][C]112[/C][C]4721.47120715584[/C][C]3839.76627625276[/C][C]5603.17613805891[/C][/ROW]
[ROW][C]113[/C][C]4651.31915108877[/C][C]3762.10069863915[/C][C]5540.53760353839[/C][/ROW]
[ROW][C]114[/C][C]4874.89834486338[/C][C]3974.97061975755[/C][C]5774.82606996921[/C][/ROW]
[ROW][C]115[/C][C]5020.45106603222[/C][C]4106.14837131323[/C][C]5934.75376075122[/C][/ROW]
[ROW][C]116[/C][C]5118.50801488531[/C][C]4185.76343713342[/C][C]6051.25259263719[/C][/ROW]
[ROW][C]117[/C][C]5112.02987435538[/C][C]4156.45493257458[/C][C]6067.60481613617[/C][/ROW]
[ROW][C]118[/C][C]5557.71263089855[/C][C]4574.68315354207[/C][C]6540.74210825503[/C][/ROW]
[ROW][C]119[/C][C]5267.56835312474[/C][C]4252.31106111323[/C][C]6282.82564513624[/C][/ROW]
[ROW][C]120[/C][C]4948.27305470996[/C][C]3895.94744638734[/C][C]6000.59866303257[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302282&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302282&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
1094882.935152660134010.026924482045755.84338083822
1104739.431019719793865.304190146025613.55784929357
1114631.077052539853754.214561758075507.93954332162
1124721.471207155843839.766276252765603.17613805891
1134651.319151088773762.100698639155540.53760353839
1144874.898344863383974.970619757555774.82606996921
1155020.451066032224106.148371313235934.75376075122
1165118.508014885314185.763437133426051.25259263719
1175112.029874355384156.454932574586067.60481613617
1185557.712630898554574.683153542076540.74210825503
1195267.568353124744252.311061113236282.82564513624
1204948.273054709963895.947446387346000.59866303257



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):
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')