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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 23:27:41 +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/2010/Aug/20/t1282260487n4w4f5bb7oxnsdh.htm/, Retrieved Thu, 09 May 2024 01:58:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79427, Retrieved Thu, 09 May 2024 01:58:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVanhille Olivier
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks B - sta...] [2010-08-19 23:27:41] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataseries X:
31
30
29
27
25
24
25
27
28
28
29
31
31
27
25
16
20
21
25
24
28
27
23
36
37
30
27
22
22
25
33
35
35
29
25
34
31
29
21
19
18
25
23
22
20
15
17
25
26
26
23
24
24
42
40
45
47
40
39
49
55
54
48
44
48
62
57
60
56
57
54
62
65
68
69
67
72
82
72
77
79
78
76
79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79427&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79427&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.915448264006933
beta0.0348360292320682
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.915448264006933 \tabularnewline
beta & 0.0348360292320682 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79427&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]0.915448264006933[/C][/ROW]
[ROW][C]beta[/C][C]0.0348360292320682[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79427&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
alpha0.915448264006933
beta0.0348360292320682
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
329290
42728-1
52526.0526611535077-1.05266115350767
62424.0235437681110-0.0235437681110433
72522.93577928215622.06422071784385
82723.82508437159443.17491562840556
92825.83242309747962.16757690252039
102826.98672062548951.01327937451050
112927.11663255480881.88336744519118
123128.10312678282712.89687321717292
133130.1098160846490.890183915350995
142730.3078736322964-3.30787363229643
152526.5573366688268-1.55733666882682
161624.3596613561507-8.35966135615068
172015.66821524722424.33178475277585
182118.73327458541932.26672541458069
192519.98016613119785.01983386880217
202423.90747145807220.0925285419277877
212823.32703446632594.67296553367407
222727.0887741598699-0.088774159869942
232326.4885564576383-3.48855645763829
243622.664761855445813.3352381445542
253734.66754932785092.33245067214909
263036.6722373199588-6.67223731995882
272730.2208177871532-3.22081778715321
282226.8262805187025-4.82628051870249
292221.80811228274780.191887717252165
302521.38993685796763.61006314203244
313324.2160512082828.783948791718
323532.05871543826122.94128456173879
333534.64652211965970.353477880340307
342934.8765982824861-5.87659828248615
352529.215953895161-4.21595389516102
363424.94109430389739.05890569610271
373133.1075756597207-2.10757565972067
382930.9845092278692-1.98450922786923
392128.9108165921893-7.91081659218934
401921.1596156188111-2.15961561881108
411818.6044701924385-0.604470192438495
422517.45370304038517.5462969596149
432324.0051973336536-1.00519733365357
442222.6961846930013-0.696184693001253
452021.6478554024131-1.64785540241308
461519.6757697443529-4.67576974435294
471714.78267213768732.21732786231272
482516.27056064576438.72943935423572
492623.99833721991932.00166278008074
502625.63101660063370.368983399366336
512325.7808295721264-2.78082957212639
522422.95846945207191.04153054792814
532423.66849728418030.331502715819653
544223.739103184691518.2608968153085
554040.8054924244217-0.805492424421665
564540.3919011111584.60809888884199
574745.08112752538001.91887247461996
584047.3697002481117-7.36970024811174
593940.9200411630615-1.92004116306153
604939.39803179576429.6019682042358
615548.73003826067016.2699617393299
625455.2117179236464-1.21171792364638
634854.805664536902-6.80566453690197
644449.0616058278233-5.0616058278233
654844.75272507813613.24727492186387
666248.153752275339113.8462477246609
675761.6991556302958-4.69915563029581
686058.11734286840941.88265713159058
695660.6208782059573-4.6208782059573
705757.0234009112572-0.0234009112572053
715457.6339299561109-3.63392995611092
726254.82331831169527.1766816883048
736562.13813088936532.86186911063474
746865.5942224562272.40577754377293
756968.70950743717820.290492562821754
766769.8976224314738-2.89762243147378
777268.07477622162463.92522377837544
788272.6230704028469.376929597154
797282.4611549585225-10.4611549585225
807773.8048871213853.19511287861501
817977.75211997937431.24788002062567
827879.9565575186297-1.95655751862971
837679.1651025165198-3.16510251651981
847977.16635013123941.83364986876062

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 29 & 29 & 0 \tabularnewline
4 & 27 & 28 & -1 \tabularnewline
5 & 25 & 26.0526611535077 & -1.05266115350767 \tabularnewline
6 & 24 & 24.0235437681110 & -0.0235437681110433 \tabularnewline
7 & 25 & 22.9357792821562 & 2.06422071784385 \tabularnewline
8 & 27 & 23.8250843715944 & 3.17491562840556 \tabularnewline
9 & 28 & 25.8324230974796 & 2.16757690252039 \tabularnewline
10 & 28 & 26.9867206254895 & 1.01327937451050 \tabularnewline
11 & 29 & 27.1166325548088 & 1.88336744519118 \tabularnewline
12 & 31 & 28.1031267828271 & 2.89687321717292 \tabularnewline
13 & 31 & 30.109816084649 & 0.890183915350995 \tabularnewline
14 & 27 & 30.3078736322964 & -3.30787363229643 \tabularnewline
15 & 25 & 26.5573366688268 & -1.55733666882682 \tabularnewline
16 & 16 & 24.3596613561507 & -8.35966135615068 \tabularnewline
17 & 20 & 15.6682152472242 & 4.33178475277585 \tabularnewline
18 & 21 & 18.7332745854193 & 2.26672541458069 \tabularnewline
19 & 25 & 19.9801661311978 & 5.01983386880217 \tabularnewline
20 & 24 & 23.9074714580722 & 0.0925285419277877 \tabularnewline
21 & 28 & 23.3270344663259 & 4.67296553367407 \tabularnewline
22 & 27 & 27.0887741598699 & -0.088774159869942 \tabularnewline
23 & 23 & 26.4885564576383 & -3.48855645763829 \tabularnewline
24 & 36 & 22.6647618554458 & 13.3352381445542 \tabularnewline
25 & 37 & 34.6675493278509 & 2.33245067214909 \tabularnewline
26 & 30 & 36.6722373199588 & -6.67223731995882 \tabularnewline
27 & 27 & 30.2208177871532 & -3.22081778715321 \tabularnewline
28 & 22 & 26.8262805187025 & -4.82628051870249 \tabularnewline
29 & 22 & 21.8081122827478 & 0.191887717252165 \tabularnewline
30 & 25 & 21.3899368579676 & 3.61006314203244 \tabularnewline
31 & 33 & 24.216051208282 & 8.783948791718 \tabularnewline
32 & 35 & 32.0587154382612 & 2.94128456173879 \tabularnewline
33 & 35 & 34.6465221196597 & 0.353477880340307 \tabularnewline
34 & 29 & 34.8765982824861 & -5.87659828248615 \tabularnewline
35 & 25 & 29.215953895161 & -4.21595389516102 \tabularnewline
36 & 34 & 24.9410943038973 & 9.05890569610271 \tabularnewline
37 & 31 & 33.1075756597207 & -2.10757565972067 \tabularnewline
38 & 29 & 30.9845092278692 & -1.98450922786923 \tabularnewline
39 & 21 & 28.9108165921893 & -7.91081659218934 \tabularnewline
40 & 19 & 21.1596156188111 & -2.15961561881108 \tabularnewline
41 & 18 & 18.6044701924385 & -0.604470192438495 \tabularnewline
42 & 25 & 17.4537030403851 & 7.5462969596149 \tabularnewline
43 & 23 & 24.0051973336536 & -1.00519733365357 \tabularnewline
44 & 22 & 22.6961846930013 & -0.696184693001253 \tabularnewline
45 & 20 & 21.6478554024131 & -1.64785540241308 \tabularnewline
46 & 15 & 19.6757697443529 & -4.67576974435294 \tabularnewline
47 & 17 & 14.7826721376873 & 2.21732786231272 \tabularnewline
48 & 25 & 16.2705606457643 & 8.72943935423572 \tabularnewline
49 & 26 & 23.9983372199193 & 2.00166278008074 \tabularnewline
50 & 26 & 25.6310166006337 & 0.368983399366336 \tabularnewline
51 & 23 & 25.7808295721264 & -2.78082957212639 \tabularnewline
52 & 24 & 22.9584694520719 & 1.04153054792814 \tabularnewline
53 & 24 & 23.6684972841803 & 0.331502715819653 \tabularnewline
54 & 42 & 23.7391031846915 & 18.2608968153085 \tabularnewline
55 & 40 & 40.8054924244217 & -0.805492424421665 \tabularnewline
56 & 45 & 40.391901111158 & 4.60809888884199 \tabularnewline
57 & 47 & 45.0811275253800 & 1.91887247461996 \tabularnewline
58 & 40 & 47.3697002481117 & -7.36970024811174 \tabularnewline
59 & 39 & 40.9200411630615 & -1.92004116306153 \tabularnewline
60 & 49 & 39.3980317957642 & 9.6019682042358 \tabularnewline
61 & 55 & 48.7300382606701 & 6.2699617393299 \tabularnewline
62 & 54 & 55.2117179236464 & -1.21171792364638 \tabularnewline
63 & 48 & 54.805664536902 & -6.80566453690197 \tabularnewline
64 & 44 & 49.0616058278233 & -5.0616058278233 \tabularnewline
65 & 48 & 44.7527250781361 & 3.24727492186387 \tabularnewline
66 & 62 & 48.1537522753391 & 13.8462477246609 \tabularnewline
67 & 57 & 61.6991556302958 & -4.69915563029581 \tabularnewline
68 & 60 & 58.1173428684094 & 1.88265713159058 \tabularnewline
69 & 56 & 60.6208782059573 & -4.6208782059573 \tabularnewline
70 & 57 & 57.0234009112572 & -0.0234009112572053 \tabularnewline
71 & 54 & 57.6339299561109 & -3.63392995611092 \tabularnewline
72 & 62 & 54.8233183116952 & 7.1766816883048 \tabularnewline
73 & 65 & 62.1381308893653 & 2.86186911063474 \tabularnewline
74 & 68 & 65.594222456227 & 2.40577754377293 \tabularnewline
75 & 69 & 68.7095074371782 & 0.290492562821754 \tabularnewline
76 & 67 & 69.8976224314738 & -2.89762243147378 \tabularnewline
77 & 72 & 68.0747762216246 & 3.92522377837544 \tabularnewline
78 & 82 & 72.623070402846 & 9.376929597154 \tabularnewline
79 & 72 & 82.4611549585225 & -10.4611549585225 \tabularnewline
80 & 77 & 73.804887121385 & 3.19511287861501 \tabularnewline
81 & 79 & 77.7521199793743 & 1.24788002062567 \tabularnewline
82 & 78 & 79.9565575186297 & -1.95655751862971 \tabularnewline
83 & 76 & 79.1651025165198 & -3.16510251651981 \tabularnewline
84 & 79 & 77.1663501312394 & 1.83364986876062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79427&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]29[/C][C]29[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]27[/C][C]28[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]25[/C][C]26.0526611535077[/C][C]-1.05266115350767[/C][/ROW]
[ROW][C]6[/C][C]24[/C][C]24.0235437681110[/C][C]-0.0235437681110433[/C][/ROW]
[ROW][C]7[/C][C]25[/C][C]22.9357792821562[/C][C]2.06422071784385[/C][/ROW]
[ROW][C]8[/C][C]27[/C][C]23.8250843715944[/C][C]3.17491562840556[/C][/ROW]
[ROW][C]9[/C][C]28[/C][C]25.8324230974796[/C][C]2.16757690252039[/C][/ROW]
[ROW][C]10[/C][C]28[/C][C]26.9867206254895[/C][C]1.01327937451050[/C][/ROW]
[ROW][C]11[/C][C]29[/C][C]27.1166325548088[/C][C]1.88336744519118[/C][/ROW]
[ROW][C]12[/C][C]31[/C][C]28.1031267828271[/C][C]2.89687321717292[/C][/ROW]
[ROW][C]13[/C][C]31[/C][C]30.109816084649[/C][C]0.890183915350995[/C][/ROW]
[ROW][C]14[/C][C]27[/C][C]30.3078736322964[/C][C]-3.30787363229643[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]26.5573366688268[/C][C]-1.55733666882682[/C][/ROW]
[ROW][C]16[/C][C]16[/C][C]24.3596613561507[/C][C]-8.35966135615068[/C][/ROW]
[ROW][C]17[/C][C]20[/C][C]15.6682152472242[/C][C]4.33178475277585[/C][/ROW]
[ROW][C]18[/C][C]21[/C][C]18.7332745854193[/C][C]2.26672541458069[/C][/ROW]
[ROW][C]19[/C][C]25[/C][C]19.9801661311978[/C][C]5.01983386880217[/C][/ROW]
[ROW][C]20[/C][C]24[/C][C]23.9074714580722[/C][C]0.0925285419277877[/C][/ROW]
[ROW][C]21[/C][C]28[/C][C]23.3270344663259[/C][C]4.67296553367407[/C][/ROW]
[ROW][C]22[/C][C]27[/C][C]27.0887741598699[/C][C]-0.088774159869942[/C][/ROW]
[ROW][C]23[/C][C]23[/C][C]26.4885564576383[/C][C]-3.48855645763829[/C][/ROW]
[ROW][C]24[/C][C]36[/C][C]22.6647618554458[/C][C]13.3352381445542[/C][/ROW]
[ROW][C]25[/C][C]37[/C][C]34.6675493278509[/C][C]2.33245067214909[/C][/ROW]
[ROW][C]26[/C][C]30[/C][C]36.6722373199588[/C][C]-6.67223731995882[/C][/ROW]
[ROW][C]27[/C][C]27[/C][C]30.2208177871532[/C][C]-3.22081778715321[/C][/ROW]
[ROW][C]28[/C][C]22[/C][C]26.8262805187025[/C][C]-4.82628051870249[/C][/ROW]
[ROW][C]29[/C][C]22[/C][C]21.8081122827478[/C][C]0.191887717252165[/C][/ROW]
[ROW][C]30[/C][C]25[/C][C]21.3899368579676[/C][C]3.61006314203244[/C][/ROW]
[ROW][C]31[/C][C]33[/C][C]24.216051208282[/C][C]8.783948791718[/C][/ROW]
[ROW][C]32[/C][C]35[/C][C]32.0587154382612[/C][C]2.94128456173879[/C][/ROW]
[ROW][C]33[/C][C]35[/C][C]34.6465221196597[/C][C]0.353477880340307[/C][/ROW]
[ROW][C]34[/C][C]29[/C][C]34.8765982824861[/C][C]-5.87659828248615[/C][/ROW]
[ROW][C]35[/C][C]25[/C][C]29.215953895161[/C][C]-4.21595389516102[/C][/ROW]
[ROW][C]36[/C][C]34[/C][C]24.9410943038973[/C][C]9.05890569610271[/C][/ROW]
[ROW][C]37[/C][C]31[/C][C]33.1075756597207[/C][C]-2.10757565972067[/C][/ROW]
[ROW][C]38[/C][C]29[/C][C]30.9845092278692[/C][C]-1.98450922786923[/C][/ROW]
[ROW][C]39[/C][C]21[/C][C]28.9108165921893[/C][C]-7.91081659218934[/C][/ROW]
[ROW][C]40[/C][C]19[/C][C]21.1596156188111[/C][C]-2.15961561881108[/C][/ROW]
[ROW][C]41[/C][C]18[/C][C]18.6044701924385[/C][C]-0.604470192438495[/C][/ROW]
[ROW][C]42[/C][C]25[/C][C]17.4537030403851[/C][C]7.5462969596149[/C][/ROW]
[ROW][C]43[/C][C]23[/C][C]24.0051973336536[/C][C]-1.00519733365357[/C][/ROW]
[ROW][C]44[/C][C]22[/C][C]22.6961846930013[/C][C]-0.696184693001253[/C][/ROW]
[ROW][C]45[/C][C]20[/C][C]21.6478554024131[/C][C]-1.64785540241308[/C][/ROW]
[ROW][C]46[/C][C]15[/C][C]19.6757697443529[/C][C]-4.67576974435294[/C][/ROW]
[ROW][C]47[/C][C]17[/C][C]14.7826721376873[/C][C]2.21732786231272[/C][/ROW]
[ROW][C]48[/C][C]25[/C][C]16.2705606457643[/C][C]8.72943935423572[/C][/ROW]
[ROW][C]49[/C][C]26[/C][C]23.9983372199193[/C][C]2.00166278008074[/C][/ROW]
[ROW][C]50[/C][C]26[/C][C]25.6310166006337[/C][C]0.368983399366336[/C][/ROW]
[ROW][C]51[/C][C]23[/C][C]25.7808295721264[/C][C]-2.78082957212639[/C][/ROW]
[ROW][C]52[/C][C]24[/C][C]22.9584694520719[/C][C]1.04153054792814[/C][/ROW]
[ROW][C]53[/C][C]24[/C][C]23.6684972841803[/C][C]0.331502715819653[/C][/ROW]
[ROW][C]54[/C][C]42[/C][C]23.7391031846915[/C][C]18.2608968153085[/C][/ROW]
[ROW][C]55[/C][C]40[/C][C]40.8054924244217[/C][C]-0.805492424421665[/C][/ROW]
[ROW][C]56[/C][C]45[/C][C]40.391901111158[/C][C]4.60809888884199[/C][/ROW]
[ROW][C]57[/C][C]47[/C][C]45.0811275253800[/C][C]1.91887247461996[/C][/ROW]
[ROW][C]58[/C][C]40[/C][C]47.3697002481117[/C][C]-7.36970024811174[/C][/ROW]
[ROW][C]59[/C][C]39[/C][C]40.9200411630615[/C][C]-1.92004116306153[/C][/ROW]
[ROW][C]60[/C][C]49[/C][C]39.3980317957642[/C][C]9.6019682042358[/C][/ROW]
[ROW][C]61[/C][C]55[/C][C]48.7300382606701[/C][C]6.2699617393299[/C][/ROW]
[ROW][C]62[/C][C]54[/C][C]55.2117179236464[/C][C]-1.21171792364638[/C][/ROW]
[ROW][C]63[/C][C]48[/C][C]54.805664536902[/C][C]-6.80566453690197[/C][/ROW]
[ROW][C]64[/C][C]44[/C][C]49.0616058278233[/C][C]-5.0616058278233[/C][/ROW]
[ROW][C]65[/C][C]48[/C][C]44.7527250781361[/C][C]3.24727492186387[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]48.1537522753391[/C][C]13.8462477246609[/C][/ROW]
[ROW][C]67[/C][C]57[/C][C]61.6991556302958[/C][C]-4.69915563029581[/C][/ROW]
[ROW][C]68[/C][C]60[/C][C]58.1173428684094[/C][C]1.88265713159058[/C][/ROW]
[ROW][C]69[/C][C]56[/C][C]60.6208782059573[/C][C]-4.6208782059573[/C][/ROW]
[ROW][C]70[/C][C]57[/C][C]57.0234009112572[/C][C]-0.0234009112572053[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]57.6339299561109[/C][C]-3.63392995611092[/C][/ROW]
[ROW][C]72[/C][C]62[/C][C]54.8233183116952[/C][C]7.1766816883048[/C][/ROW]
[ROW][C]73[/C][C]65[/C][C]62.1381308893653[/C][C]2.86186911063474[/C][/ROW]
[ROW][C]74[/C][C]68[/C][C]65.594222456227[/C][C]2.40577754377293[/C][/ROW]
[ROW][C]75[/C][C]69[/C][C]68.7095074371782[/C][C]0.290492562821754[/C][/ROW]
[ROW][C]76[/C][C]67[/C][C]69.8976224314738[/C][C]-2.89762243147378[/C][/ROW]
[ROW][C]77[/C][C]72[/C][C]68.0747762216246[/C][C]3.92522377837544[/C][/ROW]
[ROW][C]78[/C][C]82[/C][C]72.623070402846[/C][C]9.376929597154[/C][/ROW]
[ROW][C]79[/C][C]72[/C][C]82.4611549585225[/C][C]-10.4611549585225[/C][/ROW]
[ROW][C]80[/C][C]77[/C][C]73.804887121385[/C][C]3.19511287861501[/C][/ROW]
[ROW][C]81[/C][C]79[/C][C]77.7521199793743[/C][C]1.24788002062567[/C][/ROW]
[ROW][C]82[/C][C]78[/C][C]79.9565575186297[/C][C]-1.95655751862971[/C][/ROW]
[ROW][C]83[/C][C]76[/C][C]79.1651025165198[/C][C]-3.16510251651981[/C][/ROW]
[ROW][C]84[/C][C]79[/C][C]77.1663501312394[/C][C]1.83364986876062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79427&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79427&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
329290
42728-1
52526.0526611535077-1.05266115350767
62424.0235437681110-0.0235437681110433
72522.93577928215622.06422071784385
82723.82508437159443.17491562840556
92825.83242309747962.16757690252039
102826.98672062548951.01327937451050
112927.11663255480881.88336744519118
123128.10312678282712.89687321717292
133130.1098160846490.890183915350995
142730.3078736322964-3.30787363229643
152526.5573366688268-1.55733666882682
161624.3596613561507-8.35966135615068
172015.66821524722424.33178475277585
182118.73327458541932.26672541458069
192519.98016613119785.01983386880217
202423.90747145807220.0925285419277877
212823.32703446632594.67296553367407
222727.0887741598699-0.088774159869942
232326.4885564576383-3.48855645763829
243622.664761855445813.3352381445542
253734.66754932785092.33245067214909
263036.6722373199588-6.67223731995882
272730.2208177871532-3.22081778715321
282226.8262805187025-4.82628051870249
292221.80811228274780.191887717252165
302521.38993685796763.61006314203244
313324.2160512082828.783948791718
323532.05871543826122.94128456173879
333534.64652211965970.353477880340307
342934.8765982824861-5.87659828248615
352529.215953895161-4.21595389516102
363424.94109430389739.05890569610271
373133.1075756597207-2.10757565972067
382930.9845092278692-1.98450922786923
392128.9108165921893-7.91081659218934
401921.1596156188111-2.15961561881108
411818.6044701924385-0.604470192438495
422517.45370304038517.5462969596149
432324.0051973336536-1.00519733365357
442222.6961846930013-0.696184693001253
452021.6478554024131-1.64785540241308
461519.6757697443529-4.67576974435294
471714.78267213768732.21732786231272
482516.27056064576438.72943935423572
492623.99833721991932.00166278008074
502625.63101660063370.368983399366336
512325.7808295721264-2.78082957212639
522422.95846945207191.04153054792814
532423.66849728418030.331502715819653
544223.739103184691518.2608968153085
554040.8054924244217-0.805492424421665
564540.3919011111584.60809888884199
574745.08112752538001.91887247461996
584047.3697002481117-7.36970024811174
593940.9200411630615-1.92004116306153
604939.39803179576429.6019682042358
615548.73003826067016.2699617393299
625455.2117179236464-1.21171792364638
634854.805664536902-6.80566453690197
644449.0616058278233-5.0616058278233
654844.75272507813613.24727492186387
666248.153752275339113.8462477246609
675761.6991556302958-4.69915563029581
686058.11734286840941.88265713159058
695660.6208782059573-4.6208782059573
705757.0234009112572-0.0234009112572053
715457.6339299561109-3.63392995611092
726254.82331831169527.1766816883048
736562.13813088936532.86186911063474
746865.5942224562272.40577754377293
756968.70950743717820.290492562821754
766769.8976224314738-2.89762243147378
777268.07477622162463.92522377837544
788272.6230704028469.376929597154
797282.4611549585225-10.4611549585225
807773.8048871213853.19511287861501
817977.75211997937431.24788002062567
827879.9565575186297-1.95655751862971
837679.1651025165198-3.16510251651981
847977.16635013123941.83364986876062







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8579.802173101653569.814273261192289.7900729421147
8680.759384482914167.0012531544794.5175158113582
8781.716595864174764.836332507310598.596859221039
8882.673807245435463.0032100717013102.344404419169
8983.63101862669661.3721688342546105.889868419137
9084.588230007956759.875516606963109.300943408950
9185.545441389217358.4729326072083112.617950171226
9286.50265277047857.1382714841564115.867034056799
9387.459864151738655.8535422638901119.066186039587
9488.417075532999254.605809266997122.228341799001
9589.374286914259953.3854521465961125.363121681924
9690.331498295520552.1851223541746128.477874236866

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 79.8021731016535 & 69.8142732611922 & 89.7900729421147 \tabularnewline
86 & 80.7593844829141 & 67.00125315447 & 94.5175158113582 \tabularnewline
87 & 81.7165958641747 & 64.8363325073105 & 98.596859221039 \tabularnewline
88 & 82.6738072454354 & 63.0032100717013 & 102.344404419169 \tabularnewline
89 & 83.631018626696 & 61.3721688342546 & 105.889868419137 \tabularnewline
90 & 84.5882300079567 & 59.875516606963 & 109.300943408950 \tabularnewline
91 & 85.5454413892173 & 58.4729326072083 & 112.617950171226 \tabularnewline
92 & 86.502652770478 & 57.1382714841564 & 115.867034056799 \tabularnewline
93 & 87.4598641517386 & 55.8535422638901 & 119.066186039587 \tabularnewline
94 & 88.4170755329992 & 54.605809266997 & 122.228341799001 \tabularnewline
95 & 89.3742869142599 & 53.3854521465961 & 125.363121681924 \tabularnewline
96 & 90.3314982955205 & 52.1851223541746 & 128.477874236866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79427&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]79.8021731016535[/C][C]69.8142732611922[/C][C]89.7900729421147[/C][/ROW]
[ROW][C]86[/C][C]80.7593844829141[/C][C]67.00125315447[/C][C]94.5175158113582[/C][/ROW]
[ROW][C]87[/C][C]81.7165958641747[/C][C]64.8363325073105[/C][C]98.596859221039[/C][/ROW]
[ROW][C]88[/C][C]82.6738072454354[/C][C]63.0032100717013[/C][C]102.344404419169[/C][/ROW]
[ROW][C]89[/C][C]83.631018626696[/C][C]61.3721688342546[/C][C]105.889868419137[/C][/ROW]
[ROW][C]90[/C][C]84.5882300079567[/C][C]59.875516606963[/C][C]109.300943408950[/C][/ROW]
[ROW][C]91[/C][C]85.5454413892173[/C][C]58.4729326072083[/C][C]112.617950171226[/C][/ROW]
[ROW][C]92[/C][C]86.502652770478[/C][C]57.1382714841564[/C][C]115.867034056799[/C][/ROW]
[ROW][C]93[/C][C]87.4598641517386[/C][C]55.8535422638901[/C][C]119.066186039587[/C][/ROW]
[ROW][C]94[/C][C]88.4170755329992[/C][C]54.605809266997[/C][C]122.228341799001[/C][/ROW]
[ROW][C]95[/C][C]89.3742869142599[/C][C]53.3854521465961[/C][C]125.363121681924[/C][/ROW]
[ROW][C]96[/C][C]90.3314982955205[/C][C]52.1851223541746[/C][C]128.477874236866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79427&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79427&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
8579.802173101653569.814273261192289.7900729421147
8680.759384482914167.0012531544794.5175158113582
8781.716595864174764.836332507310598.596859221039
8882.673807245435463.0032100717013102.344404419169
8983.63101862669661.3721688342546105.889868419137
9084.588230007956759.875516606963109.300943408950
9185.545441389217358.4729326072083112.617950171226
9286.50265277047857.1382714841564115.867034056799
9387.459864151738655.8535422638901119.066186039587
9488.417075532999254.605809266997122.228341799001
9589.374286914259953.3854521465961125.363121681924
9690.331498295520552.1851223541746128.477874236866



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')