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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 computationSat, 13 Dec 2014 11:04:35 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/13/t1418468679ymkc6oippdskqzw.htm/, Retrieved Thu, 16 May 2024 20:54:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266980, Retrieved Thu, 16 May 2024 20:54:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-13 11:04:35] [c7f962214140f976f2c4b1bb2571d9df] [Current]
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Dataseries X:
325.87
302.25
294.00
285.43
286.19
276.70
267.77
267.03
257.87
257.19
275.60
305.68
358.06
320.07
295.90
291.27
272.87
269.27
271.32
267.45
260.33
277.94
277.07
312.65
319.71
318.39
304.90
303.73
273.29
274.33
270.45
278.23
274.03
279.00
287.50
336.87
334.10
296.07
286.84
277.63
261.32
264.07
261.94
252.84
257.83
271.16
273.63
304.87
323.90
336.11
335.65
282.23
273.03
270.07
246.03
242.35
250.33
267.45
268.80
302.68
313.10
306.39
305.61
277.27
264.94
268.63
293.90
248.65
256.00
258.52
266.90
281.23
306.00
325.46
291.13
282.53
256.52
258.63
252.74
245.16
255.03
268.35
293.73
278.39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266980&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266980&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266980&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266980&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2302.25325.87-23.62
3294302.251561446427-8.2515614464271
4285.43294.000545485654-8.57054548565367
5286.19285.4305665727190.759433427280783
6276.7286.189949796164-9.48994979616378
7267.77276.700627351744-8.93062735174442
8267.03267.770590376637-0.740590376637158
9257.87267.030048958179-9.1600489581794
10257.19257.870605543002-0.680605543002457
11275.6257.19004499276418.4099550072357
12305.68275.59878297381630.0812170261841
13358.06305.67801142214952.3819885778514
14320.07358.056537185906-37.9865371859055
15295.9320.072511174546-24.1725111745457
16291.27295.901597971262-4.63159797126201
17272.87291.270306180868-18.400306180868
18269.27272.87121638833-3.60121638832959
19271.32269.2702380654732.0497619345274
20267.45271.319864496467-3.86986449646702
21260.33267.450255824983-7.12025582498268
22277.94260.33047069847717.6095293015234
23277.07277.938835887527-0.868835887527041
24312.65277.070057436135.5799425638995
25319.71312.6476479181127.06235208188798
26318.39319.709533129364-1.31953312936389
27304.9318.390087230326-13.4900872303256
28303.73304.900891788675-1.17089178867514
29273.29303.730077404098-30.4400774040982
30274.33273.2920123010211.03798769897946
31270.45274.329931381787-3.87993138178729
32278.23270.4502564904747.7797435095261
33274.03278.229485704797-4.19948570479653
34279274.0302776152394.96972238476087
35287.5278.9996714667548.50032853324558
36336.87287.4994380691149.3705619308898
37334.1336.866736262171-2.76673626217053
38296.07334.100182900527-38.0301829005272
39286.84296.072514059831-9.2325140598312
40277.63286.84061033345-9.21061033345012
41261.32277.630608885461-16.3106088854614
42264.07261.3210782447912.74892175520881
43261.94264.069818277136-2.12981827713577
44252.84261.940140795815-9.1001407958145
45257.83252.8406015826564.98939841734409
46271.16257.82967016603213.3303298339684
47273.63271.1591187724012.47088122759914
48304.87273.6298366575531.2401633424499
49323.9304.86793480772919.0320651922707
50336.11323.89874184800212.2112581519982
51335.65336.109192750829-0.459192750829288
52282.23335.650030355837-53.4200303558374
53273.03282.233531435882-9.20353143588216
54270.07273.030608417497-2.96060841749687
55246.03270.070195716826-24.0401957168263
56242.35246.031589224289-3.68158922428916
57250.33242.3502433786777.97975662132345
58267.45250.32947248253717.1205275174625
59268.8267.4488682139491.35113178605098
60302.68268.79991068078333.8800893192168
61313.1302.67776029024510.4222397097553
62306.39313.099311017402-6.70931101740234
63305.61306.390443532164-0.780443532164099
64277.27305.61005159275-28.3400515927505
65264.94277.271873474695-12.3318734746953
66268.63264.9408152226833.68918477731683
67293.9268.62975611920525.2702438807955
68248.65293.898329460964-45.2483294609644
69256248.6529912295677.34700877043309
70258.52255.9995143115752.52048568842483
71266.9258.519833378358.38016662165001
72281.23266.89944601264914.330553987351
73306281.22905265062124.7709473493786
74325.46305.99836246794119.4616375320591
75291.13325.45871345028-34.3287134502798
76282.53291.132269366933-8.60226936693334
77256.52282.530568669889-26.0105686698885
78258.63256.5217194796582.10828052034225
79252.74258.629860627981-5.88986062798108
80245.16252.740389360789-7.5803893607889
81255.03245.1605011165069.86949888349352
82268.35255.02934755741913.3206524425813
83293.73268.34911941214425.3808805878562
84278.39293.728322147108-15.338322147108

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 302.25 & 325.87 & -23.62 \tabularnewline
3 & 294 & 302.251561446427 & -8.2515614464271 \tabularnewline
4 & 285.43 & 294.000545485654 & -8.57054548565367 \tabularnewline
5 & 286.19 & 285.430566572719 & 0.759433427280783 \tabularnewline
6 & 276.7 & 286.189949796164 & -9.48994979616378 \tabularnewline
7 & 267.77 & 276.700627351744 & -8.93062735174442 \tabularnewline
8 & 267.03 & 267.770590376637 & -0.740590376637158 \tabularnewline
9 & 257.87 & 267.030048958179 & -9.1600489581794 \tabularnewline
10 & 257.19 & 257.870605543002 & -0.680605543002457 \tabularnewline
11 & 275.6 & 257.190044992764 & 18.4099550072357 \tabularnewline
12 & 305.68 & 275.598782973816 & 30.0812170261841 \tabularnewline
13 & 358.06 & 305.678011422149 & 52.3819885778514 \tabularnewline
14 & 320.07 & 358.056537185906 & -37.9865371859055 \tabularnewline
15 & 295.9 & 320.072511174546 & -24.1725111745457 \tabularnewline
16 & 291.27 & 295.901597971262 & -4.63159797126201 \tabularnewline
17 & 272.87 & 291.270306180868 & -18.400306180868 \tabularnewline
18 & 269.27 & 272.87121638833 & -3.60121638832959 \tabularnewline
19 & 271.32 & 269.270238065473 & 2.0497619345274 \tabularnewline
20 & 267.45 & 271.319864496467 & -3.86986449646702 \tabularnewline
21 & 260.33 & 267.450255824983 & -7.12025582498268 \tabularnewline
22 & 277.94 & 260.330470698477 & 17.6095293015234 \tabularnewline
23 & 277.07 & 277.938835887527 & -0.868835887527041 \tabularnewline
24 & 312.65 & 277.0700574361 & 35.5799425638995 \tabularnewline
25 & 319.71 & 312.647647918112 & 7.06235208188798 \tabularnewline
26 & 318.39 & 319.709533129364 & -1.31953312936389 \tabularnewline
27 & 304.9 & 318.390087230326 & -13.4900872303256 \tabularnewline
28 & 303.73 & 304.900891788675 & -1.17089178867514 \tabularnewline
29 & 273.29 & 303.730077404098 & -30.4400774040982 \tabularnewline
30 & 274.33 & 273.292012301021 & 1.03798769897946 \tabularnewline
31 & 270.45 & 274.329931381787 & -3.87993138178729 \tabularnewline
32 & 278.23 & 270.450256490474 & 7.7797435095261 \tabularnewline
33 & 274.03 & 278.229485704797 & -4.19948570479653 \tabularnewline
34 & 279 & 274.030277615239 & 4.96972238476087 \tabularnewline
35 & 287.5 & 278.999671466754 & 8.50032853324558 \tabularnewline
36 & 336.87 & 287.49943806911 & 49.3705619308898 \tabularnewline
37 & 334.1 & 336.866736262171 & -2.76673626217053 \tabularnewline
38 & 296.07 & 334.100182900527 & -38.0301829005272 \tabularnewline
39 & 286.84 & 296.072514059831 & -9.2325140598312 \tabularnewline
40 & 277.63 & 286.84061033345 & -9.21061033345012 \tabularnewline
41 & 261.32 & 277.630608885461 & -16.3106088854614 \tabularnewline
42 & 264.07 & 261.321078244791 & 2.74892175520881 \tabularnewline
43 & 261.94 & 264.069818277136 & -2.12981827713577 \tabularnewline
44 & 252.84 & 261.940140795815 & -9.1001407958145 \tabularnewline
45 & 257.83 & 252.840601582656 & 4.98939841734409 \tabularnewline
46 & 271.16 & 257.829670166032 & 13.3303298339684 \tabularnewline
47 & 273.63 & 271.159118772401 & 2.47088122759914 \tabularnewline
48 & 304.87 & 273.62983665755 & 31.2401633424499 \tabularnewline
49 & 323.9 & 304.867934807729 & 19.0320651922707 \tabularnewline
50 & 336.11 & 323.898741848002 & 12.2112581519982 \tabularnewline
51 & 335.65 & 336.109192750829 & -0.459192750829288 \tabularnewline
52 & 282.23 & 335.650030355837 & -53.4200303558374 \tabularnewline
53 & 273.03 & 282.233531435882 & -9.20353143588216 \tabularnewline
54 & 270.07 & 273.030608417497 & -2.96060841749687 \tabularnewline
55 & 246.03 & 270.070195716826 & -24.0401957168263 \tabularnewline
56 & 242.35 & 246.031589224289 & -3.68158922428916 \tabularnewline
57 & 250.33 & 242.350243378677 & 7.97975662132345 \tabularnewline
58 & 267.45 & 250.329472482537 & 17.1205275174625 \tabularnewline
59 & 268.8 & 267.448868213949 & 1.35113178605098 \tabularnewline
60 & 302.68 & 268.799910680783 & 33.8800893192168 \tabularnewline
61 & 313.1 & 302.677760290245 & 10.4222397097553 \tabularnewline
62 & 306.39 & 313.099311017402 & -6.70931101740234 \tabularnewline
63 & 305.61 & 306.390443532164 & -0.780443532164099 \tabularnewline
64 & 277.27 & 305.61005159275 & -28.3400515927505 \tabularnewline
65 & 264.94 & 277.271873474695 & -12.3318734746953 \tabularnewline
66 & 268.63 & 264.940815222683 & 3.68918477731683 \tabularnewline
67 & 293.9 & 268.629756119205 & 25.2702438807955 \tabularnewline
68 & 248.65 & 293.898329460964 & -45.2483294609644 \tabularnewline
69 & 256 & 248.652991229567 & 7.34700877043309 \tabularnewline
70 & 258.52 & 255.999514311575 & 2.52048568842483 \tabularnewline
71 & 266.9 & 258.51983337835 & 8.38016662165001 \tabularnewline
72 & 281.23 & 266.899446012649 & 14.330553987351 \tabularnewline
73 & 306 & 281.229052650621 & 24.7709473493786 \tabularnewline
74 & 325.46 & 305.998362467941 & 19.4616375320591 \tabularnewline
75 & 291.13 & 325.45871345028 & -34.3287134502798 \tabularnewline
76 & 282.53 & 291.132269366933 & -8.60226936693334 \tabularnewline
77 & 256.52 & 282.530568669889 & -26.0105686698885 \tabularnewline
78 & 258.63 & 256.521719479658 & 2.10828052034225 \tabularnewline
79 & 252.74 & 258.629860627981 & -5.88986062798108 \tabularnewline
80 & 245.16 & 252.740389360789 & -7.5803893607889 \tabularnewline
81 & 255.03 & 245.160501116506 & 9.86949888349352 \tabularnewline
82 & 268.35 & 255.029347557419 & 13.3206524425813 \tabularnewline
83 & 293.73 & 268.349119412144 & 25.3808805878562 \tabularnewline
84 & 278.39 & 293.728322147108 & -15.338322147108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266980&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]2[/C][C]302.25[/C][C]325.87[/C][C]-23.62[/C][/ROW]
[ROW][C]3[/C][C]294[/C][C]302.251561446427[/C][C]-8.2515614464271[/C][/ROW]
[ROW][C]4[/C][C]285.43[/C][C]294.000545485654[/C][C]-8.57054548565367[/C][/ROW]
[ROW][C]5[/C][C]286.19[/C][C]285.430566572719[/C][C]0.759433427280783[/C][/ROW]
[ROW][C]6[/C][C]276.7[/C][C]286.189949796164[/C][C]-9.48994979616378[/C][/ROW]
[ROW][C]7[/C][C]267.77[/C][C]276.700627351744[/C][C]-8.93062735174442[/C][/ROW]
[ROW][C]8[/C][C]267.03[/C][C]267.770590376637[/C][C]-0.740590376637158[/C][/ROW]
[ROW][C]9[/C][C]257.87[/C][C]267.030048958179[/C][C]-9.1600489581794[/C][/ROW]
[ROW][C]10[/C][C]257.19[/C][C]257.870605543002[/C][C]-0.680605543002457[/C][/ROW]
[ROW][C]11[/C][C]275.6[/C][C]257.190044992764[/C][C]18.4099550072357[/C][/ROW]
[ROW][C]12[/C][C]305.68[/C][C]275.598782973816[/C][C]30.0812170261841[/C][/ROW]
[ROW][C]13[/C][C]358.06[/C][C]305.678011422149[/C][C]52.3819885778514[/C][/ROW]
[ROW][C]14[/C][C]320.07[/C][C]358.056537185906[/C][C]-37.9865371859055[/C][/ROW]
[ROW][C]15[/C][C]295.9[/C][C]320.072511174546[/C][C]-24.1725111745457[/C][/ROW]
[ROW][C]16[/C][C]291.27[/C][C]295.901597971262[/C][C]-4.63159797126201[/C][/ROW]
[ROW][C]17[/C][C]272.87[/C][C]291.270306180868[/C][C]-18.400306180868[/C][/ROW]
[ROW][C]18[/C][C]269.27[/C][C]272.87121638833[/C][C]-3.60121638832959[/C][/ROW]
[ROW][C]19[/C][C]271.32[/C][C]269.270238065473[/C][C]2.0497619345274[/C][/ROW]
[ROW][C]20[/C][C]267.45[/C][C]271.319864496467[/C][C]-3.86986449646702[/C][/ROW]
[ROW][C]21[/C][C]260.33[/C][C]267.450255824983[/C][C]-7.12025582498268[/C][/ROW]
[ROW][C]22[/C][C]277.94[/C][C]260.330470698477[/C][C]17.6095293015234[/C][/ROW]
[ROW][C]23[/C][C]277.07[/C][C]277.938835887527[/C][C]-0.868835887527041[/C][/ROW]
[ROW][C]24[/C][C]312.65[/C][C]277.0700574361[/C][C]35.5799425638995[/C][/ROW]
[ROW][C]25[/C][C]319.71[/C][C]312.647647918112[/C][C]7.06235208188798[/C][/ROW]
[ROW][C]26[/C][C]318.39[/C][C]319.709533129364[/C][C]-1.31953312936389[/C][/ROW]
[ROW][C]27[/C][C]304.9[/C][C]318.390087230326[/C][C]-13.4900872303256[/C][/ROW]
[ROW][C]28[/C][C]303.73[/C][C]304.900891788675[/C][C]-1.17089178867514[/C][/ROW]
[ROW][C]29[/C][C]273.29[/C][C]303.730077404098[/C][C]-30.4400774040982[/C][/ROW]
[ROW][C]30[/C][C]274.33[/C][C]273.292012301021[/C][C]1.03798769897946[/C][/ROW]
[ROW][C]31[/C][C]270.45[/C][C]274.329931381787[/C][C]-3.87993138178729[/C][/ROW]
[ROW][C]32[/C][C]278.23[/C][C]270.450256490474[/C][C]7.7797435095261[/C][/ROW]
[ROW][C]33[/C][C]274.03[/C][C]278.229485704797[/C][C]-4.19948570479653[/C][/ROW]
[ROW][C]34[/C][C]279[/C][C]274.030277615239[/C][C]4.96972238476087[/C][/ROW]
[ROW][C]35[/C][C]287.5[/C][C]278.999671466754[/C][C]8.50032853324558[/C][/ROW]
[ROW][C]36[/C][C]336.87[/C][C]287.49943806911[/C][C]49.3705619308898[/C][/ROW]
[ROW][C]37[/C][C]334.1[/C][C]336.866736262171[/C][C]-2.76673626217053[/C][/ROW]
[ROW][C]38[/C][C]296.07[/C][C]334.100182900527[/C][C]-38.0301829005272[/C][/ROW]
[ROW][C]39[/C][C]286.84[/C][C]296.072514059831[/C][C]-9.2325140598312[/C][/ROW]
[ROW][C]40[/C][C]277.63[/C][C]286.84061033345[/C][C]-9.21061033345012[/C][/ROW]
[ROW][C]41[/C][C]261.32[/C][C]277.630608885461[/C][C]-16.3106088854614[/C][/ROW]
[ROW][C]42[/C][C]264.07[/C][C]261.321078244791[/C][C]2.74892175520881[/C][/ROW]
[ROW][C]43[/C][C]261.94[/C][C]264.069818277136[/C][C]-2.12981827713577[/C][/ROW]
[ROW][C]44[/C][C]252.84[/C][C]261.940140795815[/C][C]-9.1001407958145[/C][/ROW]
[ROW][C]45[/C][C]257.83[/C][C]252.840601582656[/C][C]4.98939841734409[/C][/ROW]
[ROW][C]46[/C][C]271.16[/C][C]257.829670166032[/C][C]13.3303298339684[/C][/ROW]
[ROW][C]47[/C][C]273.63[/C][C]271.159118772401[/C][C]2.47088122759914[/C][/ROW]
[ROW][C]48[/C][C]304.87[/C][C]273.62983665755[/C][C]31.2401633424499[/C][/ROW]
[ROW][C]49[/C][C]323.9[/C][C]304.867934807729[/C][C]19.0320651922707[/C][/ROW]
[ROW][C]50[/C][C]336.11[/C][C]323.898741848002[/C][C]12.2112581519982[/C][/ROW]
[ROW][C]51[/C][C]335.65[/C][C]336.109192750829[/C][C]-0.459192750829288[/C][/ROW]
[ROW][C]52[/C][C]282.23[/C][C]335.650030355837[/C][C]-53.4200303558374[/C][/ROW]
[ROW][C]53[/C][C]273.03[/C][C]282.233531435882[/C][C]-9.20353143588216[/C][/ROW]
[ROW][C]54[/C][C]270.07[/C][C]273.030608417497[/C][C]-2.96060841749687[/C][/ROW]
[ROW][C]55[/C][C]246.03[/C][C]270.070195716826[/C][C]-24.0401957168263[/C][/ROW]
[ROW][C]56[/C][C]242.35[/C][C]246.031589224289[/C][C]-3.68158922428916[/C][/ROW]
[ROW][C]57[/C][C]250.33[/C][C]242.350243378677[/C][C]7.97975662132345[/C][/ROW]
[ROW][C]58[/C][C]267.45[/C][C]250.329472482537[/C][C]17.1205275174625[/C][/ROW]
[ROW][C]59[/C][C]268.8[/C][C]267.448868213949[/C][C]1.35113178605098[/C][/ROW]
[ROW][C]60[/C][C]302.68[/C][C]268.799910680783[/C][C]33.8800893192168[/C][/ROW]
[ROW][C]61[/C][C]313.1[/C][C]302.677760290245[/C][C]10.4222397097553[/C][/ROW]
[ROW][C]62[/C][C]306.39[/C][C]313.099311017402[/C][C]-6.70931101740234[/C][/ROW]
[ROW][C]63[/C][C]305.61[/C][C]306.390443532164[/C][C]-0.780443532164099[/C][/ROW]
[ROW][C]64[/C][C]277.27[/C][C]305.61005159275[/C][C]-28.3400515927505[/C][/ROW]
[ROW][C]65[/C][C]264.94[/C][C]277.271873474695[/C][C]-12.3318734746953[/C][/ROW]
[ROW][C]66[/C][C]268.63[/C][C]264.940815222683[/C][C]3.68918477731683[/C][/ROW]
[ROW][C]67[/C][C]293.9[/C][C]268.629756119205[/C][C]25.2702438807955[/C][/ROW]
[ROW][C]68[/C][C]248.65[/C][C]293.898329460964[/C][C]-45.2483294609644[/C][/ROW]
[ROW][C]69[/C][C]256[/C][C]248.652991229567[/C][C]7.34700877043309[/C][/ROW]
[ROW][C]70[/C][C]258.52[/C][C]255.999514311575[/C][C]2.52048568842483[/C][/ROW]
[ROW][C]71[/C][C]266.9[/C][C]258.51983337835[/C][C]8.38016662165001[/C][/ROW]
[ROW][C]72[/C][C]281.23[/C][C]266.899446012649[/C][C]14.330553987351[/C][/ROW]
[ROW][C]73[/C][C]306[/C][C]281.229052650621[/C][C]24.7709473493786[/C][/ROW]
[ROW][C]74[/C][C]325.46[/C][C]305.998362467941[/C][C]19.4616375320591[/C][/ROW]
[ROW][C]75[/C][C]291.13[/C][C]325.45871345028[/C][C]-34.3287134502798[/C][/ROW]
[ROW][C]76[/C][C]282.53[/C][C]291.132269366933[/C][C]-8.60226936693334[/C][/ROW]
[ROW][C]77[/C][C]256.52[/C][C]282.530568669889[/C][C]-26.0105686698885[/C][/ROW]
[ROW][C]78[/C][C]258.63[/C][C]256.521719479658[/C][C]2.10828052034225[/C][/ROW]
[ROW][C]79[/C][C]252.74[/C][C]258.629860627981[/C][C]-5.88986062798108[/C][/ROW]
[ROW][C]80[/C][C]245.16[/C][C]252.740389360789[/C][C]-7.5803893607889[/C][/ROW]
[ROW][C]81[/C][C]255.03[/C][C]245.160501116506[/C][C]9.86949888349352[/C][/ROW]
[ROW][C]82[/C][C]268.35[/C][C]255.029347557419[/C][C]13.3206524425813[/C][/ROW]
[ROW][C]83[/C][C]293.73[/C][C]268.349119412144[/C][C]25.3808805878562[/C][/ROW]
[ROW][C]84[/C][C]278.39[/C][C]293.728322147108[/C][C]-15.338322147108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266980&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266980&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
2302.25325.87-23.62
3294302.251561446427-8.2515614464271
4285.43294.000545485654-8.57054548565367
5286.19285.4305665727190.759433427280783
6276.7286.189949796164-9.48994979616378
7267.77276.700627351744-8.93062735174442
8267.03267.770590376637-0.740590376637158
9257.87267.030048958179-9.1600489581794
10257.19257.870605543002-0.680605543002457
11275.6257.19004499276418.4099550072357
12305.68275.59878297381630.0812170261841
13358.06305.67801142214952.3819885778514
14320.07358.056537185906-37.9865371859055
15295.9320.072511174546-24.1725111745457
16291.27295.901597971262-4.63159797126201
17272.87291.270306180868-18.400306180868
18269.27272.87121638833-3.60121638832959
19271.32269.2702380654732.0497619345274
20267.45271.319864496467-3.86986449646702
21260.33267.450255824983-7.12025582498268
22277.94260.33047069847717.6095293015234
23277.07277.938835887527-0.868835887527041
24312.65277.070057436135.5799425638995
25319.71312.6476479181127.06235208188798
26318.39319.709533129364-1.31953312936389
27304.9318.390087230326-13.4900872303256
28303.73304.900891788675-1.17089178867514
29273.29303.730077404098-30.4400774040982
30274.33273.2920123010211.03798769897946
31270.45274.329931381787-3.87993138178729
32278.23270.4502564904747.7797435095261
33274.03278.229485704797-4.19948570479653
34279274.0302776152394.96972238476087
35287.5278.9996714667548.50032853324558
36336.87287.4994380691149.3705619308898
37334.1336.866736262171-2.76673626217053
38296.07334.100182900527-38.0301829005272
39286.84296.072514059831-9.2325140598312
40277.63286.84061033345-9.21061033345012
41261.32277.630608885461-16.3106088854614
42264.07261.3210782447912.74892175520881
43261.94264.069818277136-2.12981827713577
44252.84261.940140795815-9.1001407958145
45257.83252.8406015826564.98939841734409
46271.16257.82967016603213.3303298339684
47273.63271.1591187724012.47088122759914
48304.87273.6298366575531.2401633424499
49323.9304.86793480772919.0320651922707
50336.11323.89874184800212.2112581519982
51335.65336.109192750829-0.459192750829288
52282.23335.650030355837-53.4200303558374
53273.03282.233531435882-9.20353143588216
54270.07273.030608417497-2.96060841749687
55246.03270.070195716826-24.0401957168263
56242.35246.031589224289-3.68158922428916
57250.33242.3502433786777.97975662132345
58267.45250.32947248253717.1205275174625
59268.8267.4488682139491.35113178605098
60302.68268.79991068078333.8800893192168
61313.1302.67776029024510.4222397097553
62306.39313.099311017402-6.70931101740234
63305.61306.390443532164-0.780443532164099
64277.27305.61005159275-28.3400515927505
65264.94277.271873474695-12.3318734746953
66268.63264.9408152226833.68918477731683
67293.9268.62975611920525.2702438807955
68248.65293.898329460964-45.2483294609644
69256248.6529912295677.34700877043309
70258.52255.9995143115752.52048568842483
71266.9258.519833378358.38016662165001
72281.23266.89944601264914.330553987351
73306281.22905265062124.7709473493786
74325.46305.99836246794119.4616375320591
75291.13325.45871345028-34.3287134502798
76282.53291.132269366933-8.60226936693334
77256.52282.530568669889-26.0105686698885
78258.63256.5217194796582.10828052034225
79252.74258.629860627981-5.88986062798108
80245.16252.740389360789-7.5803893607889
81255.03245.1605011165069.86949888349352
82268.35255.02934755741913.3206524425813
83293.73268.34911941214425.3808805878562
84278.39293.728322147108-15.338322147108







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85278.391013969869241.029849466316315.752178473422
86278.391013969869225.556094829732331.225933110007
87278.391013969869213.682430705915343.099597233824
88278.391013969869203.672389681735353.109638258004
89278.391013969869194.853328563852361.928699375887
90278.391013969869186.880266237824369.901761701914
91278.391013969869179.548265030146377.233762909593
92278.391013969869172.723795375622384.058232564117
93278.391013969869166.314106656508390.467921283231
94278.391013969869160.251667347285396.530360592454
95278.391013969869154.485496385323402.296531554416
96278.391013969869148.975986421374407.806041518364

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 278.391013969869 & 241.029849466316 & 315.752178473422 \tabularnewline
86 & 278.391013969869 & 225.556094829732 & 331.225933110007 \tabularnewline
87 & 278.391013969869 & 213.682430705915 & 343.099597233824 \tabularnewline
88 & 278.391013969869 & 203.672389681735 & 353.109638258004 \tabularnewline
89 & 278.391013969869 & 194.853328563852 & 361.928699375887 \tabularnewline
90 & 278.391013969869 & 186.880266237824 & 369.901761701914 \tabularnewline
91 & 278.391013969869 & 179.548265030146 & 377.233762909593 \tabularnewline
92 & 278.391013969869 & 172.723795375622 & 384.058232564117 \tabularnewline
93 & 278.391013969869 & 166.314106656508 & 390.467921283231 \tabularnewline
94 & 278.391013969869 & 160.251667347285 & 396.530360592454 \tabularnewline
95 & 278.391013969869 & 154.485496385323 & 402.296531554416 \tabularnewline
96 & 278.391013969869 & 148.975986421374 & 407.806041518364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266980&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]85[/C][C]278.391013969869[/C][C]241.029849466316[/C][C]315.752178473422[/C][/ROW]
[ROW][C]86[/C][C]278.391013969869[/C][C]225.556094829732[/C][C]331.225933110007[/C][/ROW]
[ROW][C]87[/C][C]278.391013969869[/C][C]213.682430705915[/C][C]343.099597233824[/C][/ROW]
[ROW][C]88[/C][C]278.391013969869[/C][C]203.672389681735[/C][C]353.109638258004[/C][/ROW]
[ROW][C]89[/C][C]278.391013969869[/C][C]194.853328563852[/C][C]361.928699375887[/C][/ROW]
[ROW][C]90[/C][C]278.391013969869[/C][C]186.880266237824[/C][C]369.901761701914[/C][/ROW]
[ROW][C]91[/C][C]278.391013969869[/C][C]179.548265030146[/C][C]377.233762909593[/C][/ROW]
[ROW][C]92[/C][C]278.391013969869[/C][C]172.723795375622[/C][C]384.058232564117[/C][/ROW]
[ROW][C]93[/C][C]278.391013969869[/C][C]166.314106656508[/C][C]390.467921283231[/C][/ROW]
[ROW][C]94[/C][C]278.391013969869[/C][C]160.251667347285[/C][C]396.530360592454[/C][/ROW]
[ROW][C]95[/C][C]278.391013969869[/C][C]154.485496385323[/C][C]402.296531554416[/C][/ROW]
[ROW][C]96[/C][C]278.391013969869[/C][C]148.975986421374[/C][C]407.806041518364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266980&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266980&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
85278.391013969869241.029849466316315.752178473422
86278.391013969869225.556094829732331.225933110007
87278.391013969869213.682430705915343.099597233824
88278.391013969869203.672389681735353.109638258004
89278.391013969869194.853328563852361.928699375887
90278.391013969869186.880266237824369.901761701914
91278.391013969869179.548265030146377.233762909593
92278.391013969869172.723795375622384.058232564117
93278.391013969869166.314106656508390.467921283231
94278.391013969869160.251667347285396.530360592454
95278.391013969869154.485496385323402.296531554416
96278.391013969869148.975986421374407.806041518364



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')