Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 14 Aug 2015 11:29:27 +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/2015/Aug/14/t1439548354rh6a7bux108j3cj.htm/, Retrieved Thu, 31 Oct 2024 23:35:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280064, Retrieved Thu, 31 Oct 2024 23:35:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-08-14 10:29:27] [70e23d918d09c907c02097a361cd6415] [Current]
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Dataseries X:
59400
57200
60500
48400
62700
61600
66000
68200
75900
66000
62700
78100
66000
49500
58300
44000
61600
50600
67100
60500
63800
71500
70400
83600
60500
50600
56100
40700
58300
45100
63800
60500
53900
77000
69300
79200
59400
55000
49500
40700
53900
48400
66000
63800
55000
73700
68200
88000
70400
42900
42900
42900
50600
50600
68200
62700
56100
70400
64900
93500
73700
42900
45100
37400
51700
59400
74800
73700
59400
69300
61600
88000
67100
53900
48400
36300
53900
64900
75900
71500
52800
75900
59400
91300
75900
55000
50600
34100
53900
51700
78100
78100
59400
77000
57200
89100
75900
56100
42900
29700
58300
56100
73700
84700
62700
70400
52800
91300




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280064&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280064&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280064&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616435516555998
beta0.018215348345161
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516555998 \tabularnewline
beta & 0.018215348345161 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280064&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]0.616435516555998[/C][/ROW]
[ROW][C]beta[/C][C]0.018215348345161[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280064&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280064&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
alpha0.616435516555998
beta0.018215348345161
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
360500550005500
44840056252.1525732232-7852.15257322317
56270049185.395494298713514.6045057013
66160055441.61627391656158.38372608354
76600057232.35124890228767.64875109777
86820060729.9781700447470.02182995597
97590063511.579564742412388.4204352576
106600069464.1610092336-3464.16100923361
116270065605.7505866612-2905.75058666118
127810062058.936706178416041.0632938216
136600070371.7303126583-4371.73031265828
144950066052.2645909072-16552.2645909072
155830054038.42637537944261.57362462063
164400054902.8287247942-10902.8287247942
176160046296.931510536515303.0684894635
185060054017.111928462-3417.11192846196
196710050159.138919587416940.8610804126
206050059040.76546225721459.23453774282
216380058395.35269290215404.64730709786
227150060242.719038144811257.2809618552
237040065824.25999973634575.74000026372
248360067338.440905010716261.5590949893
256050076238.7700822125-15738.7700822125
265060065236.2356534746-14636.2356534746
275610054748.99834969551351.00165030454
284070054132.0317720426-13432.0317720426
295830044251.455604130414048.5443958696
304510051468.6279138759-6368.6279138759
316380046028.41936740517771.580632595
326050055668.64249715094831.35750284907
335390057386.3018188305-3486.30181883051
347700053937.514274409523062.4857255905
356930067113.30143664392186.69856335614
367920067445.065492531911754.9345074681
375940073807.0213277881-14407.0213277881
385500063880.0479016322-8880.04790163218
394950057260.3867980747-7760.38679807471
404070051243.786381769-10543.786381769
415390043393.007775583510506.9922244165
424840048636.6554367099-236.655436709938
436600047254.879795836418745.1202041636
446380057784.62605282446015.37394717556
455500060534.8487539713-5534.84875397128
467370056102.955423545617597.0445764544
476820066127.97266487542072.02733512463
488800066606.083824084921393.9161759151
497040079235.1169750134-8835.11697501343
504290073130.6945750641-30230.6945750641
514290053497.8302409615-10597.8302409615
524290045848.362108191-2948.36210819102
535060042881.19187281947718.80812718056
545060046576.31554541614023.68445458395
556820048038.814041797520161.1859582025
566270059675.42325747543024.57674252457
575610060782.3796443758-4682.37964437585
587040057085.917879518513314.0821204815
596490064632.6126571487267.387342851267
609350064139.863782402129360.1362175979
617370081910.5914517105-8210.59145171051
624290076429.1948568956-33529.1948568956
634510054964.0263896946-9864.02638969456
643740047976.149185897-10576.149185897
655170040430.538980064311269.4610199357
665940046477.878916960512922.1210830395
677480053689.074382964221110.9256170358
687370066185.18568086777514.81431913226
695940070384.5518390743-10984.5518390743
706930063056.91066028726243.08933971285
716160066419.1004465471-4819.10044654715
728800062908.051865836325091.9481341637
736710078116.9831070526-11016.9831070526
745390070943.3815056679-17043.3815056679
754840059863.5207910924-11463.5207910924
763630052094.5652502484-15794.5652502484
775390041478.449420432512421.5505795675
786490048395.225997008316504.7740029917
797590058014.371815622817885.6281843772
807150068685.55553886512814.44446113495
815280070097.9285749242-17297.9285749242
827590058918.089241882716981.9107581173
835940069060.2432492517-9660.24324925165
849130062670.756400720828629.2435992792
857590080205.7351279052-4305.73512790522
865500077390.075906285-22390.075906285
875060063175.1778051985-12575.1778051985
883410054869.3299985936-20769.3299985936
895390041279.105509253112620.8944907469
905170048413.51612113773286.48387886229
917810049830.767078087428269.2329219126
927810066965.695406504211134.3045934958
935940073663.0678548758-14263.0678548758
947700064544.443791070112455.5562089299
955720072035.9868585277-14835.9868585277
968910062537.466298528426562.5337014716
977590078856.7238828949-2956.72388289489
985610076946.0628365685-20846.0628365685
994290063773.7060474293-20873.7060474293
1002970050349.9267630477-20649.9267630477
1015830036832.223464464921467.7765355351
1025610049518.42116572816581.57883427192
1037370053102.139732382320597.8602676177
1048470065557.276864350419142.7231356496
1056270077330.3615316162-14630.3615316162
1067040068120.23900927772279.76099072232
1075280069359.7150951649-16559.7150951649
1089130058799.926795727232500.0732042728

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 60500 & 55000 & 5500 \tabularnewline
4 & 48400 & 56252.1525732232 & -7852.15257322317 \tabularnewline
5 & 62700 & 49185.3954942987 & 13514.6045057013 \tabularnewline
6 & 61600 & 55441.6162739165 & 6158.38372608354 \tabularnewline
7 & 66000 & 57232.3512489022 & 8767.64875109777 \tabularnewline
8 & 68200 & 60729.978170044 & 7470.02182995597 \tabularnewline
9 & 75900 & 63511.5795647424 & 12388.4204352576 \tabularnewline
10 & 66000 & 69464.1610092336 & -3464.16100923361 \tabularnewline
11 & 62700 & 65605.7505866612 & -2905.75058666118 \tabularnewline
12 & 78100 & 62058.9367061784 & 16041.0632938216 \tabularnewline
13 & 66000 & 70371.7303126583 & -4371.73031265828 \tabularnewline
14 & 49500 & 66052.2645909072 & -16552.2645909072 \tabularnewline
15 & 58300 & 54038.4263753794 & 4261.57362462063 \tabularnewline
16 & 44000 & 54902.8287247942 & -10902.8287247942 \tabularnewline
17 & 61600 & 46296.9315105365 & 15303.0684894635 \tabularnewline
18 & 50600 & 54017.111928462 & -3417.11192846196 \tabularnewline
19 & 67100 & 50159.1389195874 & 16940.8610804126 \tabularnewline
20 & 60500 & 59040.7654622572 & 1459.23453774282 \tabularnewline
21 & 63800 & 58395.3526929021 & 5404.64730709786 \tabularnewline
22 & 71500 & 60242.7190381448 & 11257.2809618552 \tabularnewline
23 & 70400 & 65824.2599997363 & 4575.74000026372 \tabularnewline
24 & 83600 & 67338.4409050107 & 16261.5590949893 \tabularnewline
25 & 60500 & 76238.7700822125 & -15738.7700822125 \tabularnewline
26 & 50600 & 65236.2356534746 & -14636.2356534746 \tabularnewline
27 & 56100 & 54748.9983496955 & 1351.00165030454 \tabularnewline
28 & 40700 & 54132.0317720426 & -13432.0317720426 \tabularnewline
29 & 58300 & 44251.4556041304 & 14048.5443958696 \tabularnewline
30 & 45100 & 51468.6279138759 & -6368.6279138759 \tabularnewline
31 & 63800 & 46028.419367405 & 17771.580632595 \tabularnewline
32 & 60500 & 55668.6424971509 & 4831.35750284907 \tabularnewline
33 & 53900 & 57386.3018188305 & -3486.30181883051 \tabularnewline
34 & 77000 & 53937.5142744095 & 23062.4857255905 \tabularnewline
35 & 69300 & 67113.3014366439 & 2186.69856335614 \tabularnewline
36 & 79200 & 67445.0654925319 & 11754.9345074681 \tabularnewline
37 & 59400 & 73807.0213277881 & -14407.0213277881 \tabularnewline
38 & 55000 & 63880.0479016322 & -8880.04790163218 \tabularnewline
39 & 49500 & 57260.3867980747 & -7760.38679807471 \tabularnewline
40 & 40700 & 51243.786381769 & -10543.786381769 \tabularnewline
41 & 53900 & 43393.0077755835 & 10506.9922244165 \tabularnewline
42 & 48400 & 48636.6554367099 & -236.655436709938 \tabularnewline
43 & 66000 & 47254.8797958364 & 18745.1202041636 \tabularnewline
44 & 63800 & 57784.6260528244 & 6015.37394717556 \tabularnewline
45 & 55000 & 60534.8487539713 & -5534.84875397128 \tabularnewline
46 & 73700 & 56102.9554235456 & 17597.0445764544 \tabularnewline
47 & 68200 & 66127.9726648754 & 2072.02733512463 \tabularnewline
48 & 88000 & 66606.0838240849 & 21393.9161759151 \tabularnewline
49 & 70400 & 79235.1169750134 & -8835.11697501343 \tabularnewline
50 & 42900 & 73130.6945750641 & -30230.6945750641 \tabularnewline
51 & 42900 & 53497.8302409615 & -10597.8302409615 \tabularnewline
52 & 42900 & 45848.362108191 & -2948.36210819102 \tabularnewline
53 & 50600 & 42881.1918728194 & 7718.80812718056 \tabularnewline
54 & 50600 & 46576.3155454161 & 4023.68445458395 \tabularnewline
55 & 68200 & 48038.8140417975 & 20161.1859582025 \tabularnewline
56 & 62700 & 59675.4232574754 & 3024.57674252457 \tabularnewline
57 & 56100 & 60782.3796443758 & -4682.37964437585 \tabularnewline
58 & 70400 & 57085.9178795185 & 13314.0821204815 \tabularnewline
59 & 64900 & 64632.6126571487 & 267.387342851267 \tabularnewline
60 & 93500 & 64139.8637824021 & 29360.1362175979 \tabularnewline
61 & 73700 & 81910.5914517105 & -8210.59145171051 \tabularnewline
62 & 42900 & 76429.1948568956 & -33529.1948568956 \tabularnewline
63 & 45100 & 54964.0263896946 & -9864.02638969456 \tabularnewline
64 & 37400 & 47976.149185897 & -10576.149185897 \tabularnewline
65 & 51700 & 40430.5389800643 & 11269.4610199357 \tabularnewline
66 & 59400 & 46477.8789169605 & 12922.1210830395 \tabularnewline
67 & 74800 & 53689.0743829642 & 21110.9256170358 \tabularnewline
68 & 73700 & 66185.1856808677 & 7514.81431913226 \tabularnewline
69 & 59400 & 70384.5518390743 & -10984.5518390743 \tabularnewline
70 & 69300 & 63056.9106602872 & 6243.08933971285 \tabularnewline
71 & 61600 & 66419.1004465471 & -4819.10044654715 \tabularnewline
72 & 88000 & 62908.0518658363 & 25091.9481341637 \tabularnewline
73 & 67100 & 78116.9831070526 & -11016.9831070526 \tabularnewline
74 & 53900 & 70943.3815056679 & -17043.3815056679 \tabularnewline
75 & 48400 & 59863.5207910924 & -11463.5207910924 \tabularnewline
76 & 36300 & 52094.5652502484 & -15794.5652502484 \tabularnewline
77 & 53900 & 41478.4494204325 & 12421.5505795675 \tabularnewline
78 & 64900 & 48395.2259970083 & 16504.7740029917 \tabularnewline
79 & 75900 & 58014.3718156228 & 17885.6281843772 \tabularnewline
80 & 71500 & 68685.5555388651 & 2814.44446113495 \tabularnewline
81 & 52800 & 70097.9285749242 & -17297.9285749242 \tabularnewline
82 & 75900 & 58918.0892418827 & 16981.9107581173 \tabularnewline
83 & 59400 & 69060.2432492517 & -9660.24324925165 \tabularnewline
84 & 91300 & 62670.7564007208 & 28629.2435992792 \tabularnewline
85 & 75900 & 80205.7351279052 & -4305.73512790522 \tabularnewline
86 & 55000 & 77390.075906285 & -22390.075906285 \tabularnewline
87 & 50600 & 63175.1778051985 & -12575.1778051985 \tabularnewline
88 & 34100 & 54869.3299985936 & -20769.3299985936 \tabularnewline
89 & 53900 & 41279.1055092531 & 12620.8944907469 \tabularnewline
90 & 51700 & 48413.5161211377 & 3286.48387886229 \tabularnewline
91 & 78100 & 49830.7670780874 & 28269.2329219126 \tabularnewline
92 & 78100 & 66965.6954065042 & 11134.3045934958 \tabularnewline
93 & 59400 & 73663.0678548758 & -14263.0678548758 \tabularnewline
94 & 77000 & 64544.4437910701 & 12455.5562089299 \tabularnewline
95 & 57200 & 72035.9868585277 & -14835.9868585277 \tabularnewline
96 & 89100 & 62537.4662985284 & 26562.5337014716 \tabularnewline
97 & 75900 & 78856.7238828949 & -2956.72388289489 \tabularnewline
98 & 56100 & 76946.0628365685 & -20846.0628365685 \tabularnewline
99 & 42900 & 63773.7060474293 & -20873.7060474293 \tabularnewline
100 & 29700 & 50349.9267630477 & -20649.9267630477 \tabularnewline
101 & 58300 & 36832.2234644649 & 21467.7765355351 \tabularnewline
102 & 56100 & 49518.4211657281 & 6581.57883427192 \tabularnewline
103 & 73700 & 53102.1397323823 & 20597.8602676177 \tabularnewline
104 & 84700 & 65557.2768643504 & 19142.7231356496 \tabularnewline
105 & 62700 & 77330.3615316162 & -14630.3615316162 \tabularnewline
106 & 70400 & 68120.2390092777 & 2279.76099072232 \tabularnewline
107 & 52800 & 69359.7150951649 & -16559.7150951649 \tabularnewline
108 & 91300 & 58799.9267957272 & 32500.0732042728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280064&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]60500[/C][C]55000[/C][C]5500[/C][/ROW]
[ROW][C]4[/C][C]48400[/C][C]56252.1525732232[/C][C]-7852.15257322317[/C][/ROW]
[ROW][C]5[/C][C]62700[/C][C]49185.3954942987[/C][C]13514.6045057013[/C][/ROW]
[ROW][C]6[/C][C]61600[/C][C]55441.6162739165[/C][C]6158.38372608354[/C][/ROW]
[ROW][C]7[/C][C]66000[/C][C]57232.3512489022[/C][C]8767.64875109777[/C][/ROW]
[ROW][C]8[/C][C]68200[/C][C]60729.978170044[/C][C]7470.02182995597[/C][/ROW]
[ROW][C]9[/C][C]75900[/C][C]63511.5795647424[/C][C]12388.4204352576[/C][/ROW]
[ROW][C]10[/C][C]66000[/C][C]69464.1610092336[/C][C]-3464.16100923361[/C][/ROW]
[ROW][C]11[/C][C]62700[/C][C]65605.7505866612[/C][C]-2905.75058666118[/C][/ROW]
[ROW][C]12[/C][C]78100[/C][C]62058.9367061784[/C][C]16041.0632938216[/C][/ROW]
[ROW][C]13[/C][C]66000[/C][C]70371.7303126583[/C][C]-4371.73031265828[/C][/ROW]
[ROW][C]14[/C][C]49500[/C][C]66052.2645909072[/C][C]-16552.2645909072[/C][/ROW]
[ROW][C]15[/C][C]58300[/C][C]54038.4263753794[/C][C]4261.57362462063[/C][/ROW]
[ROW][C]16[/C][C]44000[/C][C]54902.8287247942[/C][C]-10902.8287247942[/C][/ROW]
[ROW][C]17[/C][C]61600[/C][C]46296.9315105365[/C][C]15303.0684894635[/C][/ROW]
[ROW][C]18[/C][C]50600[/C][C]54017.111928462[/C][C]-3417.11192846196[/C][/ROW]
[ROW][C]19[/C][C]67100[/C][C]50159.1389195874[/C][C]16940.8610804126[/C][/ROW]
[ROW][C]20[/C][C]60500[/C][C]59040.7654622572[/C][C]1459.23453774282[/C][/ROW]
[ROW][C]21[/C][C]63800[/C][C]58395.3526929021[/C][C]5404.64730709786[/C][/ROW]
[ROW][C]22[/C][C]71500[/C][C]60242.7190381448[/C][C]11257.2809618552[/C][/ROW]
[ROW][C]23[/C][C]70400[/C][C]65824.2599997363[/C][C]4575.74000026372[/C][/ROW]
[ROW][C]24[/C][C]83600[/C][C]67338.4409050107[/C][C]16261.5590949893[/C][/ROW]
[ROW][C]25[/C][C]60500[/C][C]76238.7700822125[/C][C]-15738.7700822125[/C][/ROW]
[ROW][C]26[/C][C]50600[/C][C]65236.2356534746[/C][C]-14636.2356534746[/C][/ROW]
[ROW][C]27[/C][C]56100[/C][C]54748.9983496955[/C][C]1351.00165030454[/C][/ROW]
[ROW][C]28[/C][C]40700[/C][C]54132.0317720426[/C][C]-13432.0317720426[/C][/ROW]
[ROW][C]29[/C][C]58300[/C][C]44251.4556041304[/C][C]14048.5443958696[/C][/ROW]
[ROW][C]30[/C][C]45100[/C][C]51468.6279138759[/C][C]-6368.6279138759[/C][/ROW]
[ROW][C]31[/C][C]63800[/C][C]46028.419367405[/C][C]17771.580632595[/C][/ROW]
[ROW][C]32[/C][C]60500[/C][C]55668.6424971509[/C][C]4831.35750284907[/C][/ROW]
[ROW][C]33[/C][C]53900[/C][C]57386.3018188305[/C][C]-3486.30181883051[/C][/ROW]
[ROW][C]34[/C][C]77000[/C][C]53937.5142744095[/C][C]23062.4857255905[/C][/ROW]
[ROW][C]35[/C][C]69300[/C][C]67113.3014366439[/C][C]2186.69856335614[/C][/ROW]
[ROW][C]36[/C][C]79200[/C][C]67445.0654925319[/C][C]11754.9345074681[/C][/ROW]
[ROW][C]37[/C][C]59400[/C][C]73807.0213277881[/C][C]-14407.0213277881[/C][/ROW]
[ROW][C]38[/C][C]55000[/C][C]63880.0479016322[/C][C]-8880.04790163218[/C][/ROW]
[ROW][C]39[/C][C]49500[/C][C]57260.3867980747[/C][C]-7760.38679807471[/C][/ROW]
[ROW][C]40[/C][C]40700[/C][C]51243.786381769[/C][C]-10543.786381769[/C][/ROW]
[ROW][C]41[/C][C]53900[/C][C]43393.0077755835[/C][C]10506.9922244165[/C][/ROW]
[ROW][C]42[/C][C]48400[/C][C]48636.6554367099[/C][C]-236.655436709938[/C][/ROW]
[ROW][C]43[/C][C]66000[/C][C]47254.8797958364[/C][C]18745.1202041636[/C][/ROW]
[ROW][C]44[/C][C]63800[/C][C]57784.6260528244[/C][C]6015.37394717556[/C][/ROW]
[ROW][C]45[/C][C]55000[/C][C]60534.8487539713[/C][C]-5534.84875397128[/C][/ROW]
[ROW][C]46[/C][C]73700[/C][C]56102.9554235456[/C][C]17597.0445764544[/C][/ROW]
[ROW][C]47[/C][C]68200[/C][C]66127.9726648754[/C][C]2072.02733512463[/C][/ROW]
[ROW][C]48[/C][C]88000[/C][C]66606.0838240849[/C][C]21393.9161759151[/C][/ROW]
[ROW][C]49[/C][C]70400[/C][C]79235.1169750134[/C][C]-8835.11697501343[/C][/ROW]
[ROW][C]50[/C][C]42900[/C][C]73130.6945750641[/C][C]-30230.6945750641[/C][/ROW]
[ROW][C]51[/C][C]42900[/C][C]53497.8302409615[/C][C]-10597.8302409615[/C][/ROW]
[ROW][C]52[/C][C]42900[/C][C]45848.362108191[/C][C]-2948.36210819102[/C][/ROW]
[ROW][C]53[/C][C]50600[/C][C]42881.1918728194[/C][C]7718.80812718056[/C][/ROW]
[ROW][C]54[/C][C]50600[/C][C]46576.3155454161[/C][C]4023.68445458395[/C][/ROW]
[ROW][C]55[/C][C]68200[/C][C]48038.8140417975[/C][C]20161.1859582025[/C][/ROW]
[ROW][C]56[/C][C]62700[/C][C]59675.4232574754[/C][C]3024.57674252457[/C][/ROW]
[ROW][C]57[/C][C]56100[/C][C]60782.3796443758[/C][C]-4682.37964437585[/C][/ROW]
[ROW][C]58[/C][C]70400[/C][C]57085.9178795185[/C][C]13314.0821204815[/C][/ROW]
[ROW][C]59[/C][C]64900[/C][C]64632.6126571487[/C][C]267.387342851267[/C][/ROW]
[ROW][C]60[/C][C]93500[/C][C]64139.8637824021[/C][C]29360.1362175979[/C][/ROW]
[ROW][C]61[/C][C]73700[/C][C]81910.5914517105[/C][C]-8210.59145171051[/C][/ROW]
[ROW][C]62[/C][C]42900[/C][C]76429.1948568956[/C][C]-33529.1948568956[/C][/ROW]
[ROW][C]63[/C][C]45100[/C][C]54964.0263896946[/C][C]-9864.02638969456[/C][/ROW]
[ROW][C]64[/C][C]37400[/C][C]47976.149185897[/C][C]-10576.149185897[/C][/ROW]
[ROW][C]65[/C][C]51700[/C][C]40430.5389800643[/C][C]11269.4610199357[/C][/ROW]
[ROW][C]66[/C][C]59400[/C][C]46477.8789169605[/C][C]12922.1210830395[/C][/ROW]
[ROW][C]67[/C][C]74800[/C][C]53689.0743829642[/C][C]21110.9256170358[/C][/ROW]
[ROW][C]68[/C][C]73700[/C][C]66185.1856808677[/C][C]7514.81431913226[/C][/ROW]
[ROW][C]69[/C][C]59400[/C][C]70384.5518390743[/C][C]-10984.5518390743[/C][/ROW]
[ROW][C]70[/C][C]69300[/C][C]63056.9106602872[/C][C]6243.08933971285[/C][/ROW]
[ROW][C]71[/C][C]61600[/C][C]66419.1004465471[/C][C]-4819.10044654715[/C][/ROW]
[ROW][C]72[/C][C]88000[/C][C]62908.0518658363[/C][C]25091.9481341637[/C][/ROW]
[ROW][C]73[/C][C]67100[/C][C]78116.9831070526[/C][C]-11016.9831070526[/C][/ROW]
[ROW][C]74[/C][C]53900[/C][C]70943.3815056679[/C][C]-17043.3815056679[/C][/ROW]
[ROW][C]75[/C][C]48400[/C][C]59863.5207910924[/C][C]-11463.5207910924[/C][/ROW]
[ROW][C]76[/C][C]36300[/C][C]52094.5652502484[/C][C]-15794.5652502484[/C][/ROW]
[ROW][C]77[/C][C]53900[/C][C]41478.4494204325[/C][C]12421.5505795675[/C][/ROW]
[ROW][C]78[/C][C]64900[/C][C]48395.2259970083[/C][C]16504.7740029917[/C][/ROW]
[ROW][C]79[/C][C]75900[/C][C]58014.3718156228[/C][C]17885.6281843772[/C][/ROW]
[ROW][C]80[/C][C]71500[/C][C]68685.5555388651[/C][C]2814.44446113495[/C][/ROW]
[ROW][C]81[/C][C]52800[/C][C]70097.9285749242[/C][C]-17297.9285749242[/C][/ROW]
[ROW][C]82[/C][C]75900[/C][C]58918.0892418827[/C][C]16981.9107581173[/C][/ROW]
[ROW][C]83[/C][C]59400[/C][C]69060.2432492517[/C][C]-9660.24324925165[/C][/ROW]
[ROW][C]84[/C][C]91300[/C][C]62670.7564007208[/C][C]28629.2435992792[/C][/ROW]
[ROW][C]85[/C][C]75900[/C][C]80205.7351279052[/C][C]-4305.73512790522[/C][/ROW]
[ROW][C]86[/C][C]55000[/C][C]77390.075906285[/C][C]-22390.075906285[/C][/ROW]
[ROW][C]87[/C][C]50600[/C][C]63175.1778051985[/C][C]-12575.1778051985[/C][/ROW]
[ROW][C]88[/C][C]34100[/C][C]54869.3299985936[/C][C]-20769.3299985936[/C][/ROW]
[ROW][C]89[/C][C]53900[/C][C]41279.1055092531[/C][C]12620.8944907469[/C][/ROW]
[ROW][C]90[/C][C]51700[/C][C]48413.5161211377[/C][C]3286.48387886229[/C][/ROW]
[ROW][C]91[/C][C]78100[/C][C]49830.7670780874[/C][C]28269.2329219126[/C][/ROW]
[ROW][C]92[/C][C]78100[/C][C]66965.6954065042[/C][C]11134.3045934958[/C][/ROW]
[ROW][C]93[/C][C]59400[/C][C]73663.0678548758[/C][C]-14263.0678548758[/C][/ROW]
[ROW][C]94[/C][C]77000[/C][C]64544.4437910701[/C][C]12455.5562089299[/C][/ROW]
[ROW][C]95[/C][C]57200[/C][C]72035.9868585277[/C][C]-14835.9868585277[/C][/ROW]
[ROW][C]96[/C][C]89100[/C][C]62537.4662985284[/C][C]26562.5337014716[/C][/ROW]
[ROW][C]97[/C][C]75900[/C][C]78856.7238828949[/C][C]-2956.72388289489[/C][/ROW]
[ROW][C]98[/C][C]56100[/C][C]76946.0628365685[/C][C]-20846.0628365685[/C][/ROW]
[ROW][C]99[/C][C]42900[/C][C]63773.7060474293[/C][C]-20873.7060474293[/C][/ROW]
[ROW][C]100[/C][C]29700[/C][C]50349.9267630477[/C][C]-20649.9267630477[/C][/ROW]
[ROW][C]101[/C][C]58300[/C][C]36832.2234644649[/C][C]21467.7765355351[/C][/ROW]
[ROW][C]102[/C][C]56100[/C][C]49518.4211657281[/C][C]6581.57883427192[/C][/ROW]
[ROW][C]103[/C][C]73700[/C][C]53102.1397323823[/C][C]20597.8602676177[/C][/ROW]
[ROW][C]104[/C][C]84700[/C][C]65557.2768643504[/C][C]19142.7231356496[/C][/ROW]
[ROW][C]105[/C][C]62700[/C][C]77330.3615316162[/C][C]-14630.3615316162[/C][/ROW]
[ROW][C]106[/C][C]70400[/C][C]68120.2390092777[/C][C]2279.76099072232[/C][/ROW]
[ROW][C]107[/C][C]52800[/C][C]69359.7150951649[/C][C]-16559.7150951649[/C][/ROW]
[ROW][C]108[/C][C]91300[/C][C]58799.9267957272[/C][C]32500.0732042728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280064&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280064&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
360500550005500
44840056252.1525732232-7852.15257322317
56270049185.395494298713514.6045057013
66160055441.61627391656158.38372608354
76600057232.35124890228767.64875109777
86820060729.9781700447470.02182995597
97590063511.579564742412388.4204352576
106600069464.1610092336-3464.16100923361
116270065605.7505866612-2905.75058666118
127810062058.936706178416041.0632938216
136600070371.7303126583-4371.73031265828
144950066052.2645909072-16552.2645909072
155830054038.42637537944261.57362462063
164400054902.8287247942-10902.8287247942
176160046296.931510536515303.0684894635
185060054017.111928462-3417.11192846196
196710050159.138919587416940.8610804126
206050059040.76546225721459.23453774282
216380058395.35269290215404.64730709786
227150060242.719038144811257.2809618552
237040065824.25999973634575.74000026372
248360067338.440905010716261.5590949893
256050076238.7700822125-15738.7700822125
265060065236.2356534746-14636.2356534746
275610054748.99834969551351.00165030454
284070054132.0317720426-13432.0317720426
295830044251.455604130414048.5443958696
304510051468.6279138759-6368.6279138759
316380046028.41936740517771.580632595
326050055668.64249715094831.35750284907
335390057386.3018188305-3486.30181883051
347700053937.514274409523062.4857255905
356930067113.30143664392186.69856335614
367920067445.065492531911754.9345074681
375940073807.0213277881-14407.0213277881
385500063880.0479016322-8880.04790163218
394950057260.3867980747-7760.38679807471
404070051243.786381769-10543.786381769
415390043393.007775583510506.9922244165
424840048636.6554367099-236.655436709938
436600047254.879795836418745.1202041636
446380057784.62605282446015.37394717556
455500060534.8487539713-5534.84875397128
467370056102.955423545617597.0445764544
476820066127.97266487542072.02733512463
488800066606.083824084921393.9161759151
497040079235.1169750134-8835.11697501343
504290073130.6945750641-30230.6945750641
514290053497.8302409615-10597.8302409615
524290045848.362108191-2948.36210819102
535060042881.19187281947718.80812718056
545060046576.31554541614023.68445458395
556820048038.814041797520161.1859582025
566270059675.42325747543024.57674252457
575610060782.3796443758-4682.37964437585
587040057085.917879518513314.0821204815
596490064632.6126571487267.387342851267
609350064139.863782402129360.1362175979
617370081910.5914517105-8210.59145171051
624290076429.1948568956-33529.1948568956
634510054964.0263896946-9864.02638969456
643740047976.149185897-10576.149185897
655170040430.538980064311269.4610199357
665940046477.878916960512922.1210830395
677480053689.074382964221110.9256170358
687370066185.18568086777514.81431913226
695940070384.5518390743-10984.5518390743
706930063056.91066028726243.08933971285
716160066419.1004465471-4819.10044654715
728800062908.051865836325091.9481341637
736710078116.9831070526-11016.9831070526
745390070943.3815056679-17043.3815056679
754840059863.5207910924-11463.5207910924
763630052094.5652502484-15794.5652502484
775390041478.449420432512421.5505795675
786490048395.225997008316504.7740029917
797590058014.371815622817885.6281843772
807150068685.55553886512814.44446113495
815280070097.9285749242-17297.9285749242
827590058918.089241882716981.9107581173
835940069060.2432492517-9660.24324925165
849130062670.756400720828629.2435992792
857590080205.7351279052-4305.73512790522
865500077390.075906285-22390.075906285
875060063175.1778051985-12575.1778051985
883410054869.3299985936-20769.3299985936
895390041279.105509253112620.8944907469
905170048413.51612113773286.48387886229
917810049830.767078087428269.2329219126
927810066965.695406504211134.3045934958
935940073663.0678548758-14263.0678548758
947700064544.443791070112455.5562089299
955720072035.9868585277-14835.9868585277
968910062537.466298528426562.5337014716
977590078856.7238828949-2956.72388289489
985610076946.0628365685-20846.0628365685
994290063773.7060474293-20873.7060474293
1002970050349.9267630477-20649.9267630477
1015830036832.223464464921467.7765355351
1025610049518.42116572816581.57883427192
1037370053102.139732382320597.8602676177
1048470065557.276864350419142.7231356496
1056270077330.3615316162-14630.3615316162
1067040068120.23900927772279.76099072232
1075280069359.7150951649-16559.7150951649
1089130058799.926795727232500.0732042728







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10978847.264359919850514.1005708239107180.428149016
11078860.402510328745408.5190503322112312.285970325
11178873.540660737740837.9582819844116909.123039491
11278886.678811146636625.5659788174121147.791643476
11378899.816961555632670.8290021925125128.804920919
11478912.955111964528910.3455343727128915.564689556
11578926.093262373525301.2016894181132550.984835329
11678939.231412782421812.8290178189136065.633807746
11778952.369563191418422.5921340017139482.146992381
11878965.507713600315113.2114413676142817.803985833
11978978.645864009311871.1676716464146086.124056372
12078991.78401441828685.66725456875149297.900774268

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 78847.2643599198 & 50514.1005708239 & 107180.428149016 \tabularnewline
110 & 78860.4025103287 & 45408.5190503322 & 112312.285970325 \tabularnewline
111 & 78873.5406607377 & 40837.9582819844 & 116909.123039491 \tabularnewline
112 & 78886.6788111466 & 36625.5659788174 & 121147.791643476 \tabularnewline
113 & 78899.8169615556 & 32670.8290021925 & 125128.804920919 \tabularnewline
114 & 78912.9551119645 & 28910.3455343727 & 128915.564689556 \tabularnewline
115 & 78926.0932623735 & 25301.2016894181 & 132550.984835329 \tabularnewline
116 & 78939.2314127824 & 21812.8290178189 & 136065.633807746 \tabularnewline
117 & 78952.3695631914 & 18422.5921340017 & 139482.146992381 \tabularnewline
118 & 78965.5077136003 & 15113.2114413676 & 142817.803985833 \tabularnewline
119 & 78978.6458640093 & 11871.1676716464 & 146086.124056372 \tabularnewline
120 & 78991.7840144182 & 8685.66725456875 & 149297.900774268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280064&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]78847.2643599198[/C][C]50514.1005708239[/C][C]107180.428149016[/C][/ROW]
[ROW][C]110[/C][C]78860.4025103287[/C][C]45408.5190503322[/C][C]112312.285970325[/C][/ROW]
[ROW][C]111[/C][C]78873.5406607377[/C][C]40837.9582819844[/C][C]116909.123039491[/C][/ROW]
[ROW][C]112[/C][C]78886.6788111466[/C][C]36625.5659788174[/C][C]121147.791643476[/C][/ROW]
[ROW][C]113[/C][C]78899.8169615556[/C][C]32670.8290021925[/C][C]125128.804920919[/C][/ROW]
[ROW][C]114[/C][C]78912.9551119645[/C][C]28910.3455343727[/C][C]128915.564689556[/C][/ROW]
[ROW][C]115[/C][C]78926.0932623735[/C][C]25301.2016894181[/C][C]132550.984835329[/C][/ROW]
[ROW][C]116[/C][C]78939.2314127824[/C][C]21812.8290178189[/C][C]136065.633807746[/C][/ROW]
[ROW][C]117[/C][C]78952.3695631914[/C][C]18422.5921340017[/C][C]139482.146992381[/C][/ROW]
[ROW][C]118[/C][C]78965.5077136003[/C][C]15113.2114413676[/C][C]142817.803985833[/C][/ROW]
[ROW][C]119[/C][C]78978.6458640093[/C][C]11871.1676716464[/C][C]146086.124056372[/C][/ROW]
[ROW][C]120[/C][C]78991.7840144182[/C][C]8685.66725456875[/C][C]149297.900774268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280064&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280064&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
10978847.264359919850514.1005708239107180.428149016
11078860.402510328745408.5190503322112312.285970325
11178873.540660737740837.9582819844116909.123039491
11278886.678811146636625.5659788174121147.791643476
11378899.816961555632670.8290021925125128.804920919
11478912.955111964528910.3455343727128915.564689556
11578926.093262373525301.2016894181132550.984835329
11678939.231412782421812.8290178189136065.633807746
11778952.369563191418422.5921340017139482.146992381
11878965.507713600315113.2114413676142817.803985833
11978978.645864009311871.1676716464146086.124056372
12078991.78401441828685.66725456875149297.900774268



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')