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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Dec 2016 16:01:30 +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/22/t1482419132fhml9ggkt3erkrl.htm/, Retrieved Sun, 28 Apr 2024 19:19:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302546, Retrieved Sun, 28 Apr 2024 19:19:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-22 15:01:30] [55eb8f21ed24cda91766c505eb72bb6f] [Current]
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Dataseries X:
3949.9
4010.65
4381.8
4238.25
4178.1
4702.25
3944.1
4208.5
4743.45
4948.25
4735.45
4843.15
4757.75
5227.15
5739.65
4981.45
5020.05
5149.15
4513.35
4762.55
4990.45
4963.35
5010
4983.3
4924.7
5175.25
5470.3
4969.4
5020.5
5519.2
4510.75
4934.45
5430.65
5254.7
4897.8
5305.7
5055.7
5409
5683
5125.55
4965.2
5373.3
4556.1
4714.25
5513.85
5258.45
5111.4
5422.25
4753.3
5455.5
5909.15
5524.4
5477.8
5907.75
5072.55
5171
5871.4
5812.45
5692.2
5838.1
5438.2
6041.05
6335.6
5891.8
5909.65
6449.75
5312.25
5828.1
6466.15
6328.35
6131.8
6734.2
6037.25
6412.4
6785.55
6386
6045.25
6597.25
5355.9
5773.35
6539.6
6149.2
6373.45
6504.7
5451.25
6119.9
6954.95
6139.7
6383.25
6643.7
5547.75
5974
6583.6
6571.55
5736.5
6027.2
5302.65
5825.85
5910.6
5733.65
5914.3
6128.25
5680.5
5926.3
6270.5
6263
6064.55
5706.6
5365
5884.2
6504.4
6174.3
6123.65
6698.95
5256.55
5838.2




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=302546&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=302546&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302546&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
alpha0.471568377610894
beta0.0305461513693716
gamma0.60596264204978

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.471568377610894 \tabularnewline
beta & 0.0305461513693716 \tabularnewline
gamma & 0.60596264204978 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302546&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]0.471568377610894[/C][/ROW]
[ROW][C]beta[/C][C]0.0305461513693716[/C][/ROW]
[ROW][C]gamma[/C][C]0.60596264204978[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302546&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302546&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
alpha0.471568377610894
beta0.0305461513693716
gamma0.60596264204978







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134757.754374.12659685749383.623403142514
145227.155015.7823163907211.367683609301
155739.655646.7560466198992.8939533801076
164981.454987.64250876495-6.19250876495062
175020.055071.05518616349-51.0051861634902
185149.155219.35960035327-70.2096003532661
194513.354526.2838084324-12.9338084324008
204762.554786.80287772516-24.2528777251646
214990.455316.26331398277-325.813313982767
224963.355340.74188620844-377.391886208443
2350104919.4512700050390.5487299949664
244983.35067.43255669506-84.1325566950618
254924.75075.84328568742-151.143285687424
265175.255421.95532176953-246.705321769527
275470.35789.76155218134-319.461552181345
284969.44894.2227321238475.1772678761636
295020.54981.05575585539.4442441450001
305519.25145.57268504884373.627314951157
314510.754647.58411653246-136.834116532465
324934.454835.4005946451199.049405354891
335430.655319.62959368141111.020406318587
345254.75528.979265934-274.279265933998
354897.85290.54905492057-392.749054920566
365305.75142.16128158966163.538718410343
375055.75235.56518990928-179.865189909285
3854095539.2454864518-130.245486451799
3956835946.84871713937-263.848717139373
405125.555162.71217821242-37.1621782124221
414965.25176.34816124907-211.148161249067
425373.35315.5347536251657.7652463748364
434556.14505.7184892646650.3815107353448
444714.254843.62989608976-129.379896089756
455513.855195.6455910725318.204408927496
465258.455362.99876443294-104.548764432938
475111.45150.47244057857-39.0724405785732
485422.255344.8115653247177.4384346752877
494753.35276.03545655971-522.735456559708
505455.55415.0738812326440.4261187673637
515909.155846.2671900395162.8828099604934
525524.45267.18123345736257.218766542637
535477.85357.37217205033120.427827949669
545907.755765.2938081915142.456191808496
555072.554920.05683727612152.493162723882
5651715275.29160254643-104.291602546426
575871.45839.0311688503532.3688311496498
585812.455726.1390676609586.3109323390472
595692.25612.7664262688479.4335737311549
605838.15928.92548873624-90.8254887362436
615438.25554.03370723527-115.833707235272
626041.056146.17372839518-105.123728395176
636335.66571.05237879632-235.452378796315
645891.85860.5419396478431.2580603521628
655909.655792.722140981116.927859019003
666449.756229.50086762079220.249132379212
675312.255352.0163451828-39.7663451827975
685828.15542.24646262067285.853537379333
696466.156396.2778914823569.8721085176485
706328.356309.1392853276519.2107146723456
716131.86148.38091593592-16.5809159359223
726734.26382.43088777437351.769112225628
736037.256172.17946197867-134.929461978674
746412.46840.24068203049-427.840682030486
756785.557112.09680582495-326.546805824954
7663866398.15919576576-12.1591957657583
776045.256331.93562860496-286.685628604961
786597.256626.66654872077-29.4165487207692
795355.95506.27159790752-150.37159790752
805773.355744.3084681192629.0415318807427
816539.66393.61811510829145.981884891708
826149.26314.04487846826-164.844878468261
836373.456044.11009753071329.33990246929
846504.76550.27327486525-45.5732748652508
855451.255993.77641736667-542.526417366667
866119.96317.96875236566-198.068752365661
876954.956688.57858626911266.371413730885
886139.76347.11278663066-207.412786630655
896383.256089.79714398778293.452856012224
906643.76745.10483603532-101.404836035318
915547.755529.7065006557818.0434993442232
9259745911.401321324262.5986786757976
936583.66630.35457341638-46.7545734163787
946571.556350.34079105237221.209208947634
955736.56415.77792954126-679.277929541259
966027.26304.80577956878-277.605779568783
975302.655493.96770754871-191.31770754871
985825.856061.25483694179-235.404836941791
995910.66526.73168748042-616.131687480423
1005733.655653.285463733380.3645362667021
1015914.35671.00331184932243.296688150679
1026128.256122.35898265055.89101734949963
1035680.55071.36017217867609.139827821326
1045926.35724.25354571438202.046454285623
1056270.56450.72063086437-180.220630864371
10662636189.328311305773.6716886942995
1076064.555890.8126357366173.737364263405
1085706.66314.68397238468-608.083972384678
10953655377.12303381071-12.1230338107089
1105884.26015.53660437855-131.336604378551
1116504.46405.0769809201999.3230190798131
1126174.36077.1299156319297.170084368081
1136123.656165.6711943412-42.021194341196
1146698.956424.96813804397273.981861956026
1155256.555630.78921222273-374.239212222733
1165838.25678.25489140401159.945108595992

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4757.75 & 4374.12659685749 & 383.623403142514 \tabularnewline
14 & 5227.15 & 5015.7823163907 & 211.367683609301 \tabularnewline
15 & 5739.65 & 5646.75604661989 & 92.8939533801076 \tabularnewline
16 & 4981.45 & 4987.64250876495 & -6.19250876495062 \tabularnewline
17 & 5020.05 & 5071.05518616349 & -51.0051861634902 \tabularnewline
18 & 5149.15 & 5219.35960035327 & -70.2096003532661 \tabularnewline
19 & 4513.35 & 4526.2838084324 & -12.9338084324008 \tabularnewline
20 & 4762.55 & 4786.80287772516 & -24.2528777251646 \tabularnewline
21 & 4990.45 & 5316.26331398277 & -325.813313982767 \tabularnewline
22 & 4963.35 & 5340.74188620844 & -377.391886208443 \tabularnewline
23 & 5010 & 4919.45127000503 & 90.5487299949664 \tabularnewline
24 & 4983.3 & 5067.43255669506 & -84.1325566950618 \tabularnewline
25 & 4924.7 & 5075.84328568742 & -151.143285687424 \tabularnewline
26 & 5175.25 & 5421.95532176953 & -246.705321769527 \tabularnewline
27 & 5470.3 & 5789.76155218134 & -319.461552181345 \tabularnewline
28 & 4969.4 & 4894.22273212384 & 75.1772678761636 \tabularnewline
29 & 5020.5 & 4981.055755855 & 39.4442441450001 \tabularnewline
30 & 5519.2 & 5145.57268504884 & 373.627314951157 \tabularnewline
31 & 4510.75 & 4647.58411653246 & -136.834116532465 \tabularnewline
32 & 4934.45 & 4835.40059464511 & 99.049405354891 \tabularnewline
33 & 5430.65 & 5319.62959368141 & 111.020406318587 \tabularnewline
34 & 5254.7 & 5528.979265934 & -274.279265933998 \tabularnewline
35 & 4897.8 & 5290.54905492057 & -392.749054920566 \tabularnewline
36 & 5305.7 & 5142.16128158966 & 163.538718410343 \tabularnewline
37 & 5055.7 & 5235.56518990928 & -179.865189909285 \tabularnewline
38 & 5409 & 5539.2454864518 & -130.245486451799 \tabularnewline
39 & 5683 & 5946.84871713937 & -263.848717139373 \tabularnewline
40 & 5125.55 & 5162.71217821242 & -37.1621782124221 \tabularnewline
41 & 4965.2 & 5176.34816124907 & -211.148161249067 \tabularnewline
42 & 5373.3 & 5315.53475362516 & 57.7652463748364 \tabularnewline
43 & 4556.1 & 4505.71848926466 & 50.3815107353448 \tabularnewline
44 & 4714.25 & 4843.62989608976 & -129.379896089756 \tabularnewline
45 & 5513.85 & 5195.6455910725 & 318.204408927496 \tabularnewline
46 & 5258.45 & 5362.99876443294 & -104.548764432938 \tabularnewline
47 & 5111.4 & 5150.47244057857 & -39.0724405785732 \tabularnewline
48 & 5422.25 & 5344.81156532471 & 77.4384346752877 \tabularnewline
49 & 4753.3 & 5276.03545655971 & -522.735456559708 \tabularnewline
50 & 5455.5 & 5415.07388123264 & 40.4261187673637 \tabularnewline
51 & 5909.15 & 5846.26719003951 & 62.8828099604934 \tabularnewline
52 & 5524.4 & 5267.18123345736 & 257.218766542637 \tabularnewline
53 & 5477.8 & 5357.37217205033 & 120.427827949669 \tabularnewline
54 & 5907.75 & 5765.2938081915 & 142.456191808496 \tabularnewline
55 & 5072.55 & 4920.05683727612 & 152.493162723882 \tabularnewline
56 & 5171 & 5275.29160254643 & -104.291602546426 \tabularnewline
57 & 5871.4 & 5839.03116885035 & 32.3688311496498 \tabularnewline
58 & 5812.45 & 5726.13906766095 & 86.3109323390472 \tabularnewline
59 & 5692.2 & 5612.76642626884 & 79.4335737311549 \tabularnewline
60 & 5838.1 & 5928.92548873624 & -90.8254887362436 \tabularnewline
61 & 5438.2 & 5554.03370723527 & -115.833707235272 \tabularnewline
62 & 6041.05 & 6146.17372839518 & -105.123728395176 \tabularnewline
63 & 6335.6 & 6571.05237879632 & -235.452378796315 \tabularnewline
64 & 5891.8 & 5860.54193964784 & 31.2580603521628 \tabularnewline
65 & 5909.65 & 5792.722140981 & 116.927859019003 \tabularnewline
66 & 6449.75 & 6229.50086762079 & 220.249132379212 \tabularnewline
67 & 5312.25 & 5352.0163451828 & -39.7663451827975 \tabularnewline
68 & 5828.1 & 5542.24646262067 & 285.853537379333 \tabularnewline
69 & 6466.15 & 6396.27789148235 & 69.8721085176485 \tabularnewline
70 & 6328.35 & 6309.13928532765 & 19.2107146723456 \tabularnewline
71 & 6131.8 & 6148.38091593592 & -16.5809159359223 \tabularnewline
72 & 6734.2 & 6382.43088777437 & 351.769112225628 \tabularnewline
73 & 6037.25 & 6172.17946197867 & -134.929461978674 \tabularnewline
74 & 6412.4 & 6840.24068203049 & -427.840682030486 \tabularnewline
75 & 6785.55 & 7112.09680582495 & -326.546805824954 \tabularnewline
76 & 6386 & 6398.15919576576 & -12.1591957657583 \tabularnewline
77 & 6045.25 & 6331.93562860496 & -286.685628604961 \tabularnewline
78 & 6597.25 & 6626.66654872077 & -29.4165487207692 \tabularnewline
79 & 5355.9 & 5506.27159790752 & -150.37159790752 \tabularnewline
80 & 5773.35 & 5744.30846811926 & 29.0415318807427 \tabularnewline
81 & 6539.6 & 6393.61811510829 & 145.981884891708 \tabularnewline
82 & 6149.2 & 6314.04487846826 & -164.844878468261 \tabularnewline
83 & 6373.45 & 6044.11009753071 & 329.33990246929 \tabularnewline
84 & 6504.7 & 6550.27327486525 & -45.5732748652508 \tabularnewline
85 & 5451.25 & 5993.77641736667 & -542.526417366667 \tabularnewline
86 & 6119.9 & 6317.96875236566 & -198.068752365661 \tabularnewline
87 & 6954.95 & 6688.57858626911 & 266.371413730885 \tabularnewline
88 & 6139.7 & 6347.11278663066 & -207.412786630655 \tabularnewline
89 & 6383.25 & 6089.79714398778 & 293.452856012224 \tabularnewline
90 & 6643.7 & 6745.10483603532 & -101.404836035318 \tabularnewline
91 & 5547.75 & 5529.70650065578 & 18.0434993442232 \tabularnewline
92 & 5974 & 5911.4013213242 & 62.5986786757976 \tabularnewline
93 & 6583.6 & 6630.35457341638 & -46.7545734163787 \tabularnewline
94 & 6571.55 & 6350.34079105237 & 221.209208947634 \tabularnewline
95 & 5736.5 & 6415.77792954126 & -679.277929541259 \tabularnewline
96 & 6027.2 & 6304.80577956878 & -277.605779568783 \tabularnewline
97 & 5302.65 & 5493.96770754871 & -191.31770754871 \tabularnewline
98 & 5825.85 & 6061.25483694179 & -235.404836941791 \tabularnewline
99 & 5910.6 & 6526.73168748042 & -616.131687480423 \tabularnewline
100 & 5733.65 & 5653.2854637333 & 80.3645362667021 \tabularnewline
101 & 5914.3 & 5671.00331184932 & 243.296688150679 \tabularnewline
102 & 6128.25 & 6122.3589826505 & 5.89101734949963 \tabularnewline
103 & 5680.5 & 5071.36017217867 & 609.139827821326 \tabularnewline
104 & 5926.3 & 5724.25354571438 & 202.046454285623 \tabularnewline
105 & 6270.5 & 6450.72063086437 & -180.220630864371 \tabularnewline
106 & 6263 & 6189.3283113057 & 73.6716886942995 \tabularnewline
107 & 6064.55 & 5890.8126357366 & 173.737364263405 \tabularnewline
108 & 5706.6 & 6314.68397238468 & -608.083972384678 \tabularnewline
109 & 5365 & 5377.12303381071 & -12.1230338107089 \tabularnewline
110 & 5884.2 & 6015.53660437855 & -131.336604378551 \tabularnewline
111 & 6504.4 & 6405.07698092019 & 99.3230190798131 \tabularnewline
112 & 6174.3 & 6077.12991563192 & 97.170084368081 \tabularnewline
113 & 6123.65 & 6165.6711943412 & -42.021194341196 \tabularnewline
114 & 6698.95 & 6424.96813804397 & 273.981861956026 \tabularnewline
115 & 5256.55 & 5630.78921222273 & -374.239212222733 \tabularnewline
116 & 5838.2 & 5678.25489140401 & 159.945108595992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302546&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]4757.75[/C][C]4374.12659685749[/C][C]383.623403142514[/C][/ROW]
[ROW][C]14[/C][C]5227.15[/C][C]5015.7823163907[/C][C]211.367683609301[/C][/ROW]
[ROW][C]15[/C][C]5739.65[/C][C]5646.75604661989[/C][C]92.8939533801076[/C][/ROW]
[ROW][C]16[/C][C]4981.45[/C][C]4987.64250876495[/C][C]-6.19250876495062[/C][/ROW]
[ROW][C]17[/C][C]5020.05[/C][C]5071.05518616349[/C][C]-51.0051861634902[/C][/ROW]
[ROW][C]18[/C][C]5149.15[/C][C]5219.35960035327[/C][C]-70.2096003532661[/C][/ROW]
[ROW][C]19[/C][C]4513.35[/C][C]4526.2838084324[/C][C]-12.9338084324008[/C][/ROW]
[ROW][C]20[/C][C]4762.55[/C][C]4786.80287772516[/C][C]-24.2528777251646[/C][/ROW]
[ROW][C]21[/C][C]4990.45[/C][C]5316.26331398277[/C][C]-325.813313982767[/C][/ROW]
[ROW][C]22[/C][C]4963.35[/C][C]5340.74188620844[/C][C]-377.391886208443[/C][/ROW]
[ROW][C]23[/C][C]5010[/C][C]4919.45127000503[/C][C]90.5487299949664[/C][/ROW]
[ROW][C]24[/C][C]4983.3[/C][C]5067.43255669506[/C][C]-84.1325566950618[/C][/ROW]
[ROW][C]25[/C][C]4924.7[/C][C]5075.84328568742[/C][C]-151.143285687424[/C][/ROW]
[ROW][C]26[/C][C]5175.25[/C][C]5421.95532176953[/C][C]-246.705321769527[/C][/ROW]
[ROW][C]27[/C][C]5470.3[/C][C]5789.76155218134[/C][C]-319.461552181345[/C][/ROW]
[ROW][C]28[/C][C]4969.4[/C][C]4894.22273212384[/C][C]75.1772678761636[/C][/ROW]
[ROW][C]29[/C][C]5020.5[/C][C]4981.055755855[/C][C]39.4442441450001[/C][/ROW]
[ROW][C]30[/C][C]5519.2[/C][C]5145.57268504884[/C][C]373.627314951157[/C][/ROW]
[ROW][C]31[/C][C]4510.75[/C][C]4647.58411653246[/C][C]-136.834116532465[/C][/ROW]
[ROW][C]32[/C][C]4934.45[/C][C]4835.40059464511[/C][C]99.049405354891[/C][/ROW]
[ROW][C]33[/C][C]5430.65[/C][C]5319.62959368141[/C][C]111.020406318587[/C][/ROW]
[ROW][C]34[/C][C]5254.7[/C][C]5528.979265934[/C][C]-274.279265933998[/C][/ROW]
[ROW][C]35[/C][C]4897.8[/C][C]5290.54905492057[/C][C]-392.749054920566[/C][/ROW]
[ROW][C]36[/C][C]5305.7[/C][C]5142.16128158966[/C][C]163.538718410343[/C][/ROW]
[ROW][C]37[/C][C]5055.7[/C][C]5235.56518990928[/C][C]-179.865189909285[/C][/ROW]
[ROW][C]38[/C][C]5409[/C][C]5539.2454864518[/C][C]-130.245486451799[/C][/ROW]
[ROW][C]39[/C][C]5683[/C][C]5946.84871713937[/C][C]-263.848717139373[/C][/ROW]
[ROW][C]40[/C][C]5125.55[/C][C]5162.71217821242[/C][C]-37.1621782124221[/C][/ROW]
[ROW][C]41[/C][C]4965.2[/C][C]5176.34816124907[/C][C]-211.148161249067[/C][/ROW]
[ROW][C]42[/C][C]5373.3[/C][C]5315.53475362516[/C][C]57.7652463748364[/C][/ROW]
[ROW][C]43[/C][C]4556.1[/C][C]4505.71848926466[/C][C]50.3815107353448[/C][/ROW]
[ROW][C]44[/C][C]4714.25[/C][C]4843.62989608976[/C][C]-129.379896089756[/C][/ROW]
[ROW][C]45[/C][C]5513.85[/C][C]5195.6455910725[/C][C]318.204408927496[/C][/ROW]
[ROW][C]46[/C][C]5258.45[/C][C]5362.99876443294[/C][C]-104.548764432938[/C][/ROW]
[ROW][C]47[/C][C]5111.4[/C][C]5150.47244057857[/C][C]-39.0724405785732[/C][/ROW]
[ROW][C]48[/C][C]5422.25[/C][C]5344.81156532471[/C][C]77.4384346752877[/C][/ROW]
[ROW][C]49[/C][C]4753.3[/C][C]5276.03545655971[/C][C]-522.735456559708[/C][/ROW]
[ROW][C]50[/C][C]5455.5[/C][C]5415.07388123264[/C][C]40.4261187673637[/C][/ROW]
[ROW][C]51[/C][C]5909.15[/C][C]5846.26719003951[/C][C]62.8828099604934[/C][/ROW]
[ROW][C]52[/C][C]5524.4[/C][C]5267.18123345736[/C][C]257.218766542637[/C][/ROW]
[ROW][C]53[/C][C]5477.8[/C][C]5357.37217205033[/C][C]120.427827949669[/C][/ROW]
[ROW][C]54[/C][C]5907.75[/C][C]5765.2938081915[/C][C]142.456191808496[/C][/ROW]
[ROW][C]55[/C][C]5072.55[/C][C]4920.05683727612[/C][C]152.493162723882[/C][/ROW]
[ROW][C]56[/C][C]5171[/C][C]5275.29160254643[/C][C]-104.291602546426[/C][/ROW]
[ROW][C]57[/C][C]5871.4[/C][C]5839.03116885035[/C][C]32.3688311496498[/C][/ROW]
[ROW][C]58[/C][C]5812.45[/C][C]5726.13906766095[/C][C]86.3109323390472[/C][/ROW]
[ROW][C]59[/C][C]5692.2[/C][C]5612.76642626884[/C][C]79.4335737311549[/C][/ROW]
[ROW][C]60[/C][C]5838.1[/C][C]5928.92548873624[/C][C]-90.8254887362436[/C][/ROW]
[ROW][C]61[/C][C]5438.2[/C][C]5554.03370723527[/C][C]-115.833707235272[/C][/ROW]
[ROW][C]62[/C][C]6041.05[/C][C]6146.17372839518[/C][C]-105.123728395176[/C][/ROW]
[ROW][C]63[/C][C]6335.6[/C][C]6571.05237879632[/C][C]-235.452378796315[/C][/ROW]
[ROW][C]64[/C][C]5891.8[/C][C]5860.54193964784[/C][C]31.2580603521628[/C][/ROW]
[ROW][C]65[/C][C]5909.65[/C][C]5792.722140981[/C][C]116.927859019003[/C][/ROW]
[ROW][C]66[/C][C]6449.75[/C][C]6229.50086762079[/C][C]220.249132379212[/C][/ROW]
[ROW][C]67[/C][C]5312.25[/C][C]5352.0163451828[/C][C]-39.7663451827975[/C][/ROW]
[ROW][C]68[/C][C]5828.1[/C][C]5542.24646262067[/C][C]285.853537379333[/C][/ROW]
[ROW][C]69[/C][C]6466.15[/C][C]6396.27789148235[/C][C]69.8721085176485[/C][/ROW]
[ROW][C]70[/C][C]6328.35[/C][C]6309.13928532765[/C][C]19.2107146723456[/C][/ROW]
[ROW][C]71[/C][C]6131.8[/C][C]6148.38091593592[/C][C]-16.5809159359223[/C][/ROW]
[ROW][C]72[/C][C]6734.2[/C][C]6382.43088777437[/C][C]351.769112225628[/C][/ROW]
[ROW][C]73[/C][C]6037.25[/C][C]6172.17946197867[/C][C]-134.929461978674[/C][/ROW]
[ROW][C]74[/C][C]6412.4[/C][C]6840.24068203049[/C][C]-427.840682030486[/C][/ROW]
[ROW][C]75[/C][C]6785.55[/C][C]7112.09680582495[/C][C]-326.546805824954[/C][/ROW]
[ROW][C]76[/C][C]6386[/C][C]6398.15919576576[/C][C]-12.1591957657583[/C][/ROW]
[ROW][C]77[/C][C]6045.25[/C][C]6331.93562860496[/C][C]-286.685628604961[/C][/ROW]
[ROW][C]78[/C][C]6597.25[/C][C]6626.66654872077[/C][C]-29.4165487207692[/C][/ROW]
[ROW][C]79[/C][C]5355.9[/C][C]5506.27159790752[/C][C]-150.37159790752[/C][/ROW]
[ROW][C]80[/C][C]5773.35[/C][C]5744.30846811926[/C][C]29.0415318807427[/C][/ROW]
[ROW][C]81[/C][C]6539.6[/C][C]6393.61811510829[/C][C]145.981884891708[/C][/ROW]
[ROW][C]82[/C][C]6149.2[/C][C]6314.04487846826[/C][C]-164.844878468261[/C][/ROW]
[ROW][C]83[/C][C]6373.45[/C][C]6044.11009753071[/C][C]329.33990246929[/C][/ROW]
[ROW][C]84[/C][C]6504.7[/C][C]6550.27327486525[/C][C]-45.5732748652508[/C][/ROW]
[ROW][C]85[/C][C]5451.25[/C][C]5993.77641736667[/C][C]-542.526417366667[/C][/ROW]
[ROW][C]86[/C][C]6119.9[/C][C]6317.96875236566[/C][C]-198.068752365661[/C][/ROW]
[ROW][C]87[/C][C]6954.95[/C][C]6688.57858626911[/C][C]266.371413730885[/C][/ROW]
[ROW][C]88[/C][C]6139.7[/C][C]6347.11278663066[/C][C]-207.412786630655[/C][/ROW]
[ROW][C]89[/C][C]6383.25[/C][C]6089.79714398778[/C][C]293.452856012224[/C][/ROW]
[ROW][C]90[/C][C]6643.7[/C][C]6745.10483603532[/C][C]-101.404836035318[/C][/ROW]
[ROW][C]91[/C][C]5547.75[/C][C]5529.70650065578[/C][C]18.0434993442232[/C][/ROW]
[ROW][C]92[/C][C]5974[/C][C]5911.4013213242[/C][C]62.5986786757976[/C][/ROW]
[ROW][C]93[/C][C]6583.6[/C][C]6630.35457341638[/C][C]-46.7545734163787[/C][/ROW]
[ROW][C]94[/C][C]6571.55[/C][C]6350.34079105237[/C][C]221.209208947634[/C][/ROW]
[ROW][C]95[/C][C]5736.5[/C][C]6415.77792954126[/C][C]-679.277929541259[/C][/ROW]
[ROW][C]96[/C][C]6027.2[/C][C]6304.80577956878[/C][C]-277.605779568783[/C][/ROW]
[ROW][C]97[/C][C]5302.65[/C][C]5493.96770754871[/C][C]-191.31770754871[/C][/ROW]
[ROW][C]98[/C][C]5825.85[/C][C]6061.25483694179[/C][C]-235.404836941791[/C][/ROW]
[ROW][C]99[/C][C]5910.6[/C][C]6526.73168748042[/C][C]-616.131687480423[/C][/ROW]
[ROW][C]100[/C][C]5733.65[/C][C]5653.2854637333[/C][C]80.3645362667021[/C][/ROW]
[ROW][C]101[/C][C]5914.3[/C][C]5671.00331184932[/C][C]243.296688150679[/C][/ROW]
[ROW][C]102[/C][C]6128.25[/C][C]6122.3589826505[/C][C]5.89101734949963[/C][/ROW]
[ROW][C]103[/C][C]5680.5[/C][C]5071.36017217867[/C][C]609.139827821326[/C][/ROW]
[ROW][C]104[/C][C]5926.3[/C][C]5724.25354571438[/C][C]202.046454285623[/C][/ROW]
[ROW][C]105[/C][C]6270.5[/C][C]6450.72063086437[/C][C]-180.220630864371[/C][/ROW]
[ROW][C]106[/C][C]6263[/C][C]6189.3283113057[/C][C]73.6716886942995[/C][/ROW]
[ROW][C]107[/C][C]6064.55[/C][C]5890.8126357366[/C][C]173.737364263405[/C][/ROW]
[ROW][C]108[/C][C]5706.6[/C][C]6314.68397238468[/C][C]-608.083972384678[/C][/ROW]
[ROW][C]109[/C][C]5365[/C][C]5377.12303381071[/C][C]-12.1230338107089[/C][/ROW]
[ROW][C]110[/C][C]5884.2[/C][C]6015.53660437855[/C][C]-131.336604378551[/C][/ROW]
[ROW][C]111[/C][C]6504.4[/C][C]6405.07698092019[/C][C]99.3230190798131[/C][/ROW]
[ROW][C]112[/C][C]6174.3[/C][C]6077.12991563192[/C][C]97.170084368081[/C][/ROW]
[ROW][C]113[/C][C]6123.65[/C][C]6165.6711943412[/C][C]-42.021194341196[/C][/ROW]
[ROW][C]114[/C][C]6698.95[/C][C]6424.96813804397[/C][C]273.981861956026[/C][/ROW]
[ROW][C]115[/C][C]5256.55[/C][C]5630.78921222273[/C][C]-374.239212222733[/C][/ROW]
[ROW][C]116[/C][C]5838.2[/C][C]5678.25489140401[/C][C]159.945108595992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302546&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302546&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
134757.754374.12659685749383.623403142514
145227.155015.7823163907211.367683609301
155739.655646.7560466198992.8939533801076
164981.454987.64250876495-6.19250876495062
175020.055071.05518616349-51.0051861634902
185149.155219.35960035327-70.2096003532661
194513.354526.2838084324-12.9338084324008
204762.554786.80287772516-24.2528777251646
214990.455316.26331398277-325.813313982767
224963.355340.74188620844-377.391886208443
2350104919.4512700050390.5487299949664
244983.35067.43255669506-84.1325566950618
254924.75075.84328568742-151.143285687424
265175.255421.95532176953-246.705321769527
275470.35789.76155218134-319.461552181345
284969.44894.2227321238475.1772678761636
295020.54981.05575585539.4442441450001
305519.25145.57268504884373.627314951157
314510.754647.58411653246-136.834116532465
324934.454835.4005946451199.049405354891
335430.655319.62959368141111.020406318587
345254.75528.979265934-274.279265933998
354897.85290.54905492057-392.749054920566
365305.75142.16128158966163.538718410343
375055.75235.56518990928-179.865189909285
3854095539.2454864518-130.245486451799
3956835946.84871713937-263.848717139373
405125.555162.71217821242-37.1621782124221
414965.25176.34816124907-211.148161249067
425373.35315.5347536251657.7652463748364
434556.14505.7184892646650.3815107353448
444714.254843.62989608976-129.379896089756
455513.855195.6455910725318.204408927496
465258.455362.99876443294-104.548764432938
475111.45150.47244057857-39.0724405785732
485422.255344.8115653247177.4384346752877
494753.35276.03545655971-522.735456559708
505455.55415.0738812326440.4261187673637
515909.155846.2671900395162.8828099604934
525524.45267.18123345736257.218766542637
535477.85357.37217205033120.427827949669
545907.755765.2938081915142.456191808496
555072.554920.05683727612152.493162723882
5651715275.29160254643-104.291602546426
575871.45839.0311688503532.3688311496498
585812.455726.1390676609586.3109323390472
595692.25612.7664262688479.4335737311549
605838.15928.92548873624-90.8254887362436
615438.25554.03370723527-115.833707235272
626041.056146.17372839518-105.123728395176
636335.66571.05237879632-235.452378796315
645891.85860.5419396478431.2580603521628
655909.655792.722140981116.927859019003
666449.756229.50086762079220.249132379212
675312.255352.0163451828-39.7663451827975
685828.15542.24646262067285.853537379333
696466.156396.2778914823569.8721085176485
706328.356309.1392853276519.2107146723456
716131.86148.38091593592-16.5809159359223
726734.26382.43088777437351.769112225628
736037.256172.17946197867-134.929461978674
746412.46840.24068203049-427.840682030486
756785.557112.09680582495-326.546805824954
7663866398.15919576576-12.1591957657583
776045.256331.93562860496-286.685628604961
786597.256626.66654872077-29.4165487207692
795355.95506.27159790752-150.37159790752
805773.355744.3084681192629.0415318807427
816539.66393.61811510829145.981884891708
826149.26314.04487846826-164.844878468261
836373.456044.11009753071329.33990246929
846504.76550.27327486525-45.5732748652508
855451.255993.77641736667-542.526417366667
866119.96317.96875236566-198.068752365661
876954.956688.57858626911266.371413730885
886139.76347.11278663066-207.412786630655
896383.256089.79714398778293.452856012224
906643.76745.10483603532-101.404836035318
915547.755529.7065006557818.0434993442232
9259745911.401321324262.5986786757976
936583.66630.35457341638-46.7545734163787
946571.556350.34079105237221.209208947634
955736.56415.77792954126-679.277929541259
966027.26304.80577956878-277.605779568783
975302.655493.96770754871-191.31770754871
985825.856061.25483694179-235.404836941791
995910.66526.73168748042-616.131687480423
1005733.655653.285463733380.3645362667021
1015914.35671.00331184932243.296688150679
1026128.256122.35898265055.89101734949963
1035680.55071.36017217867609.139827821326
1045926.35724.25354571438202.046454285623
1056270.56450.72063086437-180.220630864371
10662636189.328311305773.6716886942995
1076064.555890.8126357366173.737364263405
1085706.66314.68397238468-608.083972384678
10953655377.12303381071-12.1230338107089
1105884.26015.53660437855-131.336604378551
1116504.46405.0769809201999.3230190798131
1126174.36077.1299156319297.170084368081
1136123.656165.6711943412-42.021194341196
1146698.956424.96813804397273.981861956026
1155256.555630.78921222273-374.239212222733
1165838.25678.25489140401159.945108595992







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1176243.242817148565885.298237649436601.18739664768
1186144.262491414945726.203111332896562.32187149699
1195841.872339139845376.815880583446306.92879769623
1205913.883547919425391.412979126896436.35411671194
1215447.700181351744901.0573114675994.34305123648
1226062.629150636545421.626065923686703.63223534939
1236603.57653922315869.363780697797337.78929774841
1246221.857188983355476.674294905086967.04008306161
1256219.493942969845428.51959534147010.46829059829
1266603.592812922565724.708242155377482.47738368975
1275472.25853399774680.86734612626263.64972186919
1285878.993256077795065.199849728046692.78666242755
1296322.850784299165305.284051552437340.41751704589
1306222.525193401875176.344947732677268.70543907107
1315916.20443817574870.948819486966961.46005686444
1325989.052215031124891.443216068467086.66121399377
1335516.870139413844450.608993603456583.13128522422
1346139.525555857694929.763771013887349.28734070149

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 6243.24281714856 & 5885.29823764943 & 6601.18739664768 \tabularnewline
118 & 6144.26249141494 & 5726.20311133289 & 6562.32187149699 \tabularnewline
119 & 5841.87233913984 & 5376.81588058344 & 6306.92879769623 \tabularnewline
120 & 5913.88354791942 & 5391.41297912689 & 6436.35411671194 \tabularnewline
121 & 5447.70018135174 & 4901.057311467 & 5994.34305123648 \tabularnewline
122 & 6062.62915063654 & 5421.62606592368 & 6703.63223534939 \tabularnewline
123 & 6603.5765392231 & 5869.36378069779 & 7337.78929774841 \tabularnewline
124 & 6221.85718898335 & 5476.67429490508 & 6967.04008306161 \tabularnewline
125 & 6219.49394296984 & 5428.5195953414 & 7010.46829059829 \tabularnewline
126 & 6603.59281292256 & 5724.70824215537 & 7482.47738368975 \tabularnewline
127 & 5472.2585339977 & 4680.8673461262 & 6263.64972186919 \tabularnewline
128 & 5878.99325607779 & 5065.19984972804 & 6692.78666242755 \tabularnewline
129 & 6322.85078429916 & 5305.28405155243 & 7340.41751704589 \tabularnewline
130 & 6222.52519340187 & 5176.34494773267 & 7268.70543907107 \tabularnewline
131 & 5916.2044381757 & 4870.94881948696 & 6961.46005686444 \tabularnewline
132 & 5989.05221503112 & 4891.44321606846 & 7086.66121399377 \tabularnewline
133 & 5516.87013941384 & 4450.60899360345 & 6583.13128522422 \tabularnewline
134 & 6139.52555585769 & 4929.76377101388 & 7349.28734070149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302546&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]117[/C][C]6243.24281714856[/C][C]5885.29823764943[/C][C]6601.18739664768[/C][/ROW]
[ROW][C]118[/C][C]6144.26249141494[/C][C]5726.20311133289[/C][C]6562.32187149699[/C][/ROW]
[ROW][C]119[/C][C]5841.87233913984[/C][C]5376.81588058344[/C][C]6306.92879769623[/C][/ROW]
[ROW][C]120[/C][C]5913.88354791942[/C][C]5391.41297912689[/C][C]6436.35411671194[/C][/ROW]
[ROW][C]121[/C][C]5447.70018135174[/C][C]4901.057311467[/C][C]5994.34305123648[/C][/ROW]
[ROW][C]122[/C][C]6062.62915063654[/C][C]5421.62606592368[/C][C]6703.63223534939[/C][/ROW]
[ROW][C]123[/C][C]6603.5765392231[/C][C]5869.36378069779[/C][C]7337.78929774841[/C][/ROW]
[ROW][C]124[/C][C]6221.85718898335[/C][C]5476.67429490508[/C][C]6967.04008306161[/C][/ROW]
[ROW][C]125[/C][C]6219.49394296984[/C][C]5428.5195953414[/C][C]7010.46829059829[/C][/ROW]
[ROW][C]126[/C][C]6603.59281292256[/C][C]5724.70824215537[/C][C]7482.47738368975[/C][/ROW]
[ROW][C]127[/C][C]5472.2585339977[/C][C]4680.8673461262[/C][C]6263.64972186919[/C][/ROW]
[ROW][C]128[/C][C]5878.99325607779[/C][C]5065.19984972804[/C][C]6692.78666242755[/C][/ROW]
[ROW][C]129[/C][C]6322.85078429916[/C][C]5305.28405155243[/C][C]7340.41751704589[/C][/ROW]
[ROW][C]130[/C][C]6222.52519340187[/C][C]5176.34494773267[/C][C]7268.70543907107[/C][/ROW]
[ROW][C]131[/C][C]5916.2044381757[/C][C]4870.94881948696[/C][C]6961.46005686444[/C][/ROW]
[ROW][C]132[/C][C]5989.05221503112[/C][C]4891.44321606846[/C][C]7086.66121399377[/C][/ROW]
[ROW][C]133[/C][C]5516.87013941384[/C][C]4450.60899360345[/C][C]6583.13128522422[/C][/ROW]
[ROW][C]134[/C][C]6139.52555585769[/C][C]4929.76377101388[/C][C]7349.28734070149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302546&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302546&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
1176243.242817148565885.298237649436601.18739664768
1186144.262491414945726.203111332896562.32187149699
1195841.872339139845376.815880583446306.92879769623
1205913.883547919425391.412979126896436.35411671194
1215447.700181351744901.0573114675994.34305123648
1226062.629150636545421.626065923686703.63223534939
1236603.57653922315869.363780697797337.78929774841
1246221.857188983355476.674294905086967.04008306161
1256219.493942969845428.51959534147010.46829059829
1266603.592812922565724.708242155377482.47738368975
1275472.25853399774680.86734612626263.64972186919
1285878.993256077795065.199849728046692.78666242755
1296322.850784299165305.284051552437340.41751704589
1306222.525193401875176.344947732677268.70543907107
1315916.20443817574870.948819486966961.46005686444
1325989.052215031124891.443216068467086.66121399377
1335516.870139413844450.608993603456583.13128522422
1346139.525555857694929.763771013887349.28734070149



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
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')