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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, 02 Apr 2015 14:00:11 +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/Apr/02/t1427979701lmhbl8q4efb6u26.htm/, Retrieved Thu, 09 May 2024 10:27:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278550, Retrieved Thu, 09 May 2024 10:27:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Bouwvergunningen ...] [2015-04-02 13:00:11] [4436f154edbd6dc391df500b76aea682] [Current]
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Dataseries X:
65
96
66
55
36
63
49
59
89
33
65
62
63
69
84
46
54
83
34
87
55
47
77
38
73
64
75
81
133
107
43
50
27
34
52
29
48
37
64
48
38
39
52
66
67
58
40
31
101
82
72
46
45
62
64
29
57
71
46
71
56
75
78
76
53
43
52
93
52
67
58
52




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278550&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278550&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278550&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.628082758160126
beta0.197467380740361
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.628082758160126 \tabularnewline
beta & 0.197467380740361 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278550&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]0.628082758160126[/C][/ROW]
[ROW][C]beta[/C][C]0.197467380740361[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278550&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278550&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
alpha0.628082758160126
beta0.197467380740361
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
366127-61
455112.121374466567-57.1213744665666
53692.5943193266937-56.5943193266937
66366.3791394689099-3.37913946890993
74973.1683958831561-24.1683958831561
85963.9027727734873-4.90277277348727
98966.129484768608222.8705152313918
103388.6366553518631-55.6366553518631
116554.934441831307410.0655581686926
126263.7470452754533-1.74704527545326
136364.9236773795941-1.9236773795941
146965.75078416871763.24921583128241
158470.229882771910513.7701172280895
164683.0248287349012-37.0248287349012
175459.324308817478-5.32430881747803
188354.873986920123328.1260130798767
193474.9215883416237-40.9215883416237
208746.526246748282640.4737532517174
215574.2737077430734-19.2737077430734
224762.1043805200511-15.1043805200511
237750.680402098337626.3195979016624
243868.5384209870875-30.5384209870875
257346.897344709982226.1026552900178
266464.0689560421875-0.0689560421875086
277564.79407721112910.205922788871
288173.23847093785837.76152906214169
2913381.110213405339351.8897865946607
30107123.133828835967-16.1338288359667
3143120.431972316538-77.4319723165378
325069.6262420329777-19.6262420329777
332752.6931327727587-25.6931327727587
343428.76290122843575.23709877156426
355224.908950487083427.0910495129166
362938.1410800407726-9.14108004077265
374827.482703443104720.5172965568953
383737.9969171131586-0.996917113158617
396434.874780622219729.1252193777803
404854.2841189979652-6.28411899796524
413850.674069216942-12.674069216942
423941.4786895797689-2.47868957976885
435238.379430505881113.6205694941189
446647.081141281726318.9188587182737
456761.45704383569225.54295616430782
465868.1192425100612-10.1192425100612
474063.689236516242-23.689236516242
483147.7980733948364-16.7980733948364
4910134.151735562524866.8482644374753
508281.33313360124220.666866398757833
517287.029845297614-15.029845297614
524681.0036335719351-35.0036335719351
534558.0908741591683-13.0908741591683
546247.317534228941714.6824657710583
556455.8091556476258.19084435237498
562961.2393780722509-32.2393780722509
575737.277558384252519.7224416157475
587148.398154451238622.6018455487614
594664.1304677495068-18.1304677495068
607152.030870562137318.9691294378627
615665.5855532406101-9.58555324061007
627560.01667560715314.983324392847
637871.73740605327676.26259394672334
647678.757519649803-2.75751964980303
655379.7702516815526-26.7702516815526
664362.3807973371276-19.3807973371276
675247.22881185681354.77118814318648
689347.838022731063245.1619772689368
695279.4172447846883-27.4172447846883
706762.01026158086174.98973841913835
715865.5764023556916-7.57640235569163
725260.3102969770202-8.31029697702019

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 66 & 127 & -61 \tabularnewline
4 & 55 & 112.121374466567 & -57.1213744665666 \tabularnewline
5 & 36 & 92.5943193266937 & -56.5943193266937 \tabularnewline
6 & 63 & 66.3791394689099 & -3.37913946890993 \tabularnewline
7 & 49 & 73.1683958831561 & -24.1683958831561 \tabularnewline
8 & 59 & 63.9027727734873 & -4.90277277348727 \tabularnewline
9 & 89 & 66.1294847686082 & 22.8705152313918 \tabularnewline
10 & 33 & 88.6366553518631 & -55.6366553518631 \tabularnewline
11 & 65 & 54.9344418313074 & 10.0655581686926 \tabularnewline
12 & 62 & 63.7470452754533 & -1.74704527545326 \tabularnewline
13 & 63 & 64.9236773795941 & -1.9236773795941 \tabularnewline
14 & 69 & 65.7507841687176 & 3.24921583128241 \tabularnewline
15 & 84 & 70.2298827719105 & 13.7701172280895 \tabularnewline
16 & 46 & 83.0248287349012 & -37.0248287349012 \tabularnewline
17 & 54 & 59.324308817478 & -5.32430881747803 \tabularnewline
18 & 83 & 54.8739869201233 & 28.1260130798767 \tabularnewline
19 & 34 & 74.9215883416237 & -40.9215883416237 \tabularnewline
20 & 87 & 46.5262467482826 & 40.4737532517174 \tabularnewline
21 & 55 & 74.2737077430734 & -19.2737077430734 \tabularnewline
22 & 47 & 62.1043805200511 & -15.1043805200511 \tabularnewline
23 & 77 & 50.6804020983376 & 26.3195979016624 \tabularnewline
24 & 38 & 68.5384209870875 & -30.5384209870875 \tabularnewline
25 & 73 & 46.8973447099822 & 26.1026552900178 \tabularnewline
26 & 64 & 64.0689560421875 & -0.0689560421875086 \tabularnewline
27 & 75 & 64.794077211129 & 10.205922788871 \tabularnewline
28 & 81 & 73.2384709378583 & 7.76152906214169 \tabularnewline
29 & 133 & 81.1102134053393 & 51.8897865946607 \tabularnewline
30 & 107 & 123.133828835967 & -16.1338288359667 \tabularnewline
31 & 43 & 120.431972316538 & -77.4319723165378 \tabularnewline
32 & 50 & 69.6262420329777 & -19.6262420329777 \tabularnewline
33 & 27 & 52.6931327727587 & -25.6931327727587 \tabularnewline
34 & 34 & 28.7629012284357 & 5.23709877156426 \tabularnewline
35 & 52 & 24.9089504870834 & 27.0910495129166 \tabularnewline
36 & 29 & 38.1410800407726 & -9.14108004077265 \tabularnewline
37 & 48 & 27.4827034431047 & 20.5172965568953 \tabularnewline
38 & 37 & 37.9969171131586 & -0.996917113158617 \tabularnewline
39 & 64 & 34.8747806222197 & 29.1252193777803 \tabularnewline
40 & 48 & 54.2841189979652 & -6.28411899796524 \tabularnewline
41 & 38 & 50.674069216942 & -12.674069216942 \tabularnewline
42 & 39 & 41.4786895797689 & -2.47868957976885 \tabularnewline
43 & 52 & 38.3794305058811 & 13.6205694941189 \tabularnewline
44 & 66 & 47.0811412817263 & 18.9188587182737 \tabularnewline
45 & 67 & 61.4570438356922 & 5.54295616430782 \tabularnewline
46 & 58 & 68.1192425100612 & -10.1192425100612 \tabularnewline
47 & 40 & 63.689236516242 & -23.689236516242 \tabularnewline
48 & 31 & 47.7980733948364 & -16.7980733948364 \tabularnewline
49 & 101 & 34.1517355625248 & 66.8482644374753 \tabularnewline
50 & 82 & 81.3331336012422 & 0.666866398757833 \tabularnewline
51 & 72 & 87.029845297614 & -15.029845297614 \tabularnewline
52 & 46 & 81.0036335719351 & -35.0036335719351 \tabularnewline
53 & 45 & 58.0908741591683 & -13.0908741591683 \tabularnewline
54 & 62 & 47.3175342289417 & 14.6824657710583 \tabularnewline
55 & 64 & 55.809155647625 & 8.19084435237498 \tabularnewline
56 & 29 & 61.2393780722509 & -32.2393780722509 \tabularnewline
57 & 57 & 37.2775583842525 & 19.7224416157475 \tabularnewline
58 & 71 & 48.3981544512386 & 22.6018455487614 \tabularnewline
59 & 46 & 64.1304677495068 & -18.1304677495068 \tabularnewline
60 & 71 & 52.0308705621373 & 18.9691294378627 \tabularnewline
61 & 56 & 65.5855532406101 & -9.58555324061007 \tabularnewline
62 & 75 & 60.016675607153 & 14.983324392847 \tabularnewline
63 & 78 & 71.7374060532767 & 6.26259394672334 \tabularnewline
64 & 76 & 78.757519649803 & -2.75751964980303 \tabularnewline
65 & 53 & 79.7702516815526 & -26.7702516815526 \tabularnewline
66 & 43 & 62.3807973371276 & -19.3807973371276 \tabularnewline
67 & 52 & 47.2288118568135 & 4.77118814318648 \tabularnewline
68 & 93 & 47.8380227310632 & 45.1619772689368 \tabularnewline
69 & 52 & 79.4172447846883 & -27.4172447846883 \tabularnewline
70 & 67 & 62.0102615808617 & 4.98973841913835 \tabularnewline
71 & 58 & 65.5764023556916 & -7.57640235569163 \tabularnewline
72 & 52 & 60.3102969770202 & -8.31029697702019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278550&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]66[/C][C]127[/C][C]-61[/C][/ROW]
[ROW][C]4[/C][C]55[/C][C]112.121374466567[/C][C]-57.1213744665666[/C][/ROW]
[ROW][C]5[/C][C]36[/C][C]92.5943193266937[/C][C]-56.5943193266937[/C][/ROW]
[ROW][C]6[/C][C]63[/C][C]66.3791394689099[/C][C]-3.37913946890993[/C][/ROW]
[ROW][C]7[/C][C]49[/C][C]73.1683958831561[/C][C]-24.1683958831561[/C][/ROW]
[ROW][C]8[/C][C]59[/C][C]63.9027727734873[/C][C]-4.90277277348727[/C][/ROW]
[ROW][C]9[/C][C]89[/C][C]66.1294847686082[/C][C]22.8705152313918[/C][/ROW]
[ROW][C]10[/C][C]33[/C][C]88.6366553518631[/C][C]-55.6366553518631[/C][/ROW]
[ROW][C]11[/C][C]65[/C][C]54.9344418313074[/C][C]10.0655581686926[/C][/ROW]
[ROW][C]12[/C][C]62[/C][C]63.7470452754533[/C][C]-1.74704527545326[/C][/ROW]
[ROW][C]13[/C][C]63[/C][C]64.9236773795941[/C][C]-1.9236773795941[/C][/ROW]
[ROW][C]14[/C][C]69[/C][C]65.7507841687176[/C][C]3.24921583128241[/C][/ROW]
[ROW][C]15[/C][C]84[/C][C]70.2298827719105[/C][C]13.7701172280895[/C][/ROW]
[ROW][C]16[/C][C]46[/C][C]83.0248287349012[/C][C]-37.0248287349012[/C][/ROW]
[ROW][C]17[/C][C]54[/C][C]59.324308817478[/C][C]-5.32430881747803[/C][/ROW]
[ROW][C]18[/C][C]83[/C][C]54.8739869201233[/C][C]28.1260130798767[/C][/ROW]
[ROW][C]19[/C][C]34[/C][C]74.9215883416237[/C][C]-40.9215883416237[/C][/ROW]
[ROW][C]20[/C][C]87[/C][C]46.5262467482826[/C][C]40.4737532517174[/C][/ROW]
[ROW][C]21[/C][C]55[/C][C]74.2737077430734[/C][C]-19.2737077430734[/C][/ROW]
[ROW][C]22[/C][C]47[/C][C]62.1043805200511[/C][C]-15.1043805200511[/C][/ROW]
[ROW][C]23[/C][C]77[/C][C]50.6804020983376[/C][C]26.3195979016624[/C][/ROW]
[ROW][C]24[/C][C]38[/C][C]68.5384209870875[/C][C]-30.5384209870875[/C][/ROW]
[ROW][C]25[/C][C]73[/C][C]46.8973447099822[/C][C]26.1026552900178[/C][/ROW]
[ROW][C]26[/C][C]64[/C][C]64.0689560421875[/C][C]-0.0689560421875086[/C][/ROW]
[ROW][C]27[/C][C]75[/C][C]64.794077211129[/C][C]10.205922788871[/C][/ROW]
[ROW][C]28[/C][C]81[/C][C]73.2384709378583[/C][C]7.76152906214169[/C][/ROW]
[ROW][C]29[/C][C]133[/C][C]81.1102134053393[/C][C]51.8897865946607[/C][/ROW]
[ROW][C]30[/C][C]107[/C][C]123.133828835967[/C][C]-16.1338288359667[/C][/ROW]
[ROW][C]31[/C][C]43[/C][C]120.431972316538[/C][C]-77.4319723165378[/C][/ROW]
[ROW][C]32[/C][C]50[/C][C]69.6262420329777[/C][C]-19.6262420329777[/C][/ROW]
[ROW][C]33[/C][C]27[/C][C]52.6931327727587[/C][C]-25.6931327727587[/C][/ROW]
[ROW][C]34[/C][C]34[/C][C]28.7629012284357[/C][C]5.23709877156426[/C][/ROW]
[ROW][C]35[/C][C]52[/C][C]24.9089504870834[/C][C]27.0910495129166[/C][/ROW]
[ROW][C]36[/C][C]29[/C][C]38.1410800407726[/C][C]-9.14108004077265[/C][/ROW]
[ROW][C]37[/C][C]48[/C][C]27.4827034431047[/C][C]20.5172965568953[/C][/ROW]
[ROW][C]38[/C][C]37[/C][C]37.9969171131586[/C][C]-0.996917113158617[/C][/ROW]
[ROW][C]39[/C][C]64[/C][C]34.8747806222197[/C][C]29.1252193777803[/C][/ROW]
[ROW][C]40[/C][C]48[/C][C]54.2841189979652[/C][C]-6.28411899796524[/C][/ROW]
[ROW][C]41[/C][C]38[/C][C]50.674069216942[/C][C]-12.674069216942[/C][/ROW]
[ROW][C]42[/C][C]39[/C][C]41.4786895797689[/C][C]-2.47868957976885[/C][/ROW]
[ROW][C]43[/C][C]52[/C][C]38.3794305058811[/C][C]13.6205694941189[/C][/ROW]
[ROW][C]44[/C][C]66[/C][C]47.0811412817263[/C][C]18.9188587182737[/C][/ROW]
[ROW][C]45[/C][C]67[/C][C]61.4570438356922[/C][C]5.54295616430782[/C][/ROW]
[ROW][C]46[/C][C]58[/C][C]68.1192425100612[/C][C]-10.1192425100612[/C][/ROW]
[ROW][C]47[/C][C]40[/C][C]63.689236516242[/C][C]-23.689236516242[/C][/ROW]
[ROW][C]48[/C][C]31[/C][C]47.7980733948364[/C][C]-16.7980733948364[/C][/ROW]
[ROW][C]49[/C][C]101[/C][C]34.1517355625248[/C][C]66.8482644374753[/C][/ROW]
[ROW][C]50[/C][C]82[/C][C]81.3331336012422[/C][C]0.666866398757833[/C][/ROW]
[ROW][C]51[/C][C]72[/C][C]87.029845297614[/C][C]-15.029845297614[/C][/ROW]
[ROW][C]52[/C][C]46[/C][C]81.0036335719351[/C][C]-35.0036335719351[/C][/ROW]
[ROW][C]53[/C][C]45[/C][C]58.0908741591683[/C][C]-13.0908741591683[/C][/ROW]
[ROW][C]54[/C][C]62[/C][C]47.3175342289417[/C][C]14.6824657710583[/C][/ROW]
[ROW][C]55[/C][C]64[/C][C]55.809155647625[/C][C]8.19084435237498[/C][/ROW]
[ROW][C]56[/C][C]29[/C][C]61.2393780722509[/C][C]-32.2393780722509[/C][/ROW]
[ROW][C]57[/C][C]57[/C][C]37.2775583842525[/C][C]19.7224416157475[/C][/ROW]
[ROW][C]58[/C][C]71[/C][C]48.3981544512386[/C][C]22.6018455487614[/C][/ROW]
[ROW][C]59[/C][C]46[/C][C]64.1304677495068[/C][C]-18.1304677495068[/C][/ROW]
[ROW][C]60[/C][C]71[/C][C]52.0308705621373[/C][C]18.9691294378627[/C][/ROW]
[ROW][C]61[/C][C]56[/C][C]65.5855532406101[/C][C]-9.58555324061007[/C][/ROW]
[ROW][C]62[/C][C]75[/C][C]60.016675607153[/C][C]14.983324392847[/C][/ROW]
[ROW][C]63[/C][C]78[/C][C]71.7374060532767[/C][C]6.26259394672334[/C][/ROW]
[ROW][C]64[/C][C]76[/C][C]78.757519649803[/C][C]-2.75751964980303[/C][/ROW]
[ROW][C]65[/C][C]53[/C][C]79.7702516815526[/C][C]-26.7702516815526[/C][/ROW]
[ROW][C]66[/C][C]43[/C][C]62.3807973371276[/C][C]-19.3807973371276[/C][/ROW]
[ROW][C]67[/C][C]52[/C][C]47.2288118568135[/C][C]4.77118814318648[/C][/ROW]
[ROW][C]68[/C][C]93[/C][C]47.8380227310632[/C][C]45.1619772689368[/C][/ROW]
[ROW][C]69[/C][C]52[/C][C]79.4172447846883[/C][C]-27.4172447846883[/C][/ROW]
[ROW][C]70[/C][C]67[/C][C]62.0102615808617[/C][C]4.98973841913835[/C][/ROW]
[ROW][C]71[/C][C]58[/C][C]65.5764023556916[/C][C]-7.57640235569163[/C][/ROW]
[ROW][C]72[/C][C]52[/C][C]60.3102969770202[/C][C]-8.31029697702019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278550&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278550&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
366127-61
455112.121374466567-57.1213744665666
53692.5943193266937-56.5943193266937
66366.3791394689099-3.37913946890993
74973.1683958831561-24.1683958831561
85963.9027727734873-4.90277277348727
98966.129484768608222.8705152313918
103388.6366553518631-55.6366553518631
116554.934441831307410.0655581686926
126263.7470452754533-1.74704527545326
136364.9236773795941-1.9236773795941
146965.75078416871763.24921583128241
158470.229882771910513.7701172280895
164683.0248287349012-37.0248287349012
175459.324308817478-5.32430881747803
188354.873986920123328.1260130798767
193474.9215883416237-40.9215883416237
208746.526246748282640.4737532517174
215574.2737077430734-19.2737077430734
224762.1043805200511-15.1043805200511
237750.680402098337626.3195979016624
243868.5384209870875-30.5384209870875
257346.897344709982226.1026552900178
266464.0689560421875-0.0689560421875086
277564.79407721112910.205922788871
288173.23847093785837.76152906214169
2913381.110213405339351.8897865946607
30107123.133828835967-16.1338288359667
3143120.431972316538-77.4319723165378
325069.6262420329777-19.6262420329777
332752.6931327727587-25.6931327727587
343428.76290122843575.23709877156426
355224.908950487083427.0910495129166
362938.1410800407726-9.14108004077265
374827.482703443104720.5172965568953
383737.9969171131586-0.996917113158617
396434.874780622219729.1252193777803
404854.2841189979652-6.28411899796524
413850.674069216942-12.674069216942
423941.4786895797689-2.47868957976885
435238.379430505881113.6205694941189
446647.081141281726318.9188587182737
456761.45704383569225.54295616430782
465868.1192425100612-10.1192425100612
474063.689236516242-23.689236516242
483147.7980733948364-16.7980733948364
4910134.151735562524866.8482644374753
508281.33313360124220.666866398757833
517287.029845297614-15.029845297614
524681.0036335719351-35.0036335719351
534558.0908741591683-13.0908741591683
546247.317534228941714.6824657710583
556455.8091556476258.19084435237498
562961.2393780722509-32.2393780722509
575737.277558384252519.7224416157475
587148.398154451238622.6018455487614
594664.1304677495068-18.1304677495068
607152.030870562137318.9691294378627
615665.5855532406101-9.58555324061007
627560.01667560715314.983324392847
637871.73740605327676.26259394672334
647678.757519649803-2.75751964980303
655379.7702516815526-26.7702516815526
664362.3807973371276-19.3807973371276
675247.22881185681354.77118814318648
689347.838022731063245.1619772689368
695279.4172447846883-27.4172447846883
706762.01026158086174.98973841913835
715865.5764023556916-7.57640235569163
725260.3102969770202-8.31029697702019







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7353.55255333470581.01328124207981106.091825427332
7452.014363938848-13.7262569867159117.754984864412
7550.4761745429902-29.777954535371130.730303621351
7648.9379851471325-46.9889951905485144.864965484813
7747.3997957512747-65.2524686234706160.05206012602
7845.8616063554169-84.4890324294446176.212245140278
7944.3234169595591-104.63690361823193.283737537348
8042.7852275637013-125.646121522941211.216576650344
8141.2470381678435-147.475080934523229.96915727021
8239.7088487719858-170.088329993607249.506027537578
8338.170659376128-193.45510722817269.796425980426
8436.6324699802702-217.548330456955290.813270417496

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 53.5525533347058 & 1.01328124207981 & 106.091825427332 \tabularnewline
74 & 52.014363938848 & -13.7262569867159 & 117.754984864412 \tabularnewline
75 & 50.4761745429902 & -29.777954535371 & 130.730303621351 \tabularnewline
76 & 48.9379851471325 & -46.9889951905485 & 144.864965484813 \tabularnewline
77 & 47.3997957512747 & -65.2524686234706 & 160.05206012602 \tabularnewline
78 & 45.8616063554169 & -84.4890324294446 & 176.212245140278 \tabularnewline
79 & 44.3234169595591 & -104.63690361823 & 193.283737537348 \tabularnewline
80 & 42.7852275637013 & -125.646121522941 & 211.216576650344 \tabularnewline
81 & 41.2470381678435 & -147.475080934523 & 229.96915727021 \tabularnewline
82 & 39.7088487719858 & -170.088329993607 & 249.506027537578 \tabularnewline
83 & 38.170659376128 & -193.45510722817 & 269.796425980426 \tabularnewline
84 & 36.6324699802702 & -217.548330456955 & 290.813270417496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278550&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]73[/C][C]53.5525533347058[/C][C]1.01328124207981[/C][C]106.091825427332[/C][/ROW]
[ROW][C]74[/C][C]52.014363938848[/C][C]-13.7262569867159[/C][C]117.754984864412[/C][/ROW]
[ROW][C]75[/C][C]50.4761745429902[/C][C]-29.777954535371[/C][C]130.730303621351[/C][/ROW]
[ROW][C]76[/C][C]48.9379851471325[/C][C]-46.9889951905485[/C][C]144.864965484813[/C][/ROW]
[ROW][C]77[/C][C]47.3997957512747[/C][C]-65.2524686234706[/C][C]160.05206012602[/C][/ROW]
[ROW][C]78[/C][C]45.8616063554169[/C][C]-84.4890324294446[/C][C]176.212245140278[/C][/ROW]
[ROW][C]79[/C][C]44.3234169595591[/C][C]-104.63690361823[/C][C]193.283737537348[/C][/ROW]
[ROW][C]80[/C][C]42.7852275637013[/C][C]-125.646121522941[/C][C]211.216576650344[/C][/ROW]
[ROW][C]81[/C][C]41.2470381678435[/C][C]-147.475080934523[/C][C]229.96915727021[/C][/ROW]
[ROW][C]82[/C][C]39.7088487719858[/C][C]-170.088329993607[/C][C]249.506027537578[/C][/ROW]
[ROW][C]83[/C][C]38.170659376128[/C][C]-193.45510722817[/C][C]269.796425980426[/C][/ROW]
[ROW][C]84[/C][C]36.6324699802702[/C][C]-217.548330456955[/C][C]290.813270417496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278550&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278550&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
7353.55255333470581.01328124207981106.091825427332
7452.014363938848-13.7262569867159117.754984864412
7550.4761745429902-29.777954535371130.730303621351
7648.9379851471325-46.9889951905485144.864965484813
7747.3997957512747-65.2524686234706160.05206012602
7845.8616063554169-84.4890324294446176.212245140278
7944.3234169595591-104.63690361823193.283737537348
8042.7852275637013-125.646121522941211.216576650344
8141.2470381678435-147.475080934523229.96915727021
8239.7088487719858-170.088329993607249.506027537578
8338.170659376128-193.45510722817269.796425980426
8436.6324699802702-217.548330456955290.813270417496



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')