Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 14 Aug 2012 11:41:46 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/14/t1344958921fahhvbydpnq37xm.htm/, Retrieved Thu, 02 May 2024 01:47:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169313, Retrieved Thu, 02 May 2024 01:47:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBuytaert Madelaine
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 stap 31] [2012-08-14 15:41:46] [d5bad77c67fde5063ee1c54428b9a54e] [Current]
Feedback Forum

Post a new message
Dataseries X:
2120
2100
2080
2040
2440
2420
2120
1920
1940
1940
1960
2000
2120
2080
2140
2240
2800
2800
2680
2560
2660
2780
2800
2860
3040
2920
2920
3100
3600
3640
3540
3300
3480
3480
3500
3600
3680
3720
3720
3840
4300
4420
4440
4140
4300
4240
4120
4380
4440
4340
4360
4500
5020
5280
5280
5160
5340
5160
5060
5440
5500
5360
5720
5860
6280
6560
6520
6500
6660
6640
6400
6760
6880
6760
7260
7500
8060
8280
8220
8100
8200
8320
7920
8240
8440
8360
8880
9060
9820
9960
9780
9880
9940
10000
9620
9980
10180
9980
10560
10740
11520
11640
11680
11880
11880
11960
11600
11780
11900
11680
12320
12440
13240
13380
13580
13760
13780
13800
13440
13800




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169313&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169313&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.972814985680872
beta0.0392069048110908
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.972814985680872 \tabularnewline
beta & 0.0392069048110908 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169313&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]0.972814985680872[/C][/ROW]
[ROW][C]beta[/C][C]0.0392069048110908[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169313&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
alpha0.972814985680872
beta0.0392069048110908
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3208020800
420402060-20
524402019.78087899553420.219121004465
624202423.84112050365-3.84112050365275
721202415.22269981618-295.222699816179
819202111.88380417405-191.883804174052
919401901.7558822566638.2441177433441
1019401916.9585227673223.0414772326842
1119601918.2506332375741.7493667624294
1220001939.3344242851160.6655757148862
1321201981.13403651272138.865963487279
1420802104.30465352748-24.3046535274766
1521402067.8134437286172.1865562713883
1622402127.9436009104112.0563990896
1728002231.13368901255568.866310987451
1828002800.41247169985-0.412471699851721
1926802815.87259144906-135.872591449056
2025602694.37275146411-134.372751464109
2126602569.2068585063190.7931414936902
2227802666.54866755179113.45133244821
2328002790.259858899579.74014110042663
2428602813.4507484717846.5492515282194
2530402874.22553028466165.774469715336
2629203057.30720576994-137.30720576994
2729202940.30944246047-20.3094424604656
2831002936.35423283389163.645767166113
2936003117.59503159368482.404968406318
3036403627.3289971791712.6710028208304
3135403680.5820072962-140.582007296198
3233003579.3862451569-279.386245156896
3334803332.50355154191147.496448458091
3434803506.52441096381-26.5244109638106
3535003510.2435012485-10.2435012485025
3636003529.410206442570.5897935574958
3736803629.9051220378550.0948779621485
3837203712.372948585387.62705141462175
3937203753.81834091845-33.818340918448
4038403753.655166978886.3448330212027
4143003873.68181322378426.318186776221
4244204340.6998622112679.3001377887449
4344404473.1581445156-33.1581445155971
4441404494.95063760027-354.95063760027
4543004190.16037595449109.83962404551
4642404341.71444622629-101.71444622629
4741204283.58604939749-163.586049397487
4843804159.02868374734220.97131625266
4944404417.0025674908222.9974325091762
5043404483.26163691285-143.261636912845
5143604382.31724075583-22.3172407558259
5245004398.1781622944101.821837705596
5350204538.68703295262481.312967047379
5452805066.72835010873213.271649891273
5552805342.1494649173-62.1494649172992
5651605347.26634511447-187.266345114474
5753405223.52511153857116.47488846143
5851605399.71037799288-239.710377992876
5950605220.25047056319-160.25047056319
6054405111.97822830122328.021771698782
6155005491.215639969378.78436003063325
6253605560.22915841966-200.229158419659
6357205418.27424065707301.725759342932
6458605776.1367306913483.8632693086638
6562805925.25795996996354.742040030043
6665606351.42435575383208.575644246166
6765206643.35318842536-123.353188425359
6865006607.67185657322-107.671856573224
6966606583.1388401113276.8611598886782
7066406741.05387387657-101.05387387657
7164006722.03619429128-322.036194291281
7267606475.76079856458284.23920143542
7368806830.1203789778449.8796210221599
7467606958.39390937196-198.393909371956
7572606837.57627394861422.423726051392
7675007336.81102823962163.188971760379
7780607590.08252985156469.917470148443
7882808159.66726378932120.332736210677
7982208393.76034844554-173.760348445543
8081008335.12786849811-235.12786849811
8182008207.82811820137-7.82811820136521
8283208301.3503984732518.6496015267494
8379208421.34191693883-501.341916938825
8482408016.35617940237223.643820597633
8584408325.1774451422114.822554857803
8683608532.51520728531-172.515207285312
8788808453.74657480799426.253425192013
8890608973.7268003619186.2731996380899
8998209166.25971933749653.740280662512
9099609935.7674688529224.2325311470831
91978010093.804900572-313.804900572004
9298809911.02560002725-31.0256000272511
93994010002.1548912797-62.1548912796843
941000010060.6304877882-60.6304877882012
95962010118.2765355095-498.276535509491
9699809731.16915208268248.830847917323
971018010080.349700596899.6502994031543
98998010288.2059444455-308.205944445541
991056010087.5382194553472.461780544731
1001074010664.335951438575.6640485615026
1011152010858.008810824661.991189176018
1021164011647.3185477835-7.31854778354136
1031168011785.2346053633-105.234605363348
1041188011823.882694915556.1173050845264
1051188012021.6367146747-141.636714674703
1061196012021.6104854575-61.6104854575424
1071160012097.085081768-497.085081768044
1081178011729.964110717650.0358892824152
1091190011896.99904136783.00095863215938
1101168012018.3921463879-338.392146387945
1111232011794.7662861403525.233713859654
1121244012431.32157774338.67842225669301
1131324012565.6951450056674.304854994425
1141338013373.3187858966.68121410399908
1151358013531.722972751848.277027248243
1161376013732.43352718827.5664728119955
1171378013914.0479585256-134.04795852564
1181380013933.3287173178-133.328717317829
1191344013948.2238655227-508.223865522721
1201380013579.031196238220.968803762042

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2080 & 2080 & 0 \tabularnewline
4 & 2040 & 2060 & -20 \tabularnewline
5 & 2440 & 2019.78087899553 & 420.219121004465 \tabularnewline
6 & 2420 & 2423.84112050365 & -3.84112050365275 \tabularnewline
7 & 2120 & 2415.22269981618 & -295.222699816179 \tabularnewline
8 & 1920 & 2111.88380417405 & -191.883804174052 \tabularnewline
9 & 1940 & 1901.75588225666 & 38.2441177433441 \tabularnewline
10 & 1940 & 1916.95852276732 & 23.0414772326842 \tabularnewline
11 & 1960 & 1918.25063323757 & 41.7493667624294 \tabularnewline
12 & 2000 & 1939.33442428511 & 60.6655757148862 \tabularnewline
13 & 2120 & 1981.13403651272 & 138.865963487279 \tabularnewline
14 & 2080 & 2104.30465352748 & -24.3046535274766 \tabularnewline
15 & 2140 & 2067.81344372861 & 72.1865562713883 \tabularnewline
16 & 2240 & 2127.9436009104 & 112.0563990896 \tabularnewline
17 & 2800 & 2231.13368901255 & 568.866310987451 \tabularnewline
18 & 2800 & 2800.41247169985 & -0.412471699851721 \tabularnewline
19 & 2680 & 2815.87259144906 & -135.872591449056 \tabularnewline
20 & 2560 & 2694.37275146411 & -134.372751464109 \tabularnewline
21 & 2660 & 2569.20685850631 & 90.7931414936902 \tabularnewline
22 & 2780 & 2666.54866755179 & 113.45133244821 \tabularnewline
23 & 2800 & 2790.25985889957 & 9.74014110042663 \tabularnewline
24 & 2860 & 2813.45074847178 & 46.5492515282194 \tabularnewline
25 & 3040 & 2874.22553028466 & 165.774469715336 \tabularnewline
26 & 2920 & 3057.30720576994 & -137.30720576994 \tabularnewline
27 & 2920 & 2940.30944246047 & -20.3094424604656 \tabularnewline
28 & 3100 & 2936.35423283389 & 163.645767166113 \tabularnewline
29 & 3600 & 3117.59503159368 & 482.404968406318 \tabularnewline
30 & 3640 & 3627.32899717917 & 12.6710028208304 \tabularnewline
31 & 3540 & 3680.5820072962 & -140.582007296198 \tabularnewline
32 & 3300 & 3579.3862451569 & -279.386245156896 \tabularnewline
33 & 3480 & 3332.50355154191 & 147.496448458091 \tabularnewline
34 & 3480 & 3506.52441096381 & -26.5244109638106 \tabularnewline
35 & 3500 & 3510.2435012485 & -10.2435012485025 \tabularnewline
36 & 3600 & 3529.4102064425 & 70.5897935574958 \tabularnewline
37 & 3680 & 3629.90512203785 & 50.0948779621485 \tabularnewline
38 & 3720 & 3712.37294858538 & 7.62705141462175 \tabularnewline
39 & 3720 & 3753.81834091845 & -33.818340918448 \tabularnewline
40 & 3840 & 3753.6551669788 & 86.3448330212027 \tabularnewline
41 & 4300 & 3873.68181322378 & 426.318186776221 \tabularnewline
42 & 4420 & 4340.69986221126 & 79.3001377887449 \tabularnewline
43 & 4440 & 4473.1581445156 & -33.1581445155971 \tabularnewline
44 & 4140 & 4494.95063760027 & -354.95063760027 \tabularnewline
45 & 4300 & 4190.16037595449 & 109.83962404551 \tabularnewline
46 & 4240 & 4341.71444622629 & -101.71444622629 \tabularnewline
47 & 4120 & 4283.58604939749 & -163.586049397487 \tabularnewline
48 & 4380 & 4159.02868374734 & 220.97131625266 \tabularnewline
49 & 4440 & 4417.00256749082 & 22.9974325091762 \tabularnewline
50 & 4340 & 4483.26163691285 & -143.261636912845 \tabularnewline
51 & 4360 & 4382.31724075583 & -22.3172407558259 \tabularnewline
52 & 4500 & 4398.1781622944 & 101.821837705596 \tabularnewline
53 & 5020 & 4538.68703295262 & 481.312967047379 \tabularnewline
54 & 5280 & 5066.72835010873 & 213.271649891273 \tabularnewline
55 & 5280 & 5342.1494649173 & -62.1494649172992 \tabularnewline
56 & 5160 & 5347.26634511447 & -187.266345114474 \tabularnewline
57 & 5340 & 5223.52511153857 & 116.47488846143 \tabularnewline
58 & 5160 & 5399.71037799288 & -239.710377992876 \tabularnewline
59 & 5060 & 5220.25047056319 & -160.25047056319 \tabularnewline
60 & 5440 & 5111.97822830122 & 328.021771698782 \tabularnewline
61 & 5500 & 5491.21563996937 & 8.78436003063325 \tabularnewline
62 & 5360 & 5560.22915841966 & -200.229158419659 \tabularnewline
63 & 5720 & 5418.27424065707 & 301.725759342932 \tabularnewline
64 & 5860 & 5776.13673069134 & 83.8632693086638 \tabularnewline
65 & 6280 & 5925.25795996996 & 354.742040030043 \tabularnewline
66 & 6560 & 6351.42435575383 & 208.575644246166 \tabularnewline
67 & 6520 & 6643.35318842536 & -123.353188425359 \tabularnewline
68 & 6500 & 6607.67185657322 & -107.671856573224 \tabularnewline
69 & 6660 & 6583.13884011132 & 76.8611598886782 \tabularnewline
70 & 6640 & 6741.05387387657 & -101.05387387657 \tabularnewline
71 & 6400 & 6722.03619429128 & -322.036194291281 \tabularnewline
72 & 6760 & 6475.76079856458 & 284.23920143542 \tabularnewline
73 & 6880 & 6830.12037897784 & 49.8796210221599 \tabularnewline
74 & 6760 & 6958.39390937196 & -198.393909371956 \tabularnewline
75 & 7260 & 6837.57627394861 & 422.423726051392 \tabularnewline
76 & 7500 & 7336.81102823962 & 163.188971760379 \tabularnewline
77 & 8060 & 7590.08252985156 & 469.917470148443 \tabularnewline
78 & 8280 & 8159.66726378932 & 120.332736210677 \tabularnewline
79 & 8220 & 8393.76034844554 & -173.760348445543 \tabularnewline
80 & 8100 & 8335.12786849811 & -235.12786849811 \tabularnewline
81 & 8200 & 8207.82811820137 & -7.82811820136521 \tabularnewline
82 & 8320 & 8301.35039847325 & 18.6496015267494 \tabularnewline
83 & 7920 & 8421.34191693883 & -501.341916938825 \tabularnewline
84 & 8240 & 8016.35617940237 & 223.643820597633 \tabularnewline
85 & 8440 & 8325.1774451422 & 114.822554857803 \tabularnewline
86 & 8360 & 8532.51520728531 & -172.515207285312 \tabularnewline
87 & 8880 & 8453.74657480799 & 426.253425192013 \tabularnewline
88 & 9060 & 8973.72680036191 & 86.2731996380899 \tabularnewline
89 & 9820 & 9166.25971933749 & 653.740280662512 \tabularnewline
90 & 9960 & 9935.76746885292 & 24.2325311470831 \tabularnewline
91 & 9780 & 10093.804900572 & -313.804900572004 \tabularnewline
92 & 9880 & 9911.02560002725 & -31.0256000272511 \tabularnewline
93 & 9940 & 10002.1548912797 & -62.1548912796843 \tabularnewline
94 & 10000 & 10060.6304877882 & -60.6304877882012 \tabularnewline
95 & 9620 & 10118.2765355095 & -498.276535509491 \tabularnewline
96 & 9980 & 9731.16915208268 & 248.830847917323 \tabularnewline
97 & 10180 & 10080.3497005968 & 99.6502994031543 \tabularnewline
98 & 9980 & 10288.2059444455 & -308.205944445541 \tabularnewline
99 & 10560 & 10087.5382194553 & 472.461780544731 \tabularnewline
100 & 10740 & 10664.3359514385 & 75.6640485615026 \tabularnewline
101 & 11520 & 10858.008810824 & 661.991189176018 \tabularnewline
102 & 11640 & 11647.3185477835 & -7.31854778354136 \tabularnewline
103 & 11680 & 11785.2346053633 & -105.234605363348 \tabularnewline
104 & 11880 & 11823.8826949155 & 56.1173050845264 \tabularnewline
105 & 11880 & 12021.6367146747 & -141.636714674703 \tabularnewline
106 & 11960 & 12021.6104854575 & -61.6104854575424 \tabularnewline
107 & 11600 & 12097.085081768 & -497.085081768044 \tabularnewline
108 & 11780 & 11729.9641107176 & 50.0358892824152 \tabularnewline
109 & 11900 & 11896.9990413678 & 3.00095863215938 \tabularnewline
110 & 11680 & 12018.3921463879 & -338.392146387945 \tabularnewline
111 & 12320 & 11794.7662861403 & 525.233713859654 \tabularnewline
112 & 12440 & 12431.3215777433 & 8.67842225669301 \tabularnewline
113 & 13240 & 12565.6951450056 & 674.304854994425 \tabularnewline
114 & 13380 & 13373.318785896 & 6.68121410399908 \tabularnewline
115 & 13580 & 13531.7229727518 & 48.277027248243 \tabularnewline
116 & 13760 & 13732.433527188 & 27.5664728119955 \tabularnewline
117 & 13780 & 13914.0479585256 & -134.04795852564 \tabularnewline
118 & 13800 & 13933.3287173178 & -133.328717317829 \tabularnewline
119 & 13440 & 13948.2238655227 & -508.223865522721 \tabularnewline
120 & 13800 & 13579.031196238 & 220.968803762042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169313&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]3[/C][C]2080[/C][C]2080[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]2040[/C][C]2060[/C][C]-20[/C][/ROW]
[ROW][C]5[/C][C]2440[/C][C]2019.78087899553[/C][C]420.219121004465[/C][/ROW]
[ROW][C]6[/C][C]2420[/C][C]2423.84112050365[/C][C]-3.84112050365275[/C][/ROW]
[ROW][C]7[/C][C]2120[/C][C]2415.22269981618[/C][C]-295.222699816179[/C][/ROW]
[ROW][C]8[/C][C]1920[/C][C]2111.88380417405[/C][C]-191.883804174052[/C][/ROW]
[ROW][C]9[/C][C]1940[/C][C]1901.75588225666[/C][C]38.2441177433441[/C][/ROW]
[ROW][C]10[/C][C]1940[/C][C]1916.95852276732[/C][C]23.0414772326842[/C][/ROW]
[ROW][C]11[/C][C]1960[/C][C]1918.25063323757[/C][C]41.7493667624294[/C][/ROW]
[ROW][C]12[/C][C]2000[/C][C]1939.33442428511[/C][C]60.6655757148862[/C][/ROW]
[ROW][C]13[/C][C]2120[/C][C]1981.13403651272[/C][C]138.865963487279[/C][/ROW]
[ROW][C]14[/C][C]2080[/C][C]2104.30465352748[/C][C]-24.3046535274766[/C][/ROW]
[ROW][C]15[/C][C]2140[/C][C]2067.81344372861[/C][C]72.1865562713883[/C][/ROW]
[ROW][C]16[/C][C]2240[/C][C]2127.9436009104[/C][C]112.0563990896[/C][/ROW]
[ROW][C]17[/C][C]2800[/C][C]2231.13368901255[/C][C]568.866310987451[/C][/ROW]
[ROW][C]18[/C][C]2800[/C][C]2800.41247169985[/C][C]-0.412471699851721[/C][/ROW]
[ROW][C]19[/C][C]2680[/C][C]2815.87259144906[/C][C]-135.872591449056[/C][/ROW]
[ROW][C]20[/C][C]2560[/C][C]2694.37275146411[/C][C]-134.372751464109[/C][/ROW]
[ROW][C]21[/C][C]2660[/C][C]2569.20685850631[/C][C]90.7931414936902[/C][/ROW]
[ROW][C]22[/C][C]2780[/C][C]2666.54866755179[/C][C]113.45133244821[/C][/ROW]
[ROW][C]23[/C][C]2800[/C][C]2790.25985889957[/C][C]9.74014110042663[/C][/ROW]
[ROW][C]24[/C][C]2860[/C][C]2813.45074847178[/C][C]46.5492515282194[/C][/ROW]
[ROW][C]25[/C][C]3040[/C][C]2874.22553028466[/C][C]165.774469715336[/C][/ROW]
[ROW][C]26[/C][C]2920[/C][C]3057.30720576994[/C][C]-137.30720576994[/C][/ROW]
[ROW][C]27[/C][C]2920[/C][C]2940.30944246047[/C][C]-20.3094424604656[/C][/ROW]
[ROW][C]28[/C][C]3100[/C][C]2936.35423283389[/C][C]163.645767166113[/C][/ROW]
[ROW][C]29[/C][C]3600[/C][C]3117.59503159368[/C][C]482.404968406318[/C][/ROW]
[ROW][C]30[/C][C]3640[/C][C]3627.32899717917[/C][C]12.6710028208304[/C][/ROW]
[ROW][C]31[/C][C]3540[/C][C]3680.5820072962[/C][C]-140.582007296198[/C][/ROW]
[ROW][C]32[/C][C]3300[/C][C]3579.3862451569[/C][C]-279.386245156896[/C][/ROW]
[ROW][C]33[/C][C]3480[/C][C]3332.50355154191[/C][C]147.496448458091[/C][/ROW]
[ROW][C]34[/C][C]3480[/C][C]3506.52441096381[/C][C]-26.5244109638106[/C][/ROW]
[ROW][C]35[/C][C]3500[/C][C]3510.2435012485[/C][C]-10.2435012485025[/C][/ROW]
[ROW][C]36[/C][C]3600[/C][C]3529.4102064425[/C][C]70.5897935574958[/C][/ROW]
[ROW][C]37[/C][C]3680[/C][C]3629.90512203785[/C][C]50.0948779621485[/C][/ROW]
[ROW][C]38[/C][C]3720[/C][C]3712.37294858538[/C][C]7.62705141462175[/C][/ROW]
[ROW][C]39[/C][C]3720[/C][C]3753.81834091845[/C][C]-33.818340918448[/C][/ROW]
[ROW][C]40[/C][C]3840[/C][C]3753.6551669788[/C][C]86.3448330212027[/C][/ROW]
[ROW][C]41[/C][C]4300[/C][C]3873.68181322378[/C][C]426.318186776221[/C][/ROW]
[ROW][C]42[/C][C]4420[/C][C]4340.69986221126[/C][C]79.3001377887449[/C][/ROW]
[ROW][C]43[/C][C]4440[/C][C]4473.1581445156[/C][C]-33.1581445155971[/C][/ROW]
[ROW][C]44[/C][C]4140[/C][C]4494.95063760027[/C][C]-354.95063760027[/C][/ROW]
[ROW][C]45[/C][C]4300[/C][C]4190.16037595449[/C][C]109.83962404551[/C][/ROW]
[ROW][C]46[/C][C]4240[/C][C]4341.71444622629[/C][C]-101.71444622629[/C][/ROW]
[ROW][C]47[/C][C]4120[/C][C]4283.58604939749[/C][C]-163.586049397487[/C][/ROW]
[ROW][C]48[/C][C]4380[/C][C]4159.02868374734[/C][C]220.97131625266[/C][/ROW]
[ROW][C]49[/C][C]4440[/C][C]4417.00256749082[/C][C]22.9974325091762[/C][/ROW]
[ROW][C]50[/C][C]4340[/C][C]4483.26163691285[/C][C]-143.261636912845[/C][/ROW]
[ROW][C]51[/C][C]4360[/C][C]4382.31724075583[/C][C]-22.3172407558259[/C][/ROW]
[ROW][C]52[/C][C]4500[/C][C]4398.1781622944[/C][C]101.821837705596[/C][/ROW]
[ROW][C]53[/C][C]5020[/C][C]4538.68703295262[/C][C]481.312967047379[/C][/ROW]
[ROW][C]54[/C][C]5280[/C][C]5066.72835010873[/C][C]213.271649891273[/C][/ROW]
[ROW][C]55[/C][C]5280[/C][C]5342.1494649173[/C][C]-62.1494649172992[/C][/ROW]
[ROW][C]56[/C][C]5160[/C][C]5347.26634511447[/C][C]-187.266345114474[/C][/ROW]
[ROW][C]57[/C][C]5340[/C][C]5223.52511153857[/C][C]116.47488846143[/C][/ROW]
[ROW][C]58[/C][C]5160[/C][C]5399.71037799288[/C][C]-239.710377992876[/C][/ROW]
[ROW][C]59[/C][C]5060[/C][C]5220.25047056319[/C][C]-160.25047056319[/C][/ROW]
[ROW][C]60[/C][C]5440[/C][C]5111.97822830122[/C][C]328.021771698782[/C][/ROW]
[ROW][C]61[/C][C]5500[/C][C]5491.21563996937[/C][C]8.78436003063325[/C][/ROW]
[ROW][C]62[/C][C]5360[/C][C]5560.22915841966[/C][C]-200.229158419659[/C][/ROW]
[ROW][C]63[/C][C]5720[/C][C]5418.27424065707[/C][C]301.725759342932[/C][/ROW]
[ROW][C]64[/C][C]5860[/C][C]5776.13673069134[/C][C]83.8632693086638[/C][/ROW]
[ROW][C]65[/C][C]6280[/C][C]5925.25795996996[/C][C]354.742040030043[/C][/ROW]
[ROW][C]66[/C][C]6560[/C][C]6351.42435575383[/C][C]208.575644246166[/C][/ROW]
[ROW][C]67[/C][C]6520[/C][C]6643.35318842536[/C][C]-123.353188425359[/C][/ROW]
[ROW][C]68[/C][C]6500[/C][C]6607.67185657322[/C][C]-107.671856573224[/C][/ROW]
[ROW][C]69[/C][C]6660[/C][C]6583.13884011132[/C][C]76.8611598886782[/C][/ROW]
[ROW][C]70[/C][C]6640[/C][C]6741.05387387657[/C][C]-101.05387387657[/C][/ROW]
[ROW][C]71[/C][C]6400[/C][C]6722.03619429128[/C][C]-322.036194291281[/C][/ROW]
[ROW][C]72[/C][C]6760[/C][C]6475.76079856458[/C][C]284.23920143542[/C][/ROW]
[ROW][C]73[/C][C]6880[/C][C]6830.12037897784[/C][C]49.8796210221599[/C][/ROW]
[ROW][C]74[/C][C]6760[/C][C]6958.39390937196[/C][C]-198.393909371956[/C][/ROW]
[ROW][C]75[/C][C]7260[/C][C]6837.57627394861[/C][C]422.423726051392[/C][/ROW]
[ROW][C]76[/C][C]7500[/C][C]7336.81102823962[/C][C]163.188971760379[/C][/ROW]
[ROW][C]77[/C][C]8060[/C][C]7590.08252985156[/C][C]469.917470148443[/C][/ROW]
[ROW][C]78[/C][C]8280[/C][C]8159.66726378932[/C][C]120.332736210677[/C][/ROW]
[ROW][C]79[/C][C]8220[/C][C]8393.76034844554[/C][C]-173.760348445543[/C][/ROW]
[ROW][C]80[/C][C]8100[/C][C]8335.12786849811[/C][C]-235.12786849811[/C][/ROW]
[ROW][C]81[/C][C]8200[/C][C]8207.82811820137[/C][C]-7.82811820136521[/C][/ROW]
[ROW][C]82[/C][C]8320[/C][C]8301.35039847325[/C][C]18.6496015267494[/C][/ROW]
[ROW][C]83[/C][C]7920[/C][C]8421.34191693883[/C][C]-501.341916938825[/C][/ROW]
[ROW][C]84[/C][C]8240[/C][C]8016.35617940237[/C][C]223.643820597633[/C][/ROW]
[ROW][C]85[/C][C]8440[/C][C]8325.1774451422[/C][C]114.822554857803[/C][/ROW]
[ROW][C]86[/C][C]8360[/C][C]8532.51520728531[/C][C]-172.515207285312[/C][/ROW]
[ROW][C]87[/C][C]8880[/C][C]8453.74657480799[/C][C]426.253425192013[/C][/ROW]
[ROW][C]88[/C][C]9060[/C][C]8973.72680036191[/C][C]86.2731996380899[/C][/ROW]
[ROW][C]89[/C][C]9820[/C][C]9166.25971933749[/C][C]653.740280662512[/C][/ROW]
[ROW][C]90[/C][C]9960[/C][C]9935.76746885292[/C][C]24.2325311470831[/C][/ROW]
[ROW][C]91[/C][C]9780[/C][C]10093.804900572[/C][C]-313.804900572004[/C][/ROW]
[ROW][C]92[/C][C]9880[/C][C]9911.02560002725[/C][C]-31.0256000272511[/C][/ROW]
[ROW][C]93[/C][C]9940[/C][C]10002.1548912797[/C][C]-62.1548912796843[/C][/ROW]
[ROW][C]94[/C][C]10000[/C][C]10060.6304877882[/C][C]-60.6304877882012[/C][/ROW]
[ROW][C]95[/C][C]9620[/C][C]10118.2765355095[/C][C]-498.276535509491[/C][/ROW]
[ROW][C]96[/C][C]9980[/C][C]9731.16915208268[/C][C]248.830847917323[/C][/ROW]
[ROW][C]97[/C][C]10180[/C][C]10080.3497005968[/C][C]99.6502994031543[/C][/ROW]
[ROW][C]98[/C][C]9980[/C][C]10288.2059444455[/C][C]-308.205944445541[/C][/ROW]
[ROW][C]99[/C][C]10560[/C][C]10087.5382194553[/C][C]472.461780544731[/C][/ROW]
[ROW][C]100[/C][C]10740[/C][C]10664.3359514385[/C][C]75.6640485615026[/C][/ROW]
[ROW][C]101[/C][C]11520[/C][C]10858.008810824[/C][C]661.991189176018[/C][/ROW]
[ROW][C]102[/C][C]11640[/C][C]11647.3185477835[/C][C]-7.31854778354136[/C][/ROW]
[ROW][C]103[/C][C]11680[/C][C]11785.2346053633[/C][C]-105.234605363348[/C][/ROW]
[ROW][C]104[/C][C]11880[/C][C]11823.8826949155[/C][C]56.1173050845264[/C][/ROW]
[ROW][C]105[/C][C]11880[/C][C]12021.6367146747[/C][C]-141.636714674703[/C][/ROW]
[ROW][C]106[/C][C]11960[/C][C]12021.6104854575[/C][C]-61.6104854575424[/C][/ROW]
[ROW][C]107[/C][C]11600[/C][C]12097.085081768[/C][C]-497.085081768044[/C][/ROW]
[ROW][C]108[/C][C]11780[/C][C]11729.9641107176[/C][C]50.0358892824152[/C][/ROW]
[ROW][C]109[/C][C]11900[/C][C]11896.9990413678[/C][C]3.00095863215938[/C][/ROW]
[ROW][C]110[/C][C]11680[/C][C]12018.3921463879[/C][C]-338.392146387945[/C][/ROW]
[ROW][C]111[/C][C]12320[/C][C]11794.7662861403[/C][C]525.233713859654[/C][/ROW]
[ROW][C]112[/C][C]12440[/C][C]12431.3215777433[/C][C]8.67842225669301[/C][/ROW]
[ROW][C]113[/C][C]13240[/C][C]12565.6951450056[/C][C]674.304854994425[/C][/ROW]
[ROW][C]114[/C][C]13380[/C][C]13373.318785896[/C][C]6.68121410399908[/C][/ROW]
[ROW][C]115[/C][C]13580[/C][C]13531.7229727518[/C][C]48.277027248243[/C][/ROW]
[ROW][C]116[/C][C]13760[/C][C]13732.433527188[/C][C]27.5664728119955[/C][/ROW]
[ROW][C]117[/C][C]13780[/C][C]13914.0479585256[/C][C]-134.04795852564[/C][/ROW]
[ROW][C]118[/C][C]13800[/C][C]13933.3287173178[/C][C]-133.328717317829[/C][/ROW]
[ROW][C]119[/C][C]13440[/C][C]13948.2238655227[/C][C]-508.223865522721[/C][/ROW]
[ROW][C]120[/C][C]13800[/C][C]13579.031196238[/C][C]220.968803762042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169313&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
3208020800
420402060-20
524402019.78087899553420.219121004465
624202423.84112050365-3.84112050365275
721202415.22269981618-295.222699816179
819202111.88380417405-191.883804174052
919401901.7558822566638.2441177433441
1019401916.9585227673223.0414772326842
1119601918.2506332375741.7493667624294
1220001939.3344242851160.6655757148862
1321201981.13403651272138.865963487279
1420802104.30465352748-24.3046535274766
1521402067.8134437286172.1865562713883
1622402127.9436009104112.0563990896
1728002231.13368901255568.866310987451
1828002800.41247169985-0.412471699851721
1926802815.87259144906-135.872591449056
2025602694.37275146411-134.372751464109
2126602569.2068585063190.7931414936902
2227802666.54866755179113.45133244821
2328002790.259858899579.74014110042663
2428602813.4507484717846.5492515282194
2530402874.22553028466165.774469715336
2629203057.30720576994-137.30720576994
2729202940.30944246047-20.3094424604656
2831002936.35423283389163.645767166113
2936003117.59503159368482.404968406318
3036403627.3289971791712.6710028208304
3135403680.5820072962-140.582007296198
3233003579.3862451569-279.386245156896
3334803332.50355154191147.496448458091
3434803506.52441096381-26.5244109638106
3535003510.2435012485-10.2435012485025
3636003529.410206442570.5897935574958
3736803629.9051220378550.0948779621485
3837203712.372948585387.62705141462175
3937203753.81834091845-33.818340918448
4038403753.655166978886.3448330212027
4143003873.68181322378426.318186776221
4244204340.6998622112679.3001377887449
4344404473.1581445156-33.1581445155971
4441404494.95063760027-354.95063760027
4543004190.16037595449109.83962404551
4642404341.71444622629-101.71444622629
4741204283.58604939749-163.586049397487
4843804159.02868374734220.97131625266
4944404417.0025674908222.9974325091762
5043404483.26163691285-143.261636912845
5143604382.31724075583-22.3172407558259
5245004398.1781622944101.821837705596
5350204538.68703295262481.312967047379
5452805066.72835010873213.271649891273
5552805342.1494649173-62.1494649172992
5651605347.26634511447-187.266345114474
5753405223.52511153857116.47488846143
5851605399.71037799288-239.710377992876
5950605220.25047056319-160.25047056319
6054405111.97822830122328.021771698782
6155005491.215639969378.78436003063325
6253605560.22915841966-200.229158419659
6357205418.27424065707301.725759342932
6458605776.1367306913483.8632693086638
6562805925.25795996996354.742040030043
6665606351.42435575383208.575644246166
6765206643.35318842536-123.353188425359
6865006607.67185657322-107.671856573224
6966606583.1388401113276.8611598886782
7066406741.05387387657-101.05387387657
7164006722.03619429128-322.036194291281
7267606475.76079856458284.23920143542
7368806830.1203789778449.8796210221599
7467606958.39390937196-198.393909371956
7572606837.57627394861422.423726051392
7675007336.81102823962163.188971760379
7780607590.08252985156469.917470148443
7882808159.66726378932120.332736210677
7982208393.76034844554-173.760348445543
8081008335.12786849811-235.12786849811
8182008207.82811820137-7.82811820136521
8283208301.3503984732518.6496015267494
8379208421.34191693883-501.341916938825
8482408016.35617940237223.643820597633
8584408325.1774451422114.822554857803
8683608532.51520728531-172.515207285312
8788808453.74657480799426.253425192013
8890608973.7268003619186.2731996380899
8998209166.25971933749653.740280662512
9099609935.7674688529224.2325311470831
91978010093.804900572-313.804900572004
9298809911.02560002725-31.0256000272511
93994010002.1548912797-62.1548912796843
941000010060.6304877882-60.6304877882012
95962010118.2765355095-498.276535509491
9699809731.16915208268248.830847917323
971018010080.349700596899.6502994031543
98998010288.2059444455-308.205944445541
991056010087.5382194553472.461780544731
1001074010664.335951438575.6640485615026
1011152010858.008810824661.991189176018
1021164011647.3185477835-7.31854778354136
1031168011785.2346053633-105.234605363348
1041188011823.882694915556.1173050845264
1051188012021.6367146747-141.636714674703
1061196012021.6104854575-61.6104854575424
1071160012097.085081768-497.085081768044
1081178011729.964110717650.0358892824152
1091190011896.99904136783.00095863215938
1101168012018.3921463879-338.392146387945
1111232011794.7662861403525.233713859654
1121244012431.32157774338.67842225669301
1131324012565.6951450056674.304854994425
1141338013373.3187858966.68121410399908
1151358013531.722972751848.277027248243
1161376013732.43352718827.5664728119955
1171378013914.0479585256-134.04795852564
1181380013933.3287173178-133.328717317829
1191344013948.2238655227-508.223865522721
1201380013579.031196238220.968803762042







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12113927.636068488213457.459001620114397.8131353562
12214061.279177070713392.695962408714729.8623917328
12314194.922285653313364.073124926515025.77144638
12414328.565394235813353.05009353215304.0806949396
12514462.208502818413352.431036003715571.9859696331
12614595.851611400913358.563735218315833.1394875835
12714729.494719983413369.311247489816089.6781924771
12814863.13782856613383.305883519516342.9697736125
12914996.780937148513399.616262609716593.9456116873
13015130.424045731113417.578605030116843.269486432
13115264.067154313613436.703125766817091.4311828605
13215397.710262896213456.618417123117338.8021086692

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 13927.6360684882 & 13457.4590016201 & 14397.8131353562 \tabularnewline
122 & 14061.2791770707 & 13392.6959624087 & 14729.8623917328 \tabularnewline
123 & 14194.9222856533 & 13364.0731249265 & 15025.77144638 \tabularnewline
124 & 14328.5653942358 & 13353.050093532 & 15304.0806949396 \tabularnewline
125 & 14462.2085028184 & 13352.4310360037 & 15571.9859696331 \tabularnewline
126 & 14595.8516114009 & 13358.5637352183 & 15833.1394875835 \tabularnewline
127 & 14729.4947199834 & 13369.3112474898 & 16089.6781924771 \tabularnewline
128 & 14863.137828566 & 13383.3058835195 & 16342.9697736125 \tabularnewline
129 & 14996.7809371485 & 13399.6162626097 & 16593.9456116873 \tabularnewline
130 & 15130.4240457311 & 13417.5786050301 & 16843.269486432 \tabularnewline
131 & 15264.0671543136 & 13436.7031257668 & 17091.4311828605 \tabularnewline
132 & 15397.7102628962 & 13456.6184171231 & 17338.8021086692 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169313&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]121[/C][C]13927.6360684882[/C][C]13457.4590016201[/C][C]14397.8131353562[/C][/ROW]
[ROW][C]122[/C][C]14061.2791770707[/C][C]13392.6959624087[/C][C]14729.8623917328[/C][/ROW]
[ROW][C]123[/C][C]14194.9222856533[/C][C]13364.0731249265[/C][C]15025.77144638[/C][/ROW]
[ROW][C]124[/C][C]14328.5653942358[/C][C]13353.050093532[/C][C]15304.0806949396[/C][/ROW]
[ROW][C]125[/C][C]14462.2085028184[/C][C]13352.4310360037[/C][C]15571.9859696331[/C][/ROW]
[ROW][C]126[/C][C]14595.8516114009[/C][C]13358.5637352183[/C][C]15833.1394875835[/C][/ROW]
[ROW][C]127[/C][C]14729.4947199834[/C][C]13369.3112474898[/C][C]16089.6781924771[/C][/ROW]
[ROW][C]128[/C][C]14863.137828566[/C][C]13383.3058835195[/C][C]16342.9697736125[/C][/ROW]
[ROW][C]129[/C][C]14996.7809371485[/C][C]13399.6162626097[/C][C]16593.9456116873[/C][/ROW]
[ROW][C]130[/C][C]15130.4240457311[/C][C]13417.5786050301[/C][C]16843.269486432[/C][/ROW]
[ROW][C]131[/C][C]15264.0671543136[/C][C]13436.7031257668[/C][C]17091.4311828605[/C][/ROW]
[ROW][C]132[/C][C]15397.7102628962[/C][C]13456.6184171231[/C][C]17338.8021086692[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169313&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169313&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
12113927.636068488213457.459001620114397.8131353562
12214061.279177070713392.695962408714729.8623917328
12314194.922285653313364.073124926515025.77144638
12414328.565394235813353.05009353215304.0806949396
12514462.208502818413352.431036003715571.9859696331
12614595.851611400913358.563735218315833.1394875835
12714729.494719983413369.311247489816089.6781924771
12814863.13782856613383.305883519516342.9697736125
12914996.780937148513399.616262609716593.9456116873
13015130.424045731113417.578605030116843.269486432
13115264.067154313613436.703125766817091.4311828605
13215397.710262896213456.618417123117338.8021086692



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')